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Abstract

BabyIAXO is the intermediate stage of the International Axion Observatory, a program to search for solar axions through their conversion into X-rays in a strong magnetic field. Its planned surface operation requires detectors that reject cosmic-ray backgrounds while retaining a weak keV X-ray signal. This thesis develops simulation, background-modeling, and active-veto methods for the IAXO Micromegas detector program.

The software work extends REST-for-Physics and its Geant4 interface, restG4, through source generation, geometry construction, detector-response processing, and large-scale simulation workflows. For IAXO-D1 operated with argon–isobutane, a source inventory organizes cosmic, environmental, and intrinsic backgrounds under a common reconstructed-event selection. Generated-primary counts and unresolved normalization requirements are recorded explicitly. Tests of learned topology discrimination reveal substantial simulation-to-data disagreement, so no learned rejection is credited in the reference selection.

The shielding studies identify secondary showers produced by high-energy neutrons in lead as an important background mechanism. They motivate a multilayer plastic-scintillator–cadmium veto combining prompt activity with delayed capture signatures. Three layers provide a practical compromise between conditional tagging performance and detector complexity. A quantitative neutron efficiency still requires validation of waveform acceptance, quenching, and capture modeling. Neutron-induced activation is evaluated separately through production and radioactive-decay simulations, without assigning prompt-veto suppression to delayed decays.

The IAXO-D0 prototype supplies the principal experimental result. In 52.1 d of surface data, the prompt veto removes 201 of 257 Micromegas-selected events and the advanced selection removes a further 7 of 56. The resulting background level is \((8.56^{+2.30}_{-1.91})\times 10^{-7}\) counts keV⁻¹ cm⁻² s⁻¹ at 90% confidence, with 97.0% retention of the Micromegas-selected calibration sample. The additional rejection is measured without identifying the rejected events individually as neutrons. These results support further validation using the existing data and simulations. An absolute BabyIAXO prediction additionally requires its xenon–neon response, optics, final geometry, and site-specific source normalization.

Resumen

BabyIAXO es la etapa intermedia del International Axion Observatory, un programa para buscar axiones solares mediante su conversión en rayos X en un campo magnético intenso. Su operación prevista en superficie requiere detectores que rechacen el fondo cósmico y conserven una señal débil de rayos X de energía keV. Esta tesis desarrolla métodos de simulación, modelado de fondo y veto activo para los detectores Micromegas de IAXO.

El trabajo amplía REST-for-Physics y su interfaz con Geant4, restG4, mediante herramientas de generación de fuentes, geometrías, respuesta del detector y producción a gran escala. Para IAXO-D1 con argón–isobutano, un inventario organiza los fondos cósmicos, ambientales e intrínsecos bajo una selección común de sucesos reconstruidos. Se documentan los primarios generados y los requisitos de normalización pendientes. Los clasificadores topológicos muestran diferencias importantes entre simulación y datos; por ello, la selección de referencia no les atribuye rechazo de fondo.

Los estudios de blindaje identifican las cascadas secundarias producidas por neutrones de alta energía en el plomo como un mecanismo de fondo relevante. Motivan un veto multicapa de centelleador plástico y cadmio que combina actividad rápida y capturas retardadas. Tres capas ofrecen un compromiso entre identificación condicional y complejidad. Una eficiencia neutrónica cuantitativa requiere validar la aceptación temporal, el quenching y las capturas. La activación se evalúa por separado mediante simulaciones de producción y desintegración, sin aplicar rechazo rápido a desintegraciones retardadas.

El principal resultado experimental procede de IAXO-D0. En 52.1 d de datos, el veto rápido elimina 201 de 257 sucesos seleccionados por Micromegas; la selección avanzada elimina otros 7 de los 56 restantes. El fondo resultante es \((8.56^{+2.30}_{-1.91})\times 10^{-7}\) counts keV⁻¹ cm⁻² s⁻¹ al 90% de confianza, conservando el 97.0% de la muestra de calibración seleccionada por Micromegas. El rechazo adicional está medido, sin identificar individualmente como neutrones los sucesos rechazados. Estos resultados permiten avanzar con los datos disponibles y nuevas simulaciones. Una predicción absoluta para BabyIAXO requiere además su respuesta en xenón–neón, óptica, geometría final y normalización de fuentes en el emplazamiento.

Contents

Introduction

The Standard Model of particle physics provides an exceptionally successful description of the known elementary particles and their interactions. Nevertheless, several observations and theoretical questions point to physics beyond this framework. Among them, the nature of dark matter and the absence of observed \(\mathrm {CP}\) violation in the strong interaction remain two of the most compelling open problems. The axion was originally proposed as a dynamical solution to the strong \(\mathrm {CP}\) problem, but it also emerged as a well-motivated dark-matter candidate [1–7]. More generally, axion-like particles appear naturally in many extensions of the Standard Model and can be searched for through their weak couplings to photons, electrons, and nucleons [8–10].

Solar axion helioscopes exploit one of the most direct experimental signatures of these particles. If axions are produced in the solar interior, they can traverse the Sun and the interplanetary medium essentially unattenuated. Inside a strong transverse laboratory magnetic field, a small fraction can convert coherently into X-ray photons. The experimental task is therefore conceptually simple but technically demanding: point a powerful magnet toward the Sun, focus any converted photons onto a small detector area, and identify a possible excess of keV X-rays above an extremely low background [11, 12].

The International Axion Observatory (IAXO) is designed as the next major step in this technique, building on the experience of previous helioscopes and especially on the CERN Axion Solar Telescope (CAST) [13]. BabyIAXO is the intermediate stage of this program [14]. It is intended to validate the main technologies required for IAXO while also operating as a competitive helioscope in its own right. The March 2026 outdoor working baseline brings low-background X-ray detection, solar tracking, and mechanical integration together in a surface environment [15]. Its detector development must therefore address cosmic-ray backgrounds under realistic operating conditions.

This thesis focuses on the IAXO Micromegas detector program, spanning IAXO-D0, IAXO-D1, and the separate BabyIAXO projection. Microbulk Micromegas detectors are well suited to helioscope searches because they combine low intrinsic radioactivity, good energy response in the keV range, topological discrimination, and compatibility with compact shielding and focusing optics [16, 17]. However, the expected signal rate is extremely small. The physics reach of the experiment therefore depends not only on detector performance, but also on the reliability of the background model, the realism of the detector-response simulation, and the effectiveness of the shielding and active veto strategy.

The work presented here addresses these requirements from three connected directions. First, it describes contributions to the software and simulation infrastructure used by the collaboration, with particular emphasis on REST-for-Physics, its Geant4 interface restG4, and the production workflows needed for large Monte Carlo campaigns. Second, it develops a source-resolved background inventory for IAXO-D1 in argon–isobutane, combining radiopurity information, environmental measurements, cosmic-ray models, and detector-response simulations. A BabyIAXO prediction additionally requires its xenon–neon response, focusing optics, final veto, and site-specific DESY source environment. Third, it studies the surface-level cosmic-ray-induced background and the corresponding active veto system, including the optimization of a multilayer plastic-scintillator and cadmium design, waveform-level veto observables, construction and commissioning aspects, and comparison with experimental data.

A central theme of the thesis is the transition from idealized background estimates to analysis objects that can be compared with real detector data. The relevant question is not only whether a simulated particle deposits energy in the detector volume, but whether the resulting event would pass the same energy, topology, timing, and veto selections applied to the experimental data. For this reason, the simulations are propagated through a detector-response chain whenever possible, and the veto studies are expressed in terms of prompt signals, delayed activity, channel multiplicity, and reconstructed observables. This approach is especially important for surface operation, where muons, high-energy neutrons, and secondary particles produced in the shielding can generate backgrounds that are not adequately described by passive shielding arguments alone [17].

The structure of the thesis follows this logic. Chapter 1 introduces the axion and axion-like-particle motivation, the strong \(\mathrm {CP}\) problem, and the main experimental approaches used in axion searches. Chapter 2 describes the IAXO program, the helioscope figure of merit, the role of BabyIAXO, and the experimental context in which the detector work is carried out. Chapter 3 presents the Micromegas detector technology, the IAXO-D0 and IAXO-D1 detector prototypes and their relation to BabyIAXO, and the associated gas, high-voltage, slow-control, data-acquisition, and calibration systems. Chapter 4 describes the computational framework used in the thesis, including ROOT, REST-for-Physics, restG4, data production, visualization, and related software developments. Chapter 5 studies the shielding and veto system, with emphasis on cosmic-ray-induced backgrounds, passive-shielding limitations, the active scintillator–cadmium veto concept, and the comparison between simulations and prototype data. Chapter 6 presents the IAXO-D1 argon source-response model, including intrinsic, environmental, cosmic, and neutron-induced activation contributions, the common selection, the generated-primary denominators, and the unresolved inputs needed for an absolute total. The conclusions assess the established results and prioritize the response and source-validation studies needed for IAXO-D1 and the subsequent BabyIAXO projection.

Chapter 1
Axions and Axion-Like Particles

1.1 Motivation and Scope

The QCD axion is a hypothetical pseudoscalar particle predicted by the most widely studied dynamical solution to the strong \(\mathrm {CP}\) problem. Its small mass and weak interactions also make it a viable cold-dark-matter candidate over broad, cosmology-dependent regions of parameter space. Axion-like particles (ALPs) share similar interactions but need not solve the strong \(\mathrm {CP}\) problem and do not obey the QCD relation between mass and couplings. Both classes of particles arise in extensions of the Standard Model and motivate a diverse experimental program [8–10].

This chapter introduces only the physics required to place solar helioscopes in that program. It summarizes the strong \(\mathrm {CP}\) problem, the Peccei–Quinn mechanism, the interactions most relevant to experiments, and the principal cosmological and astrophysical motivations. The emphasis is on the axion-photon coupling because it governs both solar production through the Primakoff process and coherent conversion in a laboratory magnetic field. The corresponding solar spectra, conversion probability, coherence conditions, buffer-gas operation, and helioscope figure of merit are developed in the next chapter.

The observable solar signal is the product of the axion flux, the probability of conversion in the magnet, and the detector acceptance. Even a large incident flux can therefore produce only a few detected X rays. For IAXO and BabyIAXO, the detector must combine efficient, stable operation in the 1–10 keV region with strong rejection of instrumental and environmental backgrounds.

1.2 The Strong CP Problem and the QCD Axion

The most general quantum chromodynamics (QCD) Lagrangian contains a term that violates parity and \(\mathrm {CP}\),

Here, \(G_{\mu \nu }^{a}\) is the gluon field-strength tensor, \(\widetilde {G}^{a,\mu \nu }=\varepsilon ^{\mu \nu \lambda \rho }G_{\lambda \rho }^{a}/2\) is its dual, \(\alpha _{\mathrm {s}}\) is the strong coupling, and \(M_q\) is the quark mass matrix. The physical angle \(\bar {\theta }\) combines the bare QCD angle with a phase from the quark masses. This source of strong-interaction \(\mathrm {CP}\) violation is distinct from the observed Cabibbo–Kobayashi–Maskawa phase in the weak sector. Although setting \(\bar {\theta }\) to zero is compatible with observation, the Standard Model contains no symmetry that requires this value once the quark masses are complex. The difficulty is therefore not an inconsistency of QCD but the unexplained hierarchy between the allowed natural scale of the parameter and its experimental upper bound.

The neutron electric dipole moment (nEDM) provides the most direct constraint on \(\bar {\theta }\). The 2020 measurement, which remained the most stringent direct limit as of September 2026, gives [18]

Hadronic calculations place \(d_n/\bar {\theta }\) at order \(10^{-16}\,e\,\si {cm}\), with a coefficient that depends on the calculation method [10, 19, 20]. Equation 1.2 therefore requires \( |\bar {\theta }|\lesssim \mathcal {O}(10^{-10}) \). Explaining why a dimensionless parameter that could naturally be of order unity is so small constitutes the strong \(\mathrm {CP}\) problem. Other proposed solutions impose fundamental \(\mathrm {CP}\) symmetry or modify the light-quark sector, but they require additional model structure. The Peccei–Quinn (PQ) mechanism is particularly economical because the same dynamics that removes \(\bar {\theta }\) predicts a particle that can be searched for experimentally [8, 10].

The PQ mechanism promotes this fixed angle to a dynamical degree of freedom [1, 2]. A global \(U(1)_{\mathrm {PQ}}\) symmetry is spontaneously broken at a scale \(f_a\), producing a pseudo-Nambu–Goldstone field \(a(x)\). Its QCD anomaly gives the effective interaction

Nonperturbative QCD generates a potential whose minimum satisfies \(\langle a\rangle /f_a=\bar {\theta }\). The effective strong \(\mathrm {CP}\) angle then vanishes dynamically, while fluctuations about the minimum constitute the axion [3, 4]. This sign convention is consistent with Eq. 1.1; reversing the definition of \(a\) would change both axion signs without changing observables.

The same QCD dynamics fixes the axion mass through the topological susceptibility. Modern chiral and lattice calculations give [21, 22]

Consequently, a larger PQ scale produces a lighter and more weakly coupled axion. Axions with \(f_a\) near the electroweak scale were excluded by laboratory measurements, whereas invisible-axion models with \(f_a\gg v_{\mathrm {EW}}\) remain viable. This inverse relation between mass, interaction strength, and the symmetry-breaking scale explains why viable axions are challenging to detect and why large magnetic volumes, long exposures, and low-background detectors are required.

1.3 Interactions and Axion-Like Particles

The gluonic interaction in Eq. 1.3 is essential to the solution of the strong \(\mathrm {CP}\) problem, but couplings to photons, electrons, and nucleons depend on the ultraviolet realization of the PQ symmetry. The photon interaction can be written as

Here, \(E/N\) is the electromagnetic-to-color anomaly ratio of the PQ current, while \(F_{\mu \nu }\) and \(\widetilde {F}^{\mu \nu }\) are the electromagnetic field-strength tensor and its dual. The second term includes the model-independent contribution from mixing with neutral mesons [10, 21]. For QCD axions, Eqs. 1.4 and 1.5 produce an approximately linear band in the \((m_a,g_{a\gamma })\) plane rather than two independent parameters.

KSVZ and DFSZ constructions provide common reference models [23–26]. In the simplest KSVZ model, the anomaly is generated by a new heavy quark; an electrically neutral heavy quark gives \(E/N=0\). In DFSZ models, Standard Model fermions couple through an extended Higgs sector, with \(E/N=8/3\) in the commonly used benchmark. These values are useful reference lines but do not encompass all viable QCD-axion couplings. The electron coupling is defined here by \begin{equation} \mathcal {L}_{ae}=-i g_{ae}a\bar {e}\gamma _5 e, \qquad g_{ae}=\frac {C_e m_e}{f_a}. \label {eq:axion-electron-coupling} \end{equation} Thus \(g_{ae}\) is dimensionless, whereas \(g_{a\gamma }\) has dimensions of inverse energy. The coefficient \(C_e\) conventionally appears in the derivative interaction \(C_e(\partial _\mu a)\bar {e}\gamma ^\mu \gamma _5e/(2f_a)\). The electron equations of motion relate it to the pseudoscalar form above; a change of operator basis must also account consistently for the anomalous photon term [8, 27]. Electron and nucleon couplings control additional solar production channels, stellar energy loss, and searches through interactions with matter. Their model dependence is kept explicit when reporting limits on production–detection coupling products.

The interaction in Eq. 1.5 permits several physically distinct processes. In the microscopic Coulomb field of a charged particle, photon–axion scattering is the Primakoff process. In a macroscopic transverse magnetic field, axion and photon states instead undergo coherent mixing, which can be described as oscillation between the two states. A material medium changes the photon dispersion relation and can restore phase matching; it does not simply supply a second real photon. Spontaneous \(a\rightarrow \gamma \gamma \) decay is also allowed. In natural units, \(\hbar =c=1\), its decay width and lifetime are \begin{equation} \Gamma _{a\rightarrow \gamma \gamma } = \frac {g_{a\gamma }^{2}m_a^{3}}{64\pi }, \qquad \tau _{a\rightarrow \gamma \gamma } = \Gamma _{a\rightarrow \gamma \gamma }^{-1}. \label {eq:axion-two-photon-lifetime} \end{equation}

The strong inverse dependence on both mass and coupling makes this decay extraordinarily slow for the light, weakly coupled particles relevant to helioscopes. For example, \(m_a=1\,\mathrm{meV}\) and \(g_{a\gamma }=1\times10^{-14}\,\mathrm{GeV}^{-1}\) give \(\tau _{a\rightarrow \gamma \gamma }\simeq 4\times10^{34}\,\mathrm{yr}\). The decay is therefore negligible on laboratory, solar-system, and cosmological timescales for this benchmark; coherent conversion in an external field is the experimentally relevant process [10, 28, 29].

An ALP is a light pseudoscalar with axion-like interactions but without the strict QCD relation between mass and couplings. Such fields can result from approximate global symmetries, hidden sectors, or string compactifications, and they need not solve the strong \(\mathrm {CP}\) problem [30–33]. Experiments therefore report both QCD-axion interpretations, represented by a model band, and more general ALP limits in which \(m_a\) and \(g_{a\gamma }\) are independent. This broader interpretation is useful for helioscopes because the same detector can test a QCD axion and any sufficiently light ALP produced by the same solar processes. Only the mapping from the measured coupling limit to an underlying particle model changes.

1.4 Cosmological and Astrophysical Context

Axions can form cold dark matter through nonthermal production. The canonical mechanism is vacuum misalignment: after PQ symmetry breaking, the axion field is generally displaced from the minimum of its potential. When the expansion rate falls to approximately \(3H(T_{\mathrm {osc}})\simeq m_a(T_{\mathrm {osc}})\), the field begins coherent oscillations whose energy density subsequently redshifts approximately as nonrelativistic matter [9, 34].

The predicted abundance depends strongly on the cosmological history. If PQ symmetry breaking occurs before inflation and is not restored afterward, the observable Universe inherits one initial misalignment angle, and isocurvature constraints connect the model to the scale of inflation. If it occurs after inflation, different regions begin with different angles, while axion strings and domain walls can contribute to the abundance. For this reason, cosmology does not select one unique axion mass or require axions to constitute all dark matter. Haloscope interpretations also depend on the assumed local halo density and velocity distribution, whereas helioscopes do not depend on the cosmological axion abundance. The distinction is important when comparing exclusion plots: a haloscope limit can weaken if axions are only a subcomponent of the halo, while a helioscope limit continues to constrain the relevant solar-production and photon-conversion couplings.

Thermally produced axions provide a separate cosmological probe. If sufficiently light and long-lived, they contribute a hot relic component that affects the cosmic microwave background and the growth of large-scale structure. The resulting constraints depend on the thermal history, the relevant axion couplings, and the cosmological data combination, so they are best stated as model-dependent limits rather than as a single universal mass bound [10, 35].

Stellar environments constrain weakly coupled particles because axions can escape and carry away energy. The Primakoff process in horizontal-branch stars and the Sun probes \(g_{a\gamma }\), while red giants, white dwarfs, supernovae, and neutron stars test complementary electron and nucleon couplings [35, 36]. These bounds follow from agreement between observed stellar populations or evolution and models that include an additional energy-loss channel. Their reliability depends on the object and observable, so limits from several systems should not be treated as statistically interchangeable. Some stellar observations have been interpreted as possible cooling anomalies, but their present significance does not constitute evidence for axions. They instead define motivated targets that should be tested with controlled experiments. Solar helioscopes are especially valuable in this respect because they search directly for particles emitted by the Sun without requiring axions to be Galactic dark matter. Their interpretation still relies on solar modeling, but the solar interior is constrained by helioseismology and neutrino measurements, and the signal can be modulated experimentally by alternating between tracking and nontracking periods.

1.5 Search Landscape and the Role of Helioscopes

Axion experiments exploit complementary assumptions and interactions [10, 37, 38]. Figure 1.2 gives a selective orientation to the principal photon-coupling searches relevant here rather than an exhaustive compilation.

The boundaries in Figure 1.2 have different statistical and physical interpretations. CAST reports a 95% Bayesian upper limit with a prior uniform in nonnegative \(g_{a\gamma }^{4}\), using a solar Primakoff flux [40]. The globular-cluster bound uses the ratio of asymptotic-giant-branch to horizontal-branch populations and depends on the treatment of convective mixing [41]. The haloscope curve is an envelope of searches with distinct mass coverage and analysis assumptions, rather than a joint likelihood [10, 39]. The digitized curves are approximate representations of those results; in particular, the published low-mass CAST limit is \(5.8\times10^{-11}\,\mathrm{GeV}^{-1}\). The BabyIAXO and IAXO curves retain their published design assumptions [13, 14].

Haloscopes use a magnetic field and a resonant or broadband electromagnetic structure to convert nonrelativistic Galactic axions into photons. They have reached benchmark QCD-axion sensitivity in selected mass regions, but their interpretation assumes a local dark-matter population. The broader program includes microwave cavities, dielectric structures, lumped-element circuits, plasma concepts, and quantum sensors. Because resonant instruments cover a limited frequency interval at one time, much of this program proceeds through systematic scans across axion mass.

Light-shining-through-wall experiments generate ALPs from a laser in one magnetic region, block the photons, and search for regenerated photons after a second magnetic region. This is a laboratory-only test that is independent of astrophysical-source and cosmological-abundance assumptions, although its production-and-regeneration probability scales as \(g_{a\gamma }^{4}\). The ALPS II campaign of February–May 2024 found no signal and set a 95% upper limit of \(\lvert g_{a\gamma }\rvert <1.5\times10^{-9}\,\mathrm{GeV}^{-1}\) for pseudoscalar masses below approximately \(0.1\,\mathrm{meV}\) [43]. Its projected reach assumes the upgraded optical configuration and is shown separately from this measurement.

Other searches target axion interactions with matter. Low-threshold detectors can search for axion absorption through electron couplings. CASPEr uses nuclear magnetic resonance and spin-precession observables to probe oscillating axion-induced moments and fields, whereas ARIADNE searches for an axion-mediated spin-dependent force [37, 44]. Together, these approaches retain sensitivity when the photon coupling is suppressed. No single method covers the full parameter space: resonant dark-matter searches provide high sensitivity over narrow mass intervals, laboratory production minimizes source assumptions, and helioscopes combine broad mass acceptance with sensitivity to solar production.

Helioscopes search for relativistic axions continuously produced in the Sun, using coherent conversion in a transverse laboratory magnetic field. The observable is a tracking-correlated excess of focused X rays, independent of the local dark-matter density. Optics reduce the detector area collecting background while preserving the magnet aperture, linking the three principal elements of the IAXO design [45]. The next chapter develops the solar spectra, conversion probability, and exposure requirements for this search.

Chapter 2
The Helioscope Technique and the IAXO Program

Introduction

Solar helioscopes combine a well-characterized astrophysical source with magnetic conversion and a tracking-correlated X-ray signal. This chapter develops the signal yield and statistical sensitivity, then follows the progression from CAST to the International Axion Observatory (IAXO) and its intermediate stage, BabyIAXO [13, 14, 46]. The connection to the present work is the detector-background requirement: a larger magnetic aperture is useful only if the optics and detector retain the converted photons while suppressing the background collected with them. Published design projections, the March 2026 engineering and site studies, and the subsequent funding milestone are distinguished below; the project-status cutoff is September 2026.

2.1 The Helioscope Technique

2.1.1 Solar Axions

Solar axions are produced in the hot, dense plasma of the Sun through several processes. The best known is Primakoff conversion, in which thermal photons convert into axions in the electromagnetic fields of charged plasma constituents. Additional contributions arise from processes involving the axion–electron coupling: atomic axio-recombination and axio-deexcitation, electron–ion and electron–electron bremsstrahlung, and Compton-like scattering. These processes are commonly grouped as the ABC channels [27].

The coupling dependence follows directly from this chain. For Primakoff solar axions, both production in the Sun and conversion in the laboratory depend on \(g_{a\gamma }\), so the expected signal rate scales as \(g_{a\gamma }^{4}\). For ABC solar axions, production depends on \(g_{ae}\), whereas detection still requires axion–photon conversion, so the signal rate scales as \(g_{ae}^{2}g_{a\gamma }^{2}\). Primakoff data therefore constrain \(\lvert g_{a\gamma }\rvert \), whereas ABC data constrain the product \(\lvert g_{ae}g_{a\gamma }\rvert \). Separating the two couplings requires an additional model assumption or an independent constraint.

Figure 2.2 shows the corresponding spectral components in the energy range relevant to helioscope searches. The Primakoff spectrum peaks at a few kiloelectronvolts, within the reference Micromegas analysis band of approximately \(1\text{--}10\,\mathrm{keV}\). The electron-coupling channels produce a softer component, motivating focal-plane detectors with sub-kiloelectronvolt thresholds, such as GridPix and cryogenic sensors. Integrating the archived Primakoff table over \(0.01\text{--}20\,\mathrm{keV}\) gives \(\Phi _a=3.46\times10^{11}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}\) and a mean energy of \(4.14\,\mathrm{keV}\) at the stated coupling. Its preserved header specifies the generator version and couplings but not the solar-model or opacity configuration, so no particular solar model is assigned to this tabulation. It is used here to illustrate the spectrum; a quantitative signal prediction must retain the model inputs and their uncertainties. The comparison of solar models in Ref. [47] finds a Primakoff-flux systematic difference of approximately 5%, in addition to uncertainty within each model.

The continuum channels shown here are appropriate to the few-kiloelectronvolt Micromegas study. At lower thresholds, longitudinal-plasmon conversion in solar magnetic fields can provide an additional \(g_{a\gamma }\)-dependent source and may dominate below approximately \(200\,\mathrm{eV}\), depending on the solar-field profile [48]. The benefit of sub-kiloelectronvolt detectors therefore extends beyond the ABC spectrum, while requiring a broader solar-source model.

2.1.2 Axion–Photon Conversion in a Helioscope

The operating principle is illustrated in Figure 2.3. Solar axions traverse a strong transverse magnetic field and can convert into X-ray photons through the inverse Primakoff effect. Grazing-incidence optics focus those photons onto a detector optimized for the relevant energy range, while a mobile platform follows the Sun during the daily tracking window.

In natural units, \(\hbar =c=1\), the conversion probability for a homogeneous transverse magnetic field \(B_\perp \) of length \(L\), neglecting photon absorption, is \begin{equation} P_{a \rightarrow \gamma }(L) = {\left (\frac {g_{a\gamma } B_\perp L}{2}\right )}^{2} \mathcal {F}(qL). \label {eq:helioscope-conversion-probability} \end{equation}

The coherence factor is \begin{equation} \mathcal {F}(qL) = {\left (\frac {2}{qL}\right )}^{2} \sin ^{2}\left (\frac {qL}{2}\right ). \label {eq:helioscope-coherence-factor} \end{equation}

In vacuum, \(q \simeq m_a^2/(2E)\) for a relativistic axion of energy \(E\). The coherent regime corresponds to \(qL \ll 1\), for which \(\mathcal {F} \simeq 1\) and the conversion probability grows as \(B_\perp ^2L^2\).

At larger axion masses, the axion–photon momentum mismatch suppresses conversion. A buffer gas gives the photon an effective mass \(m_\gamma \), changing the mismatch to \(q \simeq \lvert m_a^2-m_\gamma ^2\rvert /(2E)\) and restoring coherence over a narrow mass interval. Equations 2.1 and 2.2 remain the negligible-absorption expression after this substitution; a realistic gas scan must also include photon absorption and density gradients [49–51]. Vacuum is recovered by setting \(m_\gamma =0\).

For X-ray energies well above the atomic resonances of a low-\(Z\) gas, the effective mass is its plasma frequency, \begin{equation} m_\gamma ^2 = \omega _{\mathrm {pl}}^2 = \frac {4\pi \alpha n_e}{m_e}. \label {eq:buffer-gas-photon-mass} \end{equation}

Here, \(n_e\) is the electron density and \(m_e\) is the electron mass. At fixed temperature and composition, \(n_e\) is proportional to the gas pressure, so each pressure setting selects a different resonant value \(m_a\simeq m_\gamma \). The coherent interval at one setting is narrow; an extended mass range is therefore covered by increasing the pressure in overlapping steps rather than by operating at one fixed pressure. This relation between gas density, effective photon mass, and coherence is the basis of the CAST buffer-gas campaigns described below.

For one detection line, the expected differential event yield can be written schematically as \begin{equation} \frac {\mathrm {d}N_\gamma }{\mathrm {d}E} = \frac {\mathrm {d}\Phi _a}{\mathrm {d}E} P_{a\rightarrow \gamma }(E) A\,\epsilon _o(E)\,\epsilon _d(E)\,\epsilon _t\,t. \label {eq:helioscope-detected-spectrum} \end{equation}

Here, \(A\) is the instrumented aperture, \(\epsilon _o\) and \(\epsilon _d\) are the optics and detector efficiencies, \(\epsilon _t\) is the tracking fraction, and \(t\) is the elapsed data-taking time. For a selected focal region, \(\epsilon _o\) includes the fraction of the solar image retained within it. For multiple detection lines, the predicted spectra are summed with their line-specific fields, apertures, and efficiencies. This expression connects the solar spectra and conversion probability to the experimental sensitivity parameters discussed next.

2.1.3 Experimental Figure of Merit

In the background-dominated regime, the principal design dependencies are summarized by the helioscope figure of merit (FOM) [13, 46]: \begin{equation} f = f_M f_{DO} f_T. \label {eq:helioscope-fom} \end{equation}

Its components are \begin{equation} f_M = B_{\mathrm {eff}}^2 L^2 A, \qquad f_{DO} = \frac {\epsilon _d \epsilon _o}{\sqrt {ba}}, \qquad f_T = \sqrt {\epsilon _t t}. \label {eq:helioscope-fom-components} \end{equation}

Here \(A\) is the total instrumented aperture and \(B_{\mathrm {eff}}\) is the corresponding aperture-weighted effective transverse field; for a uniform field, \(B_{\mathrm {eff}}=B_\perp \). For a nonuniform magnet, \(B_{\mathrm {eff}}^2L^2A\) denotes the field integral \(\int _A\lvert \int _0^L \mathbf {B}_\perp \,\mathrm {d}\ell \rvert ^2\mathrm {d}A\) in the coherent limit. The detector–optics term contains the detector efficiency \(\epsilon _d\), optics throughput \(\epsilon _o\), areal detector background level \(b\), and selected focal-region area \(a\). The latter includes the optics point-spread function and the finite angular extent of the solar source. The tracking term contains the tracking fraction \(\epsilon _t\) and total elapsed time \(t\).

This decomposition shows why a next-generation helioscope requires more than a strong magnet. The magnetic term increases with aperture, field strength, and length; the detector–optics term increases with efficiency and decreases with the selected area and background level; and the tracking term favors long daily exposure. Because the Primakoff signal scales as \(g_{a\gamma }^{4}\), the projected coupling reach scales approximately as \(\lvert g_{a\gamma }\rvert \propto f^{-1/4}\).

2.1.4 Sensitivity with Few Background Events

The figure of merit assumes coherent conversion and enough background counts for a Gaussian approximation; its original derivation uses approximately ten or more expected background events as a guide [46]. The lowest IAXO background targets can fall below this regime. For uniform background in an energy interval \(\Delta E\) and total focal area \(a\), \begin{equation} \mu _b=b\,a\,\Delta E\,T, \qquad T=\epsilon _t t, \label {eq:helioscope-expected-background} \end{equation} where \(T\) is the effective tracking exposure. Combining the full-IAXO targets in Table 2.1 with an illustrative \(2\text{--}7\,\mathrm{keV}\) window and \(3\,\mathrm{yr}\) of elapsed operation gives \(\mu _b=2.84\) for \(\epsilon _t=0.5\). If three years instead denotes effective tracking exposure, the expectation is \(5.68\) events. These are alternative exposure definitions, not an uncertainty interval. The three-year run duration is drawn from the conceptual-design study [14]; the calculation does not reproduce its spectral acceptance or gas-scan exposure allocation.

For a Primakoff search at a fixed trial axion mass, a suitable starting point is the Poisson likelihood \begin{equation} \mathcal {L}(g_{a\gamma },\boldsymbol {\nu })= \prod _{\ell ,k}\operatorname {Pois}\!\left [ n_{\ell k}\,\middle |\, \left (\frac {g_{a\gamma }}{g_0}\right )^4 S_{\ell k}(\boldsymbol {\nu })+B_{\ell k}(\boldsymbol {\nu }) \right ]\mathcal {L}_{\mathrm {aux}}(\boldsymbol {\nu }). \label {eq:helioscope-poisson-likelihood} \end{equation} Here \(\ell \) identifies a detection line and observing condition, including the gas density, and \(k\) identifies a bin in reconstructed energy and focal position. The signal \(S_{\ell k}\) at a reference coupling \(g_0\) is obtained by folding the solar flux and magnetic conversion probability with the line-specific optics and detector response. The background expectation is \(B_{\ell k}\); \(\mathcal {L}_{\mathrm {aux}}\) represents off-Sun measurements, calibrations, and finite-simulation constraints on nuisance parameters \(\boldsymbol {\nu }\). This construction preserves energy migration, focal containment, and selection losses instead of compressing them into one constant efficiency.

Figure 2.5 isolates the statistical effect using a single counting region with a known background mean \(\mu _b\). For a signal mean \(s\geq 0\), a prior uniform in \(s\), and \(n\) observed events, the 95% Bayesian upper bound satisfies \begin{equation} \frac {\displaystyle \int _0^{s_{95}}(s+\mu _b)^n e^{-(s+\mu _b)}\,\mathrm {d}s} {\displaystyle \int _0^\infty (s+\mu _b)^n e^{-(s+\mu _b)}\,\mathrm {d}s}=0.95. \label {eq:helioscope-counting-upper-limit} \end{equation} The prior is uniform in \(g_{a\gamma }^{4}\) for a fixed Primakoff response, as in the CAST analysis [40]; other interval constructions need not give identical bounds [52]. At zero observed events, \(s_{95}=-\ln (0.05)=3.00\). Expected sensitivity is evaluated over \(n\sim \operatorname {Pois}(\mu _b)\), rather than by setting an observed count equal to a possibly noninteger mean. For the illustrative \(\mu _b=2.84\) and \(5.68\), the median background-only outcomes are three and six events, respectively. Their signal upper bounds are \(s_{95}=5.48\) and \(6.91\), corresponding to coupling limits approximately 16% and 23% above the zero-background value at fixed signal response and exposure.

The background-dominated scaling is \(g_{a\gamma }^{\mathrm {lim}}\propto b^{1/8}T^{-1/8}\) when the spectrum and efficiencies are fixed. Once the median outcome is zero, further background reduction leaves the counting limit approximately unchanged, while increasing the accepted signal exposure gives \(g_{a\gamma }^{\mathrm {lim}}\propto T^{-1/4}\). A veto or topology requirement should therefore be optimized through its effect on both the signal acceptance and the Poisson limit. The literature projections below retain their original assumptions; the detector studies in this thesis do not supply all inputs required to replace them with an absolute BabyIAXO prediction.

2.2 From CAST to IAXO

2.2.1 CAST as the Reference Helioscope

The CERN Axion Solar Telescope (CAST) established the reference implementation of the modern helioscope technique [12]. It used a repurposed Large Hadron Collider (LHC) test dipole magnet with two parallel bores, instrumented at both ends by several low-background X-ray detector systems. From 2002 to 2006, the sunset end used a conventional TPC covering both bores, while the sunrise end combined a Micromegas detector on one bore with a pn-CCD behind an X-ray telescope on the other [53–55]. The optics reduced the detector area over which signal events were sought, demonstrating directly the background-count advantage later formalized in the detector–optics term of the helioscope figure of merit. After aging degraded the TPC, the sunset system and the original sunrise Micromegas were replaced by a new generation of shielded Micromegas detectors. Microbulk fabrication, improved radiopurity, refined event-topology discrimination, and progressively more complete passive and active shielding then reduced their background level. In 2014, a purpose-built slumped-glass telescope was coupled to a Micromegas detector, forming the IAXO pathfinder and demonstrating the combined optics, shielding, veto, and readout concept adopted for the next-generation program [40, 56].

CAST separated the mass scan into three principal operating regimes, summarized in Figure 2.6. The evacuated-bore phase retained coherence for \(m_a\lesssim 0.02\,\mathrm{eV}\). The first buffer-gas campaign used \(\ce {^4He}\) at \(1.8\,\mathrm{K}\): 160 density settings, equivalent to pressure increments of approximately \(0.08\,\mathrm{mbar}\) and reaching \(13.4\,\mathrm{mbar}\), covered \(0.02\text{--}0.39\,\mathrm{eV}\). The lower saturated-vapor pressure of \(\ce {^4He}\) limited the accessible density. Replacing it with \(\ce {^3He}\) allowed higher pressures at the same magnet temperature; successive scans covered \(0.39\text{--}1.17\,\mathrm{eV}\), with the pressure chosen so neighboring coherence windows overlapped [49–51].

CAST demonstrated low detector-background levels under helioscope conditions, the background-count reduction obtained by focusing, and reliable long-term operation of a Sun-tracking magnet and its detection lines. Its extended run with the IAXO pathfinder and a xenon-based Micromegas detector found no axion signal and set \(\lvert g_{a\gamma }\rvert <5.8\times10^{-11}\,\mathrm{GeV}^{-1}\) at 95% confidence for \(m_a\lesssim 0.02\,\mathrm{eV}\) [40]. This result links the strongest demonstrated helioscope limit to the detector family, focusing concept, and background-control methods developed further for the BabyIAXO stage.

2.2.2 Why a Dedicated Helioscope Is Required

CAST also exposed the limitations of a repurposed accelerator magnet: small total aperture, constrained detector and optics geometry, and limited tracking time. Because the figure of merit depends on both the magnetic aperture and the detector–optics term, a substantial sensitivity improvement requires a dedicated experimental design rather than incremental upgrades to an existing accelerator component.

Table 2.1 summarizes the resulting design shift. CAST exploited the high field of an accelerator dipole, whereas BabyIAXO and IAXO exchange some field strength for much larger aperture, systematic use of focusing optics, lower detector-background targets, and substantially longer solar tracking. The IAXO strategy is therefore to co-optimize \(f_M\), \(f_{DO}\), and \(f_T\) in a purpose-built instrument [13, 46, 57].

2.3 The IAXO Experiment

2.3.1 Physics Reach and Design Philosophy

IAXO is conceived as a next-generation axion helioscope optimized for solar axions and ALPs [13, 45, 57]. In the low-mass region, design projections improve the background-limited signal-to-noise ratio relative to CAST by approximately four to five orders of magnitude. They correspond to a projected sensitivity near \(\lvert g_{a\gamma }\rvert \sim 3\times10^{-12}\,\mathrm{GeV}^{-1}\), approximately a factor of 20 below the current CAST limit, subject to the assumed exposure and background performance [45]. The observatory is also designed to probe solar production through \(g_{ae}\) with sensitivity beyond previous laboratory searches.

These projections set the performance targets for the coupled subsystems discussed below: magnetic conversion aperture, X-ray optics and focal-plane background, and solar-tracking exposure. The IAXO+ curve is retained only as an optimistic performance benchmark; the baseline experimental stages discussed in this thesis are BabyIAXO and IAXO. The projection curves reproduce heterogeneous literature assumptions and were not recalculated from the March 2026 engineering parameters. Observed boundaries are digitized approximations; the current published CAST plateau is the \(5.8\times10^{-11}\,\mathrm{GeV}^{-1}\) limit quoted above.

2.3.2 Magnet

The 2014 reference design for IAXO uses a superconducting toroidal magnet approximately \(20\,\mathrm{m}\) long, formed by eight coils and providing eight bores of approximately \(60\,\mathrm{cm}\) diameter [13]. The useful field in the bores is approximately \(2.5\,\mathrm{T}\), while the peak field in the windings is about \(5.4\,\mathrm{T}\); the principal gain over CAST comes from the much larger integrated magnetic aperture. The toroidal layout leaves the bores accessible for optics and detectors and defines eight parallel detection lines. The bores can operate in vacuum or, for higher-mass scans, with a buffer gas.

The final magnet design remains part of the post-BabyIAXO program. Recent studies retain the large multi-bore concept while also considering high-temperature-superconductor alternatives that could change the field and cryogenic implementation [45].

2.3.3 X-ray Optics

The reference IAXO design equips every detection line with grazing-incidence X-ray optics [13, 59]. The sensitivity benchmark in Table 2.1 assumes a selected focal-region area of approximately \(0.15\,\mathrm{cm}^{2}\) per line. Detailed designs optimize both the energy-dependent throughput and the focal image of the extended solar source.

Focusing does not reduce the areal detector background level \(b\). Instead, it confines the signal to a small selected area \(a\), reducing the expected background counts in the signal region in proportion to \(ba\) when the background is approximately uniform. This coupling between optics and detector performance is the origin of the detector–optics term in Equation 2.6.

2.3.4 Detector Technologies

The focal-plane detectors must combine high efficiency in the reference \(1\text{--}10\,\mathrm{keV}\) band with stage-dependent background targets. The BabyIAXO sensitivity benchmark assumes a background level of \(1\times10^{-7}\,\mathrm{counts}\,\mathrm{keV}^{-1}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}\), whereas the full IAXO concept targets \(1\times10^{-8}\,\mathrm{counts}\,\mathrm{keV}^{-1}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}\) [13, 14]. Under the surface conditions considered for the program, meeting these targets requires radiopure construction, passive shielding, topology-based discrimination, and active-veto systems [17].

Microbulk Micromegas detectors are the most developed gaseous technology for this role because CAST and IAXO-D0 demonstrated their radiopurity, topological discrimination, stable operation, and compatibility with focused soft X rays. Alternative focal-plane concepts include GridPix detectors, metallic magnetic calorimeters, transition-edge sensors, and silicon drift detectors; their lower thresholds or improved energy resolution are particularly relevant to the softer ABC spectrum [45, 60, 61]. Chapter 3 develops the Micromegas detector line used in this thesis.

2.3.5 Tracking and Observatory Operation

The reference IAXO concept mounts the magnet, optics, and detectors on elevation and azimuth drives that provide solar tracking for up to approximately half of each day, corresponding to \(\epsilon _t\simeq 0.5\) [13]. The moving structure must support the cold mass, preserve alignment among the bores, optics, and detectors, and allow reproducible transitions between Sun-tracking data and off-Sun background measurements. These requirements enter both the sensitivity exposure and the background-control strategy.

The conceptual installations are surface facilities rather than deep-underground laboratories. Background suppression must therefore be obtained through the detector, passive shielding, event-topology analysis, and active vetoing. The evolution of the specific BabyIAXO site assumption, and its consequences for this thesis, are discussed below.

2.4 BabyIAXO as an Intermediate Stage

2.4.1 Role Within the IAXO Program

BabyIAXO is the intermediate experimental stage between CAST and the full IAXO observatory [14, 45, 58]. It provides a common environment in which the magnet, optics, detectors, cryogenics, tracking, alignment, gas handling, and data acquisition can be integrated and commissioned. At the same time, it is a physics instrument with independent discovery reach. This staged program also builds the shared analysis, software, operations, and system-integration experience required for the full observatory.

Under the 2021 conceptual-design assumptions, including \(1.5\,\mathrm{yr}\) of effective exposure for each of the vacuum and buffer-gas campaigns, the projected low-mass vacuum sensitivity is \(\lvert g_{a\gamma }\rvert \simeq 1.5\times10^{-11}\,\mathrm{GeV}^{-1}\) for \(m_a\lesssim 0.02\,\mathrm{eV}\). The projected buffer-gas scan would extend the reach to higher masses and probe the KSVZ benchmark approximately over \(0.06\text{--}0.25\,\mathrm{eV}\) [14]. BabyIAXO therefore combines new physics reach with validation of the technologies and subsystem interfaces required for the full observatory.

2.4.2 Main Experimental Features

The 2021 conceptual design established a common-coil dipole with two parallel flat racetrack coils carrying opposite currents and two \(10\,\mathrm{m}\)-class bores [14]. By March 2026, the engineering model specified two \(11\,\mathrm{m}\)-long free bores of \(0.70\,\mathrm{m}\) diameter and an aluminum-stabilized NbTi/Cu Rutherford-cable conductor operated at \(6\,\mathrm{kA}\) [62]. At that operating current, the calculated mean transverse bore field is \(2.1\,\mathrm{T}\), the peak field on the cable is \(4.7\,\mathrm{T}\), and the three-dimensional magnet figure of merit is approximately \(290\,\mathrm{T}^{2}\,\mathrm{m}^{4}\). The public June 2026 status presentation retained these engineering values [63]. Each bore can host a complete detection line with dimensions representative of the full observatory, allowing the magnet aperture, cryogenic integration, and detector interfaces to be tested at full line scale before the final toroidal observatory is designed.

On August 11, 2026, the University of Bonn announced approval of a magnet system costing EUR 6 million, financed by EUR 3 million from the German Research Foundation (DFG), EUR 2.4 million from North Rhine-Westphalia, and EUR 0.6 million from the participating universities [64]. This funding milestone concerns magnet construction; it does not establish completion of the magnet or approval of the final DESY site.

The 2021 conceptual optics baseline paired one custom, NuSTAR-derived segmented-glass telescope with an available XMM-Newton flight-spare telescope [14]. By the 23rd IAXO Collaboration Meeting in March 2026, the optics program also included BRAVO-SUN and XRISM-derived components and was developing a co-mounted telescope configuration. The final combination of components remained under development [65]. The June 2026 public comparison quoted approximately \(0.2\,\mathrm{cm}^{2}\) for the custom telescope and \(0.3\text{--}0.7\,\mathrm{cm}^{2}\) for the XMM telescope [63]. These areas cannot be applied interchangeably: each line requires its own energy-dependent throughput and focal containment, evaluated for the chosen signal region.

Micromegas remain the principal low-background technology for the detector line studied here, while the broader BabyIAXO program also develops GridPix and cryogenic focal-plane detectors [14, 61]. The detector line treated in this thesis is therefore one implementation within a broader focal-plane program.

2.4.3 Evolution of the DESY Site Scenario

When the background-model and veto-simulation program began, the reference BabyIAXO site was the HERA South Hall on the DESY campus. The hall is an underground accelerator space rather than a deep-underground low-background laboratory, but its structure, access shafts, and surrounding material could modify the cosmic-ray field relative to an outdoor installation. Early simulations therefore treated the cosmic-ray component as site dependent, with attention to overburden, openings, and local shielding.

During 2025 and 2026, internal collaboration studies shifted the working baseline toward an outdoor, on-surface location on the DESY campus. The reported considerations included simpler civil infrastructure, reduced demands on DESY infrastructure resources, lower expected cost, and a shorter route to site activation [67]. As reported at the 23rd collaboration meeting in March 2026, the DESY directorate had encouraged further site exploration and development of cost and schedule plans. This did not constitute formal project or site approval, and the exact position and site elevation remained under study [15].

The March 2026 on-surface working baseline is adopted here without credit for hall overburden. Simulations that retain boundary conditions associated with HERA South are identified separately. An outdoor source spectrum is not a demonstrated upper bound on every local contribution: the ground, housing, platform, and magnet can attenuate primaries while generating or redistributing secondaries. Transfer to the final site therefore requires a consistently normalized source boundary and transport through the local environment. The detector system must address sea-level muons, neutrons, and secondary particle production in the passive shielding. An active veto is therefore central to the mitigation strategy investigated here; Chapter 5 evaluates the proposed plastic-scintillator veto with cadmium neutron-capture layers.

2.5 Connection to the Present Thesis

Chapter 3 narrows the discussion from the helioscope to the detector-development line. It introduces time-projection-chamber signal formation and microbulk Micromegas technology, then describes the IAXO-D0 experimental prototype and the IAXO-D1 simulation geometry used in this work. Chapter 4 develops the REST-for-Physics/restG4 framework used to represent that detector and its environment. Chapters 5 and 6 evaluate the active-veto strategy and assemble the validated components and remaining limitations of the partial background model.

Chapter 3
Micromegas X-ray Detectors for BabyIAXO

Introduction

The Micromegas detector line studied in this thesis is the low-background X-ray detection system coupled to the BabyIAXO helioscope optics. Its task is narrow but demanding: it must convert a small number of soft X rays in the \(1\)–\(10\,\mathrm {keV}\) region into calibrated, position-sensitive waveforms while operating at surface level, close to passive shielding, active veto panels, gas services, high-voltage channels, and data-acquisition electronics. For that reason, the detector cannot be described only as an isolated gas volume. It is a coupled instrument in which gas transport, charge amplification, readout segmentation, calibration, slow control, and veto synchronization all determine the observables used later in the background analysis.

This chapter provides the detector foundation for the rest of the thesis. It first summarizes the signal-formation physics that is needed to interpret Micromegas waveforms, then describes the microbulk Micromegas technology and the IAXO-D0/IAXO-D1 prototype implementations. The final sections connect the detector to its operating services, data-acquisition chain, and calibration procedures, leaving the detailed software implementations and large-scale background simulations to Chapters 4 and 6.

3.1 The Time Projection Chamber (TPC)

Time Projection Chambers (TPCs) are gaseous detectors in which ionization electrons drift through an electric field toward a segmented readout plane. Large TPCs are often used as tracking detectors, but the BabyIAXO Micromegas detector is a shallow X-ray TPC: the relevant information is not a long momentum-measuring trajectory, but the amount of deposited charge, its two-dimensional distribution on the readout strips, and the relative timing of the digitized pulses. This compact topology is precisely what makes the detector useful for axion searches, because focused solar X rays should produce localized charge clusters while many background events produce more extended, asymmetric, or veto-correlated signatures.

A TPC typically consists of a gas-filled chamber subjected to a uniform drift field. An incoming particle or photon interaction produces electron-ion pairs in the gas. The electrons drift toward the anode, diffuse during transport, enter an amplification region, and finally induce signals on the readout electrodes. The ions drift more slowly toward the cathode. In the BabyIAXO detector, the readout plane is a microbulk Micromegas, which combines amplification and fine strip segmentation in a radiopure structure suitable for low-background operation.

3.1.1 Ionization in Gases

The Micromegas signal starts with an energy deposition in the gas. For the soft X rays relevant to BabyIAXO this deposition is dominated by photoelectric absorption, whereas charged particles usually produce extended ionization tracks and neutral particles contribute indirectly through recoils or secondary radiation. Only the aspects of these processes that determine the later waveform and calibration response are summarized here.

For photons, the attenuation through a material is described by

Here, \(\mu \) is the linear attenuation coefficient. Equivalently, \(\mu =\rho \mu _m\), with \(\mu _m\) the mass attenuation coefficient. In the few-keV signal region, the photoelectric effect dominates the attenuation and produces a localized primary-electron cloud. The full background simulation transports the other electromagnetic processes, but they are not needed to explain the calibration and signal topology developed in this chapter.

The preference for noble gases follows directly from the strong \(Z\) dependence of the photoelectric cross section in the X-ray range, visible in Figure 3.2. The quencher is present at much lower concentration and has a smaller attenuation contribution, but it is essential for stable proportional operation. After photoelectric absorption, the atomic vacancy relaxes through Auger emission or fluorescence. If a fluorescent x ray escapes the sensitive volume, the measured energy is reduced and an escape feature appears in the calibration spectrum; this is particularly visible for argon-based \(\ce {^{55}Fe}\) calibrations.

Charged particles instead leave ionization along their path, with a topology governed by the stopping power, multiple scattering, and possible secondary radiation. In a Micromegas TPC this typically produces broader and more track-like charge patterns than a few-keV X ray. Neutral particles are relevant because they can generate nuclear recoils or secondary photons and charged particles in the gas or surrounding materials. This indirect character is one of the reasons why the background model treats radiation transport and detector-response reconstruction together rather than as separable problems.

3.1.2 Electron Transport

Primary Charge Production

An electron-recoil energy deposit \(E\) in the gas produces a finite number of electron-ion pairs. The electrons, referred to here as primary charge, are the carriers that drift toward the Micromegas readout and seed the avalanche in the amplification gap. The mean number of primary electrons is

Here, \(W\) is the average energy required to create one electron-ion pair in the mixture. For nuclear recoils, part of the kinetic energy goes into atomic motion rather than ionization, so the corresponding charge yield requires a recoil-response model, discussed in Appendix C.1.2. The intrinsic fluctuation around this mean is smaller than Poissonian and is commonly written as

Here, \(F\) is the Fano factor [69]. This primary-charge statistics sets the best achievable energy resolution before transport, amplification, and electronics effects are included.

Electron Drift

The drift field transports the primary electrons from the conversion point to the amplification region. In the mobility approximation, the drift velocity can be written as

Here, \(\mu _e>0\) is the magnitude of the electron mobility at the operating field, gas density, and composition; the minus sign expresses motion opposite to \(\vec {E}\). At fixed temperature, transport tables are conveniently compared using the reduced field \(E/p\), where \(p\) is the pressure; \(E/N\), with \(N\) the gas number density, is the more general variable when temperature changes. In practice, drift velocities and diffusion coefficients are taken from gas-transport calculations such as Garfield++/Magboltz, because the response depends on the mixture, pressure, field, and quencher fraction. Typical electron drift velocities in noble-gas TPC mixtures are of order \(1\,\mathrm{cm}\,\mathrm{\mu s}^{-1}\), so the drift time is directly connected to the pulse timing in the digitized waveform. The gas-mixture dependence of the drift velocity and diffusion coefficients is discussed below in the context of the detector-response gas tables.

During transport the charge cloud also diffuses. The standard deviation \(\sigma _{\hat {u}}\) of the electron cloud in a given direction \(\hat {u}\) after a drift distance \(d\) can be written as

The coefficients \(D_{\hat {u}}\) in this convention have units of square-root length, as in the Garfield++ gas tables [70]. They are related to the conventional diffusion coefficients \(\mathcal {D}_{\hat {u}}\), with units of length squared per time, by \(D_{\hat {u}}=\sqrt {2\mathcal {D}_{\hat {u}}/|\vec {v}_d|}\) for uniform drift.

In the longitudinal section shown in Figure 3.3, the primary charge drifts opposite to the electric field. The longitudinal width \(\sigma _L\) is parallel to the mean drift direction, whereas the transverse width \(\sigma _T\) is perpendicular to it. Both are defined from the charge-cloud centroid to its one-standard-deviation contour; they are therefore semi-axes of the contour, not full cloud diameters. The separate longitudinal and transverse diffusion coefficients arise in the presence of the drift field. Diffusion controls the charge sharing between strips and the apparent width of a localized X-ray event. Recombination and attachment provide the competing loss mechanisms; in practice, oxygen and water contamination are the main operational concerns, which is why gas purity, material outgassing, and circulation are part of the detector response rather than purely auxiliary services.

Charge Amplification

The primary charge is too small to be measured directly, so the Micromegas gap operates in avalanche mode. The high amplification field converts each primary electron into a charge packet whose mean size is set by the gas gain.

The mean electron population \(N_a\) after amplification of \(N_e\) primary electrons across a gap of length \(L\) is, when attachment is negligible,

Here, \(\alpha \) is the first Townsend coefficient, which depends on the gas medium and the electric field. The number of electrons after amplification of the primary charge \(N_a\) can be expressed as

If the gain fluctuations of individual primary electrons are described by a variance \(\sigma _G^2\), the variance of the amplified electron population, \(\sigma _a^2\), can be written as

Here, \(b\) is defined as

For an approximately Gaussian peak, the resolution \(R = 2 \sqrt {2 \ln {2}} \sigma _a / N_a \approx 2.35 \cdot \sigma _a / N_a\) is the full width at half maximum (FWHM) of the amplified-charge distribution divided by its mean value.

Here, \(\sigma _{\mathrm {el}}\) represents additional electronic-noise contributions referred to the amplified charge. The expression assumes independent single-electron avalanches and additive noise uncorrelated with the primary charge [71]. The resolution \(R\) is commonly expressed as a percentage.

Expression 3.10 separates the primary-ionization and avalanche contributions from electronic noise, which becomes increasingly important near threshold. The approximately \(7\%\) primary-only FWHM in Figure 3.4 is an intrinsic reference for these gas mixtures and this X-ray energy. It excludes amplification, charge loss and readout fluctuations and therefore is not the predicted resolution of the complete detector. Measured microbulk resolutions also depend on gain and collection conditions [72].

Avalanche ultraviolet photons can initiate secondary avalanches by photoionizing gas species or releasing electrons from surfaces. Adding isobutane suppresses this feedback through absorption and non-radiative molecular relaxation. The quencher also changes charge transport, as illustrated in Figure 3.5.

Increasing the isobutane fraction generally reduces transverse diffusion in these scans, producing a narrower cloud after the same drift distance. Changes in drift velocity and longitudinal diffusion also affect the relation between waveform timing, drift position, and the extent of a localized ionization cluster. The dotted lines mark reference operating fields, rather than gas-optimization boundaries. Gas choice must therefore balance charge transport, attachment, amplification stability, and operational requirements. The calculation workflow is described in Section 4.6.6.

3.1.3 Micropattern Gaseous Detectors: Micromegas

Micromegas (MICRO-MEsh GAseous Structure) detectors are micropattern gaseous detectors in which a thin metallic mesh separates the drift region from a narrow amplification gap [73]. Ionization electrons produced in the drift volume pass through the mesh when the field ratio between amplification and drift regions is favorable, and then avalanche in the high-field gap before being collected by the anode strips. This separation between a relatively low-field drift volume and a very high-field amplification region gives Micromegas detectors fast signals, good spatial granularity, and stable operation at gains suitable for soft X-ray detection.

For axion helioscopes and other rare-event searches, the relevant implementation is the microbulk Micromegas. In this technology the mesh, insulating pillars, and readout pattern are manufactured from copper-clad kapton using photolithographic processes, producing a thin and mechanically uniform amplification structure [74]. The small material budget, the use of radiopure copper and kapton, and the possibility of producing fine two-dimensional strip readouts are central advantages for low-background X-ray detectors. They also make the detector naturally compatible with a TPC analysis strategy: X-ray events produce compact clusters, while tracks from cosmic rays or radioactive backgrounds tend to be more extended in at least one strip projection.

Three distinct length scales should not be conflated. The \(6\,\mathrm{cm}\)-wide IAXO readout contains 120 strips per coordinate, giving a strip pitch of \(500\,\mathrm{\mu m}\). At each X–Y strip crossing, the IAXO-D1 mesh photograph shows a \(3\times 3\) group of microscopic openings. Microbulk structures of this detector family use holes of order \(40\,\mathrm{\mu m}\) in diameter on an approximately \(100\,\mathrm{\mu m}\) triangular pitch, while the etched polyimide defines an amplification gap of approximately \(50\,\mathrm{\mu m}\) [56, 72]. The strip pitch sets the two-dimensional readout granularity; the much smaller hole pitch and gap determine electron transmission and avalanche formation.

The operating point of a Micromegas detector is defined by the drift field, mesh voltage, gas mixture, pressure, and readout threshold. The mesh transparency must be high enough that primary electrons enter the amplification gap efficiently, while the gain must be large enough to resolve keV deposits without approaching unstable discharge conditions. These two requirements are coupled: the field ratio controls electron focusing through the mesh, while the amplification field controls both signal size and discharge probability. Consequently, stable operation is not only a matter of setting a high voltage, but of choosing a consistent gas, voltage, and electronics configuration and monitoring it through calibration data.

The combination of radiopurity, segmentation, low threshold, and successful operation in CAST makes microbulk Micromegas the baseline detector technology for the IAXO Micromegas line [12, 16, 40].

3.2 The BabyIAXO Micromegas Detector Prototypes

The baseline detector technology for IAXO and BabyIAXO is the microbulk Micromegas. Its successful operation in CAST, where it provided low-background X-ray detection for the solar-axion search, makes it the established baseline choice for the IAXO program.

The TPC design of the BabyIAXO Micromegas detector remains similar to the CAST Micromegas detectors, since both experiments are designed with the same goal of detecting solar axions. The gas volume is a cylinder with a diameter of \(10~\mathrm {cm}\) and a height of \(3~\mathrm {cm}\), with a total volume of \(235.62~\mathrm {cm}^3\). The microbulk micromegas readout has a square shape with a side of \(6~\mathrm {cm}\). The readout has 120 strips for each direction, for a total of 240 channels.

The full \(6\times 6~\mathrm {cm}^{2}\) readout is not the signal-normalization area targeted by the frozen conservative background analysis. Earlier reconstruction studies integrated readout energy or required a hit centroid inside a \(15~\mathrm {mm}\)-radius central circle, representing a broad entrance/optics footprint. The background-analysis-v2-conservative-reference contract instead selects the calibrated maximum reconstructed track and requires its paired X–Y center to satisfy \(r<10~\mathrm {mm}\). This gives the explicit signal area \(A_{\mathrm {fid}}=\pi ~\mathrm {cm}^{2}\). An energy integrated inside a readout region and a containment decision on the reconstructed track are physically different observables; the background-model chapter keeps the older \(15~\mathrm {mm}\) results as auxiliary studies rather than treating the two fiducial definitions as equivalent.

There are two distinct generations of detector prototypes: IAXO-D0 and IAXO-D1. Both prototypes share the same core design scale, including TPC dimensions, readout size, number of strips, and nominal lead-shielding thickness. The main differences are in the chamber and pipe design, shielding serviceability, Micromegas PCB implementation, and electronics.

3.2.1 IAXO-D0

The IAXO-D0 prototype is, in essence, the latest CAST-derived design. The chamber is cylindrical, with a large copper backplate that protrudes laterally from the shielding. The copper pipe is thinner in the middle and the shielding is made of lead bricks. In order to access or move the detector, the lead shielding must be partially removed brick by brick. The front-end electronic chips are four AGET chips and the back-end electronics is a Feminos card [75]. The front-end and back-end electronics are physically connected into a single FEC–Feminos unit, which is connected to the readout through flat cables.

A significant data-taking campaign was performed with the IAXO-D0 prototype in Zaragoza using the same Micromegas detector that had operated in CAST, shortly after it was decommissioned. This campaign validated the detector and tested the prototype veto system, with emphasis on the reduction of cosmic-ray-induced background. Earlier measurement campaigns with the same prototype family were also performed using other Micromegas detectors from the same generation [60]. Together, these measurements provided the experimental anchor for the simulation and background-rejection studies developed later in the thesis.

3.2.2 IAXO-D1

The IAXO-D1 prototype introduces significant improvements with respect to IAXO-D0. The shielding is a lead box with a square shaft in the middle. It is designed to sit on linear rails so that it can be moved laterally to access the detector, substantially reducing the time required for service operations. The chamber has a square footprint and the copper pipe is significantly thicker. The Micromegas PCB can be bent to fit the shielding aperture, and the readout strips exit the shielding hole in parallel to the pipe.

The front-end electronics are based on four STAGE chips, while the back-end electronics follow an ARC-compatible design. The STAGE front-end cards (Figure 3.11a) are placed inside the shielding next to the readout. This minimizes the capacitance and noise pickup of the low-level analog connection. Radiopurity requirements distinguish the flexible PCB substrate from its mounted components: the March 2025 electronics report lists radiopure FEC substrates but does not classify the populated cards as fully radiopure [76]. The component inventory and assay status therefore remain relevant to the material-background model. The ARC-compatible back-end (Figure 3.11b) contains substantially more conventional, non-radiopure components and is therefore kept outside the passive shield, where it is also accessible for power, control, data transfer, and maintenance [76]. Flexible interconnects carry the digitized and control signals through the shielding penetration.

The IAXO-D1 spatial response was measured independently with the SOLEIL synchrotron X-ray beam [77]. For a \(90\,\mathrm{\mu m}\times90\,\mathrm{\mu m}\) beam at \(6\,\mathrm{keV}\) and a drift field of \(100\,\mathrm{V}\,\mathrm{cm}^{-1}\), Gaussian fits to the reconstructed event-centroid distributions gave standard deviations slightly below \(100\,\mathrm{\mu m}\) in both views. This is a centroid-resolution measurement, including finite beam size and the stated event selection; it is not the strip pitch or the width of an individual ionization cloud. Charge sharing permits centroid reconstruction finer than the \(500\,\mathrm{\mu m}\) strip pitch. The measured energy and field dependence provides an existing constraint on diffusion and reconstruction modeling, while the different beamline and laboratory noise conditions must be retained in comparisons.

3.3 Detector Ancillary Systems

3.3.1 Gas system

The IAXO Micromegas prototypes can operate with argon–isobutane or xenon–neon–isobutane mixtures. Argon with \(2\%\) isobutane at \(1.4\,\mathrm {bar}\) was used for most CAST operation [12], while equal-partial-pressure xenon and neon with \(2.3\%\) isobutane was used during its final years [40]. The xenon–neon mixture avoids the argon escape structure near the signal region and the intrinsic \(\ce {^{39}Ar}\) contribution, but its cost favors closed-loop purification and recirculation.

Recirculation reduces noble-gas consumption, but it also turns the chamber, pipework, pump, buffer volume, valves, and filters into a coupled contamination system. Leaks, outgassing, and radon emanation can then accumulate activity that an open flow would continuously remove. This is not only a gas-quality issue: IAXO-D1 measurements have shown that the low-gain alpha rate changes markedly between open-loop and recirculating configurations, motivating dedicated radon-source checks and purification studies [78]. Closed-loop operation therefore requires both chemical purification and radiological control of the complete circulation path.

For detector response, the important quantities are mixture composition, pressure, temperature, drift field, flow stability, and gas purity. These parameters determine the charge-transport properties summarized earlier and must match the gas tables used in simulation. The Garfield++/Magboltz workflow is described in Section 4.6.6; the prototype piping, open- and closed-loop implementation, and safety provisions are documented in Appendix D.2, including the full-page diagram in Figure D.2.

3.3.2 High voltage and slow control

Separate cathode and mesh channels establish the drift and amplification fields. Their stability affects electron transport, mesh transparency, gain, and reconstructed topology, while the independently biased veto photomultiplier tubes determine the veto threshold and timing response. Controlled ramping, current monitoring, filtering, and trip handling are therefore part of the detector-response contract.

The slow-control layer records these settings together with gas and environmental conditions and supports remote intervention during long runs. The reusable hvps control library developed in this thesis is described in Section 4.7.3. The prototype power-distribution and Node-RED implementation details [79] are retained in Appendix D.2.

3.4 Shielding and Veto Systems

The Micromegas detector is only one part of the complete low-background detection line. For BabyIAXO, the detector must operate inside a passive shield and in coincidence with an active veto system, so the mechanical envelope, signal feedthroughs, calibration access, gas services, high-voltage routing, and data-acquisition interfaces all have to remain compatible with the surrounding shielding. The detailed passive-shielding studies, cosmic-ray-induced background simulations, and scintillator–cadmium veto design are therefore treated in the dedicated shielding and veto chapter, Chapter 5. In the present chapter, the relevant point is the interface: Micromegas operation defines the X-ray-like event selection, timing reference, calibration strategy, and veto-coincidence information that the background model uses later.

3.5 Data Acquisition System

This section describes the detector-facing DAQ hardware: how the Micromegas strips and veto channels are connected to front-end electronics, back-end timing, and the DAQ computer. The acquisition software itself, including the feminos-daq refactor and online viewer, is treated in the software chapter.

The Data Acquisition (DAQ) system is responsible for the readout and storage of the detector signals. It is composed of three main components: the Front-End Card (FEC), the Front-End Module (FEM), and the Data Acquisition Computer (DAQ PC).

The overall architecture follows the same detector-readout philosophy adopted for the IAXO pathfinder line at CAST, where the 240 Micromegas strips were read through four AGET chips connected to a Feminos back-end board, with the external muon-veto signal routed to an otherwise unused AGET channel so that veto and TPC information could be recorded together on an event-by-event basis [80]. In this sense, the pathfinder operation serves as a practical bridge between the late CAST Micromegas generation and the more scalable BabyIAXO-oriented readout concepts.

Figure 3.13 is intentionally placed before the detailed hardware subsections because it summarizes the logic that connects the detector electronics to the later data analysis. At acquisition level, the important point is not only that the Micromegas strips are digitized, but that their waveforms are recorded in a timing-aware event structure that can also accommodate veto information. This common event record is what later allows one to compare Micromegas pulse-shape observables, reconstructed X-ray candidates, and veto coincidences within the same analysis chain. In other words, the DAQ architecture already encodes part of the future discrimination strategy.

The commissioned IAXO-D0 chain uses four AGET front-end chips for the 240 Micromegas strips and a Feminos module for configuration, timing, readout control, and Ethernet transfer [75, 81]. Multiple boards can be synchronized through a common Trigger Clock Module, allowing the TPC and veto branches to be assembled into a timing-aware event record. The board architecture, register-level configuration, and UDP data path are documented in Appendix D.2. The feminos-daq refactor, ROOT output, compression, online monitoring, and event viewer are described in Section 4.7.2.

3.5.1 Run configuration and waveform observables

At the detector-operation level, the relevant point is how a run is configured and how the digitized waveform encodes the quantities used later in reconstruction and monitoring. A typical acquisition with the FEC–Feminos chain proceeds as follows:

An instance of the acquisition software is started on the DAQ PC. The software is configured with the IP addresses of the Feminos boards and the desired acquisition settings.

The start sequence is initiated by the operator. The software sends the configuration commands to the Feminos boards to set the AGET chips to the desired settings, including the power-up sequence of the AGET chips.

A pedestal run is performed to measure the mean \(m_i\) and standard deviation \(\sigma _i\) of the channels when they are not triggered. The pedestal values are stored internally in the Feminos boards and are subtracted from the signal values during data acquisition, so that all signals have the same base level. This base level, corresponding to zero signal, can be set in the configuration and is usually set to 250 ADC counts, as recommended by the Feminos authors. Figure 3.14 shows a sample event with all channels at the same base level due to the pedestal subtraction.

Each channel can serve as a trigger. The trigger level, the value above which a signal is considered a trigger, can be configured and is set to three times the standard deviation of the pedestal values. The acquisition can be configured to return all signals or only the triggered signals.

Figure 3.15 summarizes the morphology of a typical single-channel waveform after pedestal subtraction. The relevant information is the pulse height, the collected charge, the time at which the pulse develops, and the width and symmetry of the shaped response. These quantities are not only electronics diagnostics: they are the first experimental handles used to separate compact X-ray-like events from extended tracks, pile-up, or pathological waveforms.

The most important run settings are therefore those that modify this pulse morphology. The gain sets the overall amplitude scale, the shaping time determines the width and asymmetry of the pulse, the sampling period fixes the time granularity of the waveform, and the trigger delay determines how much pre-trigger baseline and post-trigger tail are recorded. The trigger threshold also matters because it decides which channels enter the event and can therefore affect both the reconstructed charge and the timing pattern. Although some settings can in principle be adjusted channel by channel, they are normally chosen coherently for the full readout so that the event can be interpreted with a single response model.

After digitization, the reconstruction combines the channel-level pulse information into a smaller set of event-level quantities. For calibration, these are mainly energy estimators, such as the pulse height, the integrated charge around the maximum, the charge above threshold, or the reconstructed readout energy. For event selection, they are complemented by timing and topology descriptors that measure whether the active strips are compact and mutually synchronous. This is the level at which the raw waveform description becomes part of the later signal analysis: X-ray-like events should produce narrow, well-aligned strip responses, whereas background-like or poorly reconstructed events tend to be broader, more asymmetric, or less synchronous.

3.6 Detector Calibration

The operation of a Micromegas detector involves a set of coupled parameters that must remain under control in order to guarantee stable gain, reproducible energy calibration, and a well-defined trigger threshold. In the gas system, the most relevant settings are the gas flow, chamber pressure, and gas mixture. In the detector itself, the drift and amplification voltages determine the transparency of the mesh and the gas gain. At the readout level, shaping time, trigger delay, sampling configuration, and threshold settings define how the pulse is digitized and which events are retained. In addition to these explicitly configured quantities, environmental variables such as temperature, as well as slow drifts in gas quality, can also modify the detector response. For that reason, the relevant detector and DAQ settings are stored together with the run metadata and are monitored through regular calibration runs.

From the point of view of data taking, the acquisition is organized in runs, each one corresponding to a period with fixed detector and DAQ settings. The run duration may range from a few minutes to several hours depending on the purpose of the measurement. In practice, the most important distinction is between calibration runs and background or tracking runs. The former provide a controlled X-ray-like reference with which the detector gain, energy scale, resolution, and threshold can be monitored. The latter provide the physics data used for background characterization and, when relevant, for axion-sensitive exposure. In the CAST pathfinder campaign, the daily operating sequence was explicitly structured around this logic, with regular \(\ce {^{55}Fe}\) calibrations used to track the detector response and to associate each background or tracking period with the most representative nearby calibration [80].

3.6.1 Standard X-ray calibration

The standard calibration procedure uses a source of soft X rays placed in front of the detector window, typically through a dedicated calibration port. The most common choice is \(\ce {^{55}Fe}\), whose dominant manganese K-shell line at \(5.9\,\mathrm {keV}\) lies inside the energy region most relevant for the axion search and generates compact, X-ray-like events in the gas. Additional sources such as \(\ce {^{109}Cd}\) may be used for complementary checks at higher energy, but \(\ce {^{55}Fe}\) remains the reference source for routine operation. Since photons in this energy range interact predominantly through the photoelectric effect, the resulting signal is a localized ionization cluster that closely resembles the topology of a low-energy X-ray conversion in the Micromegas gas.

In routine operation, the calibration data are first used for a fast data-quality check. A reconstructed hit map verifies that the source illuminates the expected region of the detector and that no large-scale asymmetry or dead area has appeared. The corresponding energy spectrum is then inspected to verify the position and width of the main photopeak, which provides an immediate monitor of gain stability, energy resolution, and effective threshold. This daily quick-look procedure was an important part of the CAST pathfinder operation and is especially relevant for surface-running detectors, where small changes in gas quality, voltage settings, or noise conditions can translate into visible shifts of the calibration peak from run to run [80]. Figure 3.16 compares a representative IAXO-D0 \(\ce {^{55}Fe}\) spectrum with a simulated spectrum after fitting their energy scales separately and broadening the reconstructed simulated energy to the measured main-peak width. The dominant structure is the manganese \(K_{\alpha }\) line at \(5.9\,\mathrm {keV}\), while the weaker \(K_{\beta }\) contribution appears at higher energy. The fit includes both manganese lines, and the quoted FWHM refers to the fitted \(K_{\alpha }\) component. The fixed \(K_{\beta }/K_{\alpha }\) intensity ratio is applied to the integrated Gaussian areas, with the widths scaled as the square root of energy.

The energy calibration itself is obtained from fits to the reconstructed calibration spectrum. For argon-based mixtures, the main \(5.9\,\mathrm {keV}\) photopeak and the argon escape structure around \(2.9\,\mathrm {keV}\) provide two anchors for calibrating ADC units to deposited energy [80]. For xenon-based operation, the \(5.9\,\mathrm {keV}\) line supplies only a one-point scale if a zero intercept is assumed; additional lines or calibrated charge injection are required to test linearity and determine an offset. Repeating the applicable procedure run by run makes it possible to quantify gain evolution and to propagate the calibration constants to associated physics runs and selection studies.

The reconstructed calibration energy can be estimated in several ways, each one emphasizing a different aspect of the waveform or of the reconstructed hit. Table 3.2 compares a representative set of these energy estimators using the same calibration run. Integrated charge-like quantities give comparable resolutions, while a single-channel maximum-amplitude estimator performs significantly worse because it is more sensitive to charge sharing and local fluctuations. The comparison uses measured data alone so that differences between estimators are not obscured by separately fitted simulation broadening.

The display broadening in Figure 3.16 is separate from the detector-hit smearing applied before reconstruction in the production response. Neither a fitted centroid nor a fitted scalar width establishes waveform-level closure or the energy dependence of the selection efficiency. Measured traces contain correlated residual structure that can alter threshold crossings and peak multiplicity. The data-driven raw-signal emulation developed to address this limitation, including its implementation and validation status, is presented as a computational contribution in Section 4.5.

3.6.2 UV-light calibration R&D

A complementary calibration concept was explored during a three-month internship at CEA Saclay. This work is not part of the baseline BabyIAXO calibration strategy, which remains based on X-ray source runs, but it is worth retaining as detector R&D because it addresses a closely related problem: how to generate controlled, localized, and time-stamped primary electrons in a Micromegas gas volume. The idea is inspired by Micromegas-based photocathode detectors such as PICOSEC [82], where ultraviolet photons release photoelectrons that are subsequently drifted and amplified.

In the CEA setup, a pulsed ultraviolet source illuminated an aluminized cathode through a UV-transparent window. The lamp trigger provided a timing reference, while the anode pulse arrival time was measured after electron drift and amplification. By repeating the measurement with spacers of different thicknesses, the drift distance was changed in a controlled way and the drift velocity could be estimated from the variation of pulse arrival time with distance. The presentation study used argon–isobutane mixtures, several quencher fractions, and comparisons with Garfield++/Magboltz drift-velocity calculations. The measured velocities had the expected order of magnitude and qualitative field dependence, although offsets with respect to the simulation remained and were attributed to possible gas-settling, field, photocathode, or space-charge effects.

For the present thesis, the importance of this work is methodological rather than as a mature calibration proposal. A pulsed UV system could, in principle, provide single-electron or few-electron calibration, localized topological checks, timing studies, and gas-transport measurements without relying only on radioactive X-ray sources. However, the tested gas-discharge lamp had limited pulse stability, and a quantitative implementation for BabyIAXO would require a better-controlled UV source, calibrated photocathode response, stable gas conditions, and a dedicated comparison with the final detector geometry and readout. Supplementary figures from this R&D study are collected in Appendix D.3.

Chapter 4
Computational Framework

4.1 Scope and software contributions of this thesis

The background and veto studies require a traceable calculation from an incident particle to a reconstructed detector event. This chapter describes the software developed or extended in this thesis to support that calculation: particle generation, radiation transport, detector response, readout mapping, reconstruction, and large-scale production. Auxiliary tools for visualization and data acquisition provide checks on the same event and geometry representations.

The distinction between pre-existing infrastructure and thesis-specific contributions is important for understanding the role of each component. REST-for-Physics [83], Geant4 [84–86], ROOT [87], CRY [88], and the Kotlin GDML domain-specific language were already available when this work began. The contributions of this thesis lie in integrating these tools into a reproducible end-to-end simulation and analysis workflow, adding new generators and analysis processes, developing auxiliary tools for validation and monitoring, and scaling the production to the throughput required for an IAXO background model. Tables 4.1 and 4.2 summarize the main software components and their role in the thesis.

4.2 The ROOT Data Analysis Framework and Python interoperability

ROOT [87] is the data analysis framework developed by CERN and the foundation on which REST-for-Physics is built. For this thesis, the most relevant features of ROOT are its file format (.root), its TTree columnar storage, its Python bindings (PyROOT), and the serialization dictionary system that REST-for-Physics relies on for metadata persistence and versioning.

The principal 2026 NAF production stack used ROOT v6.34.04. Earlier experimental processing and the compression benchmark described below used other versions; the relevant version therefore belongs to the individual production or analysis record. The ROOT file format remains the primary data container for both Monte Carlo and experimental data within the IAXO collaboration. Every restG4 simulation, every restManager processing step, and every DAQ acquisition file uses the same underlying storage format, which is essential for maintaining a single analysis language across the full chain.

While ROOT provides extensive built-in visualization and analysis tools, most of the figures in this thesis were produced with Python libraries such as Matplotlib and Plotly. This was possible thanks to two developments: ROOT’s own PyROOT interface, which exposes C++ objects to Python, and Uproot [90], a pure-Python library that reads and writes ROOT files without requiring a ROOT installation.

4.2.1 Uproot and fsspec integration

Uproot is widely used for reading ROOT files in Python and underpins many Python-based HEP analysis workflows. A three-month IRIS-HEP fellowship during this thesis provided the opportunity to contribute to Uproot directly. At the time, Uproot supported local files and a few remote protocols (HTTP, XRootD), each requiring a hand-written implementation inside the library. The fellowship work delegated all file-I/O operations in Uproot to fsspec, a Python library that provides a uniform interface across local and remote file systems. This change, released in Uproot v5.2.0, simplified the codebase and made every fsspec-compatible protocol (including SSH, cloud object stores, and WebDAV) available to Uproot without additional maintenance burden.

This integration was directly useful for the present thesis in two ways. First, it enabled the feminos-viewer application to open remote DAQ files over SSH while they are being written, using the same code path as local files. Second, it allowed the Python-based background-analysis scripts to read simulation outputs directly from the NAF-IAXO dCache storage without copying them locally. The experience also provided a thorough understanding of the ROOT file format, which was important for designing the DAQ ROOT output and for debugging file-structure issues during analysis.

4.3 REST-for-Physics as the common event-processing framework

REST-for-Physics [83] (Rare Event Searches Toolkit for Physics) is an open-source, collaborative C++/ROOT-based framework that provides a unified environment for data acquisition, Monte Carlo simulation, detector-response emulation, and physics analysis. It was originally developed for experiments searching for rare phenomena such as neutrino interactions, dark matter, and axion signals, where precise detector modeling and reproducible analysis chains are essential.

The same architecture was used for the IAXO pathfinder detector at CAST, as documented in the thesis of Cristina Margalejo Blasco [80]. This provides a relevant application of the transport, response, and reconstruction workflow to a low-background Micromegas detector.

REST-for-Physics is structured as a core Git repository with libraries and packages as Git submodules. It is strongly rooted in the ROOT ecosystem and follows ROOT conventions for class naming, I/O patterns, and dictionary-based serialization. The framework exposes three main executables: restG4, a user-configurable Geant4 application initialized via RML configuration files; restManager, which applies a sequence of processing stages to data; and restRoot, a ROOT interpreter wrapper that loads the REST-for-Physics environment for interactive data inspection.

4.3.1 Event-based processing and the EventTree/AnalysisTree model

REST-for-Physics follows an event-driven architecture. The abstract TRestEvent class is the central data container, with libraries defining their own derived event types (e.g. TRestGeant4Event, TRestRawSignalEvent, TRestTrackEvent). Each library also provides processes that transform one event type into another or compute scalar observables.

Data persistence is organized around two complementary TTree structures. The EventTree stores the event representation selected for output. An output containing reconstructed tracks does not necessarily retain the earlier transport hits or waveforms; those stages must be saved separately if later response reprocessing is required. The AnalysisTree, implemented as TRestAnalysisTree, stores scalar observables computed by the different processes and is used for cuts, control plots, efficiency studies, and background estimates. This separation is especially valuable in rare-event searches, where thresholds and selections are often scanned many times without regenerating the complete event representation.

For the IAXO Micromegas studies, a common analysis.rml chain transformed Geant4 truth information into Micromegas and veto observables that could be treated with the same logic used for measured data. In the TPC branch this meant deriving reconstructed hit and track observables for X-ray/background discrimination. In the veto branch it meant emulating waveforms and applying peak finding to obtain timing, amplitude, and multiplicity observables. This architecture permits selections on reconstructed quantities, with transport truth retained separately for mechanism studies. A common reconstruction algorithm does not itself establish agreement between simulated and measured detector response; that comparison is part of the validation in Chapters 5 and 6.

The AnalysisTree approach also provides a systematic way of turning reconstruction outputs into reusable analysis products. Observables filled by each process can be inspected interactively, processed through ROOT macros or Python scripts, or consumed by dedicated REST-for-Physics plotting utilities. In this thesis many final figures were produced with external tools, while their underlying observables were derived from the REST-for-Physics reconstruction chain. The analysis identifier specifies which branch definitions, calibration, and selections apply to each product.

4.3.2 Reproducibility and maintainability

REST-for-Physics stores the full analysis configuration as metadata objects inside the ROOT file, including framework version, dependency versions, and RML parameters. These objects support provenance inspection and reanalysis of the event representation actually retained in the file. Reconstruction cannot be replayed from an earlier stage whose hits or waveforms were discarded. The source code is version-controlled and openly available on GitHub; periodic releases specify recommended versions of ROOT, Geant4, and Garfield++ to simplify reproducibility. Container images with pre-built dependencies are provided for users who want a consistent environment, and a comprehensive test suite with Google Test runs in GitHub Actions CI for every pull request. The CI infrastructure was migrated from GitLab to GitHub Actions during this work. For production provenance, a nominal release or repository commit is insufficient when local patches, staged configurations, or gas tables differ from that revision. Table 4.3 lists the records needed to identify those inputs. The background-model chapter distinguishes recovered campaign records from historical products whose normalization or response cannot yet be reconstructed completely.

4.4 Detector readout metadata and channel mapping

An essential intermediate layer between transport simulation and physics analysis is the detector readout description encoded in the TRestDetectorReadout metadata classes. In plain terms, this layer translates electronics channel numbers into physical detector positions and types, making it possible to know whether a signal came from a Micromegas strip, a veto scintillator panel, or a specific region of the detector. Without it, a waveform would remain only a list of ADC samples attached to an integer channel number. With it, the same processing chain can move consistently from raw signals to detector signals, and from detector signals to reconstructed hits and tracks, while preserving the physical interpretation of each channel. The readout description is organized hierarchically. TRestDetectorReadout stores the full detector readout as a collection of TRestDetectorReadoutPlane objects. Each plane defines a position and orientation in world coordinates, the normal vector that identifies the drift side, the effective height of the active volume, and a semantic type such as tpc or veto. Each plane contains TRestDetectorReadoutModule objects, which define the local geometry of a readout module. Inside each module, TRestDetectorReadoutChannel stores the correspondence between the DAQ identifier and the physical channel identifier, while TRestDetectorReadoutPixel provides the elementary polygons representing the actual sensitive pattern. A physical channel may be composed of many pixels combined into a complex strip or pad geometry, which is important for the microbulk Micromegas pattern, where each strip is constructed from multiple pixels including the special edge pieces required by the real detector layout.

For the veto system, the effort was even more detector-specific. The scintillator panels do not form a single regular plane but a distributed system of individually oriented detector elements surrounding the shielding. Dedicated readout-generation code was developed to build one TRestDetectorReadoutPlane per veto panel, using the geometry information to determine the panel position, its outward normal, and the corresponding effective sensitive depth. Each panel was assigned a unique channel identifier and an alias matching the experimental naming convention. This mapping step was essential because the later analysis is formulated in terms of physical veto groups, layers, and aliases rather than arbitrary DAQ integers.

This metadata layer bridges the simulation-side and data-side representations of the detector response. On the simulation side, processes such as TRestDetectorHits ToSignalProcess use the readout geometry to decide which channels collect charge or light from a given interaction point. On the experimental side, TRestRawToDetector SignalProcess and TRestDetectorSignalToHitsProcess use the same readout definition to transform digitized waveforms back into detector signals and then into reconstructed spatial hits. The auxiliary TRestRawReadoutMetadataProcess serializes channel-level information so that later waveform-analysis stages can distinguish TPC channels from veto channels without relying on external spreadsheets.

This was one of the most consequential software contributions of this thesis because it gave the Micromegas and veto branches a common event-level representation. That capability becomes especially important in the signal-analysis chapters, where waveform observables, strip topology, and veto coincidences must be combined in a single event-level selection strategy.

4.5 Data-driven raw-signal emulation

Matching a reconstructed \(\ce {^{55}Fe}\) peak does not ensure that simulated and measured Micromegas waveforms present the same input to the reconstruction. Measured traces also contain baseline fluctuations, coherent low-frequency structure, channel correlations, and occasional excursions near the signal region. These features can change threshold crossings and peak multiplicity and therefore cannot be added after reconstruction.

An additive residual model was developed to reduce the discrepancy between simulated and measured calibration-waveform distributions: \begin{equation} S_{\mathrm {noisy}}(c,t) = S_{\mathrm {sim}}(c,t) + N_{\mathrm {GAN}}(c,t), \end{equation} where \(c\) is the TPC channel index and \(t\) is the digitizer sample. The residual term \(N_{\mathrm {GAN}}\) is produced by a convolutional generative adversarial network (GAN) trained on separate batches of simulated and measured calibration traces. There are no event-by-event paired residual targets. Penalties on pulse modification, channel correlations, and spectral structure constrain the generated correction, but do not uniquely identify it with electronics noise: it can also absorb discrepancies in gain, shaping, diffusion, or calibration. Residuals are generated over the full channel–time array, including the signal region, because measured structure can affect low-amplitude channels near threshold.

Figure 4.4 separates fixed run conditions, the limited spectral tuning needed to align the calibration peak, and the learned residual component. Gas composition, field, readout, shaping, and sampling follow the experimental configuration. Only the energy calibration and additional resolution term are tuned at spectrum level; the residual bank supplies an empirical correction at the waveform level.

The implementation reads event-wise residual waveforms, maps them to TPC channel identifiers, and adds them to the simulated TRestRawSignalEvent before baseline correction and peak finding. This ordering allows noise to modify the same reconstructed quantities as in data. The demonstrated result is a reconstruction-compatible response model with illustrative waveform comparisons. Predictive validation requires fitting on one calibration subset and testing different runs after complete reconstruction, including pulse energy, width, active channels, false peaks, and selection retention. A measured baseline bank and a simple parametric noise model provide useful reference alternatives. The learned correction receives no efficiency credit until these comparisons close; this limitation does not affect the separate veto peak-list overlay study.

4.6 Geant4 simulation infrastructure

4.6.1 restG4 and Geant4Lib: the interface to Geant4

Geant4 [84–86] is a Monte Carlo toolkit for simulating the passage of particles through matter, widely used in high-energy physics, nuclear physics, and medical applications. Geant4 is a toolkit rather than a complete simulation application: users provide a C++ program that instantiates a geometry, physics list, and primary generator, and its run-time commands may then be exposed through macros or an interactive command interface. These applications share a large amount of boilerplate code, and Geant4 offers no built-in solution for serializing event data.

REST-for-Physics addresses this through restG4 (the executable) and Geant4Lib (the library): a modular, user-configurable Geant4 application that is driven by RML configuration files rather than recompilation. Over the period covered by this thesis, the wider restG4 and Geant4Lib development histories grew by more than 600 and 370 commits, respectively; the contributions described below are the subset authored, integrated, or validated in this work. The most significant improvements are summarized below.

Geant4 event model and REST-for-Physics representation

In the Geant4 framework, a run is a collection of events sharing a fixed detector geometry and physics configuration. A run is initialized once (an expensive operation that loads geometry and cross sections) and then executes many events. At the beginning of each event, the primary generator creates one or more particles with specified energies, directions, and positions. Radiation transport follows these particles in discrete steps whose lengths are limited by geometry boundaries, discrete and continuous processes, multiple-scattering controls, and user limits. Interactions can produce secondary particles, which are themselves tracked. The full chain of secondaries must be considered when calculating the energy deposited in a given detector region.

The principal Geant4 data structures (run, event, track, and step) are represented in Geant4Lib. Geant4 steps are stored as REST-for-Physics hits, which contain the position, momentum, time, energy, interaction process, and target information at a single point. Geant4 also provides user-action hooks at various levels (event, tracking, stepping); a stacking-action hook was added during this work to tag new tracks before processing, enabling long-lived secondaries to be isolated into separate sub-events with distinct sub-event identifiers while remaining traceable to the same Geant4 event.

Multi-threading and track pruning

Radiation transport is naturally parallelizable at the event level, since events are independent. During this work, support for Geant4 multi-threading was added to restG4, requiring a thread-safe event container and synchronization primitives with minimal performance impact. Support for interrupt-signal handling was also added, allowing a simulation to be stopped cleanly while preserving all output produced up to that point.

Track pruning was implemented to reduce output size and analysis time. The user specifies which detector volumes are of interest (e.g. the gas volume and the scintillator panels). Tracks and hits not associated with these volumes are removed, while the full track leading to a hit in a volume of interest is preserved, including intermediate steps through passive material, so that the surviving interaction paths can be visualized. Validation runs demonstrated output-size reductions of a factor of 1–10 for the tested configurations and checked the corresponding stored veto and TPC observables. This result does not establish invariance for every later response algorithm. Nonlinear quenching, for example, may depend on true step length and recoil identity in addition to deposited energy; delayed-event analysis requires times and parent–subevent associations. Those quantities must be retained and compared between pruned and unpruned records before a new response can be replayed safely.

4.6.2 Geometry-generation infrastructure for IAXO simulations

The IAXO detector geometries used in this thesis—including the IAXO-D0 and IAXO-D1 prototypes, passive-shielding scans, and successive veto-layer designs—were defined through a dedicated geometry-generation workflow rather than hand-edited Geant4 C++ code. The Geometry Description Markup Language (GDML) [91] is an XML-based format for describing detector geometries, supported natively by both Geant4 and ROOT.

The complexity of the IAXO geometry (over 400 individual components in some veto iterations) made manually writing GDML impractical. A Kotlin-based domain-specific language (commonly referred to as gdml.kt) was developed within the collaboration to build GDML files from a higher-level, parameterized description. The author collaborated in its continued development, validation, and application to the IAXO Micromegas simulation campaigns. The thesis contribution is not the invention of the Kotlin DSL itself, but the integration of that geometry-generation approach into the full simulation, analysis, veto-mapping, and visualization workflow.

The generated geometries are tracked in a dedicated Git repository, so each simulation can be associated with the commit hash of the geometry used to produce it. A hierarchical geometry description allows groups of related volumes to be enabled, disabled, or highlighted in the event viewer, connecting gdml.kt directly to the visualization package.

A technical challenge arose from Geant4’s handling of GDML assemblies: physical-volume names were converted into hashed identifiers during parsing, which prevented restG4 from mapping simulation properties (step-size limits, production cuts) to volumes by name. Significant effort was devoted to resolving these hashed names back to human-readable representations and to implementing support for logical-volume-name references, enabling properties to be assigned consistently to all instances of a repeated component. These developments made the complex IAXO geometries usable for production simulations in which detector materials, sensitive regions, and veto-channel definitions must remain traceable across many geometry versions.

The same semantic geometry information was used to validate the veto readout mapping. When the browser event viewer highlights a panel that received an energy deposit, the displayed panel, the Geant4 sensitive volume, the readout channel, and the analysis observable must all refer to the same detector element. Several iterations of the veto geometry and readout description were checked in this way, and the visualization package closed the loop: the Kotlin DSL produced the GDML, restG4 transported particles through it, the detector-response chain reconstructed signals using the readout metadata, and the browser viewer made it possible to inspect whether all these representations agreed event by event.

4.6.3 Python interface to REST-for-Physics

REST-for-Physics inherits ROOT’s PyROOT interface, which automatically generates Python bindings from the C++ class dictionaries. This allows REST-for-Physics objects to be used from Python with nearly identical syntax to the C++ API, as illustrated in Figure 4.6.

The Python interface makes it possible to prototype analysis code quickly, integrate with the Python scientific ecosystem, and use Jupyter notebooks for interactive data exploration. The performance penalty of interpreted Python loops can be mitigated by using optimized array libraries such as Awkward Array [92] or by relying on compiled C++ backends. In the present thesis, the Python interface was used extensively for generating plots, scanning cut thresholds, and performing statistical analyses that would have been more cumbersome to develop in C++ alone.

4.6.4 Probability Distribution Projection cosmic-ray generator

The cosmic-ray background simulations required for this thesis launch primary particles from the atmosphere toward the detector. The conventional approach—generating particles uniformly over a large plane above the detector and discarding those that miss—is physically intuitive but highly inefficient for compact geometries like the IAXO-D0 detector surrounded by shielding.

To address this, a new cosmic-ray generator was developed and published during this work [89]. The Probability Distribution Projection (PDP) method samples directly from the subset of trajectories that intersect a sphere enclosing the geometry of interest. For a fixed zenith angle, the allowed starting points are restricted to the ellipse obtained by projecting the enclosing sphere onto a plane tangent to it. Here the original distribution \(f_{\mathrm {plane}}(\theta )\) describes crossings of a horizontal generation plane, per unit zenith angle. The corresponding distribution for trajectories intersecting the sphere is \begin{equation} f_{\mathrm {sphere}}(\theta ) \propto f_{\mathrm {plane}}(\theta )\sec \theta . \end{equation} The measure matters: the same factor must not be applied again to a distribution already defined for an area normal to the incident direction. For directional intensity \(I(E,\Omega )\), per unit energy, solid angle, time, and area normal to the ray, the rates through a horizontal area \(A\) and a sphere of radius \(R\) are \begin{align} \dot N_{\mathrm {plane}} &= A\int I(E,\Omega )\cos \theta \,\mathrm {d}E\,\mathrm {d}\Omega ,\\ \dot N_{\mathrm {sphere}} &= \pi R^2\int I(E,\Omega )\,\mathrm {d}E\,\mathrm {d}\Omega , \end{align}

over the specified incident hemisphere and energy range. Under azimuthal symmetry, \(\mathrm {d}\Omega =2\pi \sin \theta \,\mathrm {d}\theta \). An unfolded energy-only fluence spectrum therefore needs both an explicit angular model and an adapter consistent with that model’s integration measure.

The method was validated against the standard Monte Carlo approach using two complementary observables: the zenith-angle distribution of intersecting trajectories and the distance distribution between the intersection point and the detector axis, which probes the spatial phase-space sampled by the generator. The comparison showed that the PDP method reproduces both observables within statistical uncertainties once the conventional Monte Carlo is run in its converged regime.

For the IAXO-D0 geometry, the PDP method improved the computation yield by a factor of approximately three compared with the fastest (and least accurate) conventional configuration. When compared at equal physical accuracy against the large generation disks needed for the conventional method to converge, the advantage reached up to a factor of about 37. This optimization was particularly valuable for the large cosmic-ray production campaigns discussed in the shielding and veto system chapter and the background model chapter, where the cumulative cost of low-efficiency simulations would otherwise have been prohibitive.

4.6.5 Cosmic-ray source generators

The simulation of cosmic-ray backgrounds involves two conceptually distinct tasks: generating the atmospheric secondary flux (performed with packages such as CRY [88] or CORSIKA [93]) and efficiently injecting those secondaries into the detailed IAXO Geant4 geometry. The PDP method addresses the second task; it does not replace shower generators but provides a more efficient way of sampling the already-modeled flux around the detector.

A dedicated auxiliary program was developed to precompute the cosmic-ray secondary distributions used as input for the Geant4 simulations [94]. The program runs CRY for a chosen site configuration, including latitude, date, altitude, and lateral generation box, and records the secondary particles crossing the generation surface. For each relevant particle species, the output is reduced to two-dimensional histograms in kinetic energy and zenith angle, \(H_i(E,\theta )\), stored in ROOT files for muons, electrons, positrons, photons, protons, and neutrons. The histograms retain each species’ joint energy–zenith distribution, while the later restG4 generator samples its direction and entry point around the detector. They do not retain the relative positions, arrival times, or particle-species correlations within a CRY shower. The resulting transport describes independently sampled particles; a companion from the same atmospheric shower can provide an additional veto tag that this representation omits. Conditional veto efficiencies and random-coincidence estimates therefore require a separate correlated-shower check before this approximation can be assigned an absolute uncertainty.

This design deliberately decouples the atmospheric calculation from the detector transport. Instead of calling CRY inside every detector simulation, the atmospheric source term is computed once and reused across passive-shielding scans, veto-layer geometries, and production campaigns. It also makes the source term inspectable: the same ROOT histograms can be plotted, compared with EXPACS or HENSA measurements, or replaced by a different measured spectrum without changing the detector-response chain. For HENSA, the intended angular model is proportional to \(\sin \theta \cos ^2\theta \), while the measured input supplies the energy spectrum. The historical histogram reader additionally applies the plane-to-sphere cosine transformation. The actual generated distribution and energy acceptance must consequently be checked through that complete interface, as discussed in Section 6.6.1; a test of an isolated analytic angular generator does not validate the histogram adapter.

The production interface ultimately accepted several source implementations. The background studies use the analytic Guan distribution for muons, CRY for photons, protons, electrons, and positrons, and the measured HENSA spectrum for the nominal outdoor-neutron energy distribution. CRY remains a generator-level cross-check for muons and neutrons and was used to test the neutron angular prescription.

4.6.6 Radiation transport in gases: Garfield++

Garfield++ is a widely used software package for simulating the behavior of gaseous detectors. Within REST-for-Physics, it is an optional dependency used to precompute gas-transport parameters such as electron drift velocity, diffusion coefficients, and Townsend and attachment coefficients as a function of the applied electric field. These parameters, illustrated by the gas-transport comparison in Figure 3.5, are then used by REST-for-Physics to model the drift and diffusion of ionization electrons in the TPC gas volume without performing a full Garfield++ particle-by-particle transport, which would be computationally prohibitive.

A small companion tool, gas-cli, was developed to make this gas-table workflow reproducible and scalable [95]. The program provides a command-line interface for generating, reading, and merging Garfield++ gas files, including mixtures with several components, configurable pressure and temperature, and electric-field grids defined by explicit points or linear and logarithmic ranges. This was useful because gas-file generation with Garfield++/Magboltz is compute intensive. Once the calculation is expressed as a deterministic command or Docker invocation, large scans over gas mixtures and electric fields can be dispatched to high-throughput computing resources and later merged or queried in a uniform way. The same tool can extract gas properties such as drift velocity, longitudinal and transverse diffusion, Townsend coefficient, and attachment coefficient into JSON summaries, which makes it straightforward to compare physical properties across candidate mixtures while preserving the .gas files consumed by the detector-response chain.

The full Garfield++ microscopic transport was not integrated into the restG4 simulation chain; it was used only for generating the precomputed gas-parameter tables that the REST-for-Physics detector-response processes consume. Explicit integration of Garfield++ with Geant4, as described in [96], remains a potential future improvement, but was not required for the background-model studies presented in this thesis.

4.7 Visualization, online diagnostics, and detector operations

4.7.1 Browser-based Geant4 event viewer

REST-for-Physics provides a ROOT-based 3D event viewer using TEve, but this interface has significant limitations: CPU-based rendering is slow for complex geometries, the backend technology has not seen major updates in recent years, and the largest event–geometry combinations tested in this work were not displayed reliably.

During this thesis, a dedicated browser-based event viewer was developed for REST-for-PhysicsGeant4 output files. The package converts selected windows of REST-for-PhysicsROOT files into a compact JSON scene representation and renders the detector geometry and event history in a web browser using three.js. The central design choice was to keep the heavy ROOT/REST-for-Physics dependency on the server or conversion side, while keeping the browser client simple and portable.

The viewer was developed with three primary use cases in mind:

1. Geometry and readout validation. The viewer renders the detector with a role-aware material model: gas volume, copper vessel, shielding, scintillator panels, cadmium layers, light guides, photomultipliers, and auxiliary elements are assigned distinct colors, transparency values, and visibility controls. This allowed systematic checks that the Kotlin-generated GDML, the restG4 geometry import, the sensitive-volume definitions, the readout metadata, and the reconstructed veto observables were mutually consistent. If the viewer showed a veto panel highlighted by the analysis but no plausible track or capture near that panel, the problem could be traced to the mapping, timing, or reconstruction rather than to the transport simulation.
2. Veto and delayed-capture topology debugging. The event history is displayed as a time-dependent object: particle tracks are colored by particle type, and the user can play the event in time with a configurable hit lifetime. This was particularly useful for cosmic-neutron studies, where the relevant signature can involve a prompt cascade, a delayed neutron capture, and energy deposits in different veto layers separated by microseconds. Several projection modes were added because the IAXO geometry is elongated and surrounded by a layered veto system; the four-panel orthographic view with compact veto maps immediately shows whether an event activates opposite sides, adjacent layers, a local cluster, or a delayed capture-like pattern.
3. Shareable event inspection and figure generation. The deployed viewer supports browsing a curated set of ROOT files, converting only the requested event window, and caching the resulting scene. The cache makes it possible to share stable URLs pointing to a particular file, event entry, and view direction, which is useful when discussing a suspicious topology with collaborators or preparing a thesis figure. Publication-oriented export tools include a single-frame export with veto projections attached and a sequence export that samples the event timeline and writes a reproducible set of frames. The neutron event sequence shown in the background model chapter was produced with this workflow.

The development of this package was closely connected to the geometry and readout work described in Sections 4.4 and 4.6.2. In this sense, the visualization package was not only a presentation tool but also a development instrument used to find geometry mistakes, volume-orientation problems, wrong particle color mappings, missing process labels, and inconsistencies in veto-channel interpretation.

The Phoenix event display [97], an open-source project supported by the High Energy Software Foundation (HSF), provided a useful reference during development. The IAXO viewer was not developed as a fork of Phoenix, but the Phoenix architecture demonstrated how modern browser-based event displays can replace traditional desktop-only visualization tools in high-energy physics.

4.7.2 feminos-daq: acquisition software and online viewer

The Micromegas readout hardware described in Section 3.5 requires a software layer able to configure the Feminos boards, receive UDP data frames, decode the AGET waveforms, store run metadata, and expose enough online information to diagnose the detector during data taking. The original program supplied with the Feminos electronics, mclient, was written in C and stored the received frames in a dedicated binary format, conventionally using the .aqs extension. That approach was sufficient for CAST and for the first IAXO Micromegas tests, but it made online inspection, long-term format maintenance, and integration with the later ROOT/REST-for-Physics analysis chain unnecessarily cumbersome.

During this thesis, the DAQ program was refactored into the feminos-daq repository [98]. The low-level communication with the Feminos boards was preserved where appropriate, while the surrounding software was reorganized around a modern CMake build, C++17, a clearer command-line interface, and direct output to regular ROOT files. The legacy binary output mode remains available for compatibility, but the ROOT format became the preferred output because it can be read with standard ROOT tools or with Uproot [90] without loading experiment-specific dictionaries. This makes raw acquisition data immediately usable from both the detector-control environment and the offline analysis notebooks.

The refactor also added a Prometheus exporter [99], so that acquisition counters and health information can be scraped by the slow-control and monitoring infrastructure. This is important operationally because DAQ failure modes are often visible before they appear in an offline file: malformed frames, missing boards, increasing queue occupancy, or abnormal trigger rates can all indicate detector or network problems during a run. In this sense, feminos-daq is not only a file writer, but part of the experiment-control layer that connects electronics status, detector conditions, and acquired data.

Data storage and file structure

The acquisition process is naturally I/O bound: the program must receive UDP frames from one or more Feminos boards, decode them, optionally compute lightweight online quantities, and write the result to disk without blocking packet reception. To reduce the risk of data loss, feminos-daq separates data reception from event processing and file writing. Incoming frames are passed through an internal queue to a processing thread, which writes the decoded events into the output ROOT file while the receiving thread remains available for new network data. The queue absorbs short processing delays, but it also provides a useful diagnostic because sustained queue growth signals that the writer cannot keep up with the incoming rate.

The output file is flushed periodically, so that an unexpected stop of the DAQ process does not make the entire run unrecoverable. Each file contains a tree of raw events with the event-level metadata and the waveform samples associated with each active signal. Since the file avoids custom ROOT dictionaries, it can be inspected with a plain ROOT installation, processed directly with Uproot, or converted into the REST-for-Physics raw-event format used by the later reconstruction chain.

ROOT compression

DAQ data have different storage regimes depending on the run type. Calibration runs can produce incoming rates of several MB/s because many channels are read out for source-driven events, whereas background runs are usually much lighter. The output format therefore has to balance acquisition safety, write speed, read speed, and long-term disk usage. The feminos-daq implementation exposes compression choices, with high-compression LZMA used as the default and a faster mode available for high-rate calibration conditions.

Table 4.4 summarizes a benchmark performed with a calibration run of 52 194 events, each containing approximately 272 signals with 512 samples per signal. The study compared sample storage types and compression settings using ROOT v6.32.02. The default LZMA setting reduced the file size relative to the default ZLIB output, while the maximum-compression setting saved additional space at a write-time cost too high for routine acquisition. The tested tightly packed unsigned char representation did not provide a practical advantage over unsigned short: although the uncompressed payload would be smaller, the compressed file size remained similar and the extra packing and unpacking logic would complicate the writer.

Processing tests showed no measurable difference in the downstream conversion to REST-for-Physics for the compression settings considered here. The compression choice is therefore mainly an acquisition and storage decision: fast enough writing is required during calibration, while compact files are preferable for long background campaigns.

Online event viewer

REST-for-Physics provides a ROOT-based event viewer for visualizing events throughout the processing chain, from raw signals to processed events. However, it lacks the ability to visualize events in real time as they are being acquired by the data acquisition system. For this reason, feminos-daq includes a dedicated viewer for raw acquisition files.

A Python application, feminos-viewer, was developed to visualize raw data in real time as it is being acquired. It uses Uproot to read the ROOT file and Matplotlib to render waveforms. It can display events from closed files as well as from files that are still being written, either by opening a local or remote file or by attaching to the output of a running acquisition process. The viewer uses readout mappings to translate signal identifiers into physical detector coordinates and includes online observables such as channel activity and energy-like summaries.

feminos-viewer is complementary to the browser-based Geant4 event viewer: the former is an acquisition and waveform-quality monitoring tool, while the latter is a simulation and event-history tool. Both share the broader goal of making detector information inspectable without writing ad hoc analysis code for every diagnostic question. During data taking, feminos-viewer was used to identify detector and acquisition issues quickly, including malformed events, inactive or noisy channels, and inconsistencies between waveform activity and detector-coordinate mapping.

4.7.3 High-voltage control library: hvps

Stable Micromegas operation depends on the high-voltage system as much as on the gas and readout chains. The drift field, amplification field, current limits, ramping behavior, and trip-recovery policy must remain accessible during long background runs, and the relevant quantities should be readable by the same slow-control environment that supervises pressure, flow, temperature, and acquisition status. In practice, however, high-voltage power supplies expose device-specific serial protocols, with different command names, channel conventions, response formats, and status registers. This makes direct integration into detector-control software fragile if every dashboard or script sends raw vendor commands.

To address this problem, a dedicated high-voltage power-supply library, hvps, was developed during this thesis [100]. The package provides a common Python interface for serially controlled high-voltage supplies and currently supports CAEN and iseg devices. Its design follows the physical hierarchy of the instrument: an HVPS object manages the serial connection, a Module object represents the crate or board, and a Channel object exposes the monitor and control quantities associated with one output. Typical channel-level operations include reading the set and monitored voltages, reading the monitored current, switching a channel on or off, configuring ramp parameters, checking status words, and handling trip or interlock-related states. The purpose of the abstraction is not to hide the safety behavior of each device, but to make routine control actions explicit and reusable.

The library was also packaged as an operations tool rather than only as an importable module. A command-line interface allows operators and scripts to query or set high-voltage parameters from the terminal, while keeping the same validation and response-parsing layer used by the Python API. Bindings for Node.js and a Node-RED node were added so that the same backend could be used from web-based slow-control dashboards. This choice is directly connected to the IAXO detector-control model described in the Micromegas chapter: the high-voltage backend can be called from automation flows without duplicating low-level serial-command logic in the graphical interface. The repository also includes a graphical prototype for CAEN N1471H supplies, with real-time voltage and current monitoring, channel switching, alarm indicators, interlock information, and queued command execution to avoid simultaneous serial transactions.

From a software-engineering point of view, hvps occupies a different layer from feminos-daq. feminos-daq is responsible for event acquisition and online waveform inspection, whereas hvps belongs to detector operation and slow control. Both were developed with the same practical objective: reducing the number of ad hoc scripts needed to run and diagnose the detector, and replacing them with tested, version-controlled tools that can be reused in IAXO-D0, IAXO-D1, and future BabyIAXO-oriented setups. The package was released through PyPI, with corresponding Node.js/Node-RED packages distributed through npm, and includes tests for command construction, response parsing, and device-interface behavior. For the purposes of this thesis, its relevance is therefore not only that it can set a voltage, but that it makes high-voltage operation a reproducible software component of the detector system.

4.8 Monte Carlo production at scale

The background-model studies required large-scale Monte Carlo campaigns spanning multiple particle species, shielding configurations, and veto designs. This section describes the production infrastructure that made these campaigns feasible.

4.8.1 End-to-end simulation and analysis chain

Production simulations use the following sequence, with source-specific configurations and separately recorded normalization:

1. Source generation. Source terms are frozen independently of detector transport: the current studies use the Guan parameterization for muons, the HENSA-derived reference neutron spectrum with a separately specified angular model, and CRY for photons, electrons/positrons, protons, and generator cross-checks.
2. restG4 transport. The source histograms are sampled by the primary generator inside restG4, and particles are transported through the IAXO detector geometry using Geant4. The output is a TRestGeant4Event stored in the EventTree.
3. Detector response. Geant4 energy deposits are converted into TRestDetectorHitsEvent and TRestDetectorSignalEvent representations, where quenching, light attenuation, diffusion, and smearing are applied.
4. Raw-signal emulation. Signals are converted to TRestRawSignalEvent through waveform shaping, sampling, trigger positioning, and dynamic-range effects.
5. Reconstruction. Waveforms are reconstructed back into detector hits and tracks, yielding event representations directly comparable to experimental data.
6. AnalysisTree observables. Each processing stage appends scalar observables (hit multiplicities, energies, positions, veto peak times and amplitudes) to the AnalysisTree.
7. Cuts and background-rate extraction. The observables are used to apply fiducial, topological, and energy cuts; surviving events are converted to background levels when the generated-primary denominator, source rate, and geometry have been validated.

This chain is configured through two RML files stored in the collaboration repository iaxo-simulations [101]: a source-specific simulation.rml and a common analysis.rml. This separation made it possible to treat source generation, transport, response emulation, and final selection as distinct but reproducible stages.

4.8.2 Production workflow with HTCondor

Simulations were orchestrated using HTCondor, a workload management system designed for High-Throughput Computing (HTC) [102]. Unlike traditional HPC environments that optimize for instantaneous floating-point performance, HTCondor maximizes total computational work over long periods through dynamic matchmaking between job requirements and available resources.

A dedicated Python script, restG4ToCondor.py, was developed to facilitate the submission of restG4 jobs to the HTCondor system. The script automates the creation of job description files and manages output data including log files, error reports, and the resulting ROOT files. Its command-line interface extends the restG4 interface, making it easy for users familiar with restG4 to adapt to batch submission.

Table 4.5 summarizes the typical workflow steps for a large Monte Carlo production campaign, from job splitting to the final extraction of analysis observables.

The multi-job productions used in this thesis were run on the National Analysis Facility (NAF) at DESY, referred to here as NAF-IAXO, which provides a centralized computing environment with dCache storage [103] and a HTCondor batch system. The initial validation campaign used approximately 600 jobs and produced about 40 000 saved cosmic-neutron and cosmic-muon events. The infrastructure was subsequently used for the substantially larger, source-specific campaigns whose generated-primary counts, equivalent exposures, and accepted files are recorded in Chapter 6 and its appendices.

4.8.3 Immutable analysis products and grouped evaluation

Large transport campaigns remain useful only if their physical and computational provenance can be recovered after the reconstruction or event selection changes. The final workflow developed in this thesis therefore treats the transport ROOT files, processed ROOT files, flat feature exports, and rate tables as different products rather than as interchangeable outputs. A complete campaign record stores the source RML, geometry, analysis configuration, relevant environment variables, software revision and local patches, random seed or job group, and input/output hashes. Preserved transport output can be reprocessed without repeating Geant4 only when it retains the physical information required by the revised response. Processed tracks alone cannot regenerate omitted waveforms or recoil steps. The processed response is therefore associated with the analysis identifier whose branches and cuts it actually implements.

This principle also applies to machine learning. Production file and campaign identifiers are preserved as grouping variables, so an event used in a reported rate can be scored by a fold model that did not train on that event or its production group. All delayed subevents and repeated response realizations from one parent history must remain in the same group; their reuse does not create independent transport trials. Threshold-calibration samples, untouched tests, and deployment artifacts are recorded separately. In the background-model application, the background-analysis-v1 artifacts preserve the topology-selector audit, while the machine-readable background-analysis-v2-conservative-reference contract and source-component registry govern physical normalization and final inclusion. The contract separates response compatibility from absolute normalization and from agreement with detector data. In particular, omitting the unvalidated learned topology selector does not remove the response dependence of the reconstructed energy, one-track requirement, or fiducial position. The source registry records these distinct requirements rather than treating a shared file format or selector name as evidence that all have been met.

4.9 geant4-python-application: Python prototyping with Geant4

geant4-python-application is a project developed during this thesis to make small Geant4 studies accessible from Python notebooks and scripts. It is a teaching and prototyping tool, not a replacement for the restG4 production pipeline.

The standard Geant4 workflow is based on user-written C++ applications. Although Python bindings and third-party Python interfaces exist, they do not provide the specific restG4-like, pip-installable, process-isolated application wrapper targeted here for notebooks, teaching, and rapid prototyping. The project wraps a generic user-configurable Geant4 application using Pybind11 to generate Python bindings. Repeated initialization was not reliable in the selected notebook-oriented wrapper, so process isolation was implemented with Python’s multiprocessing module. Each worker therefore runs an independent Geant4 instance without imposing a general limitation on the toolkit itself.

The following concrete outputs were demonstrated with this tool:

• A Jupyter notebook computing the transmission of 477.6 keV photons through lead in adaptive batches and analyzing the returned events with Awkward Array [92] (Figure 4.14).
• Parallel execution through Python’s concurrent.futures interface, with each task launching an isolated Geant4 worker process rather than attempting to reinitialize Geant4 inside a single process.
• Distribution as a pip-installable package on PyPI (Python Package Index), with pre-compiled binary wheels for Linux, Windows, and macOS across multiple Python versions, built via a GitHub Actions CI pipeline.

For a fixed number \(N\) of independent incident photons, the transmitted count is binomial. The usual standard-error estimate is \(\sqrt {\hat p(1-\hat p)/N}\), and the exact zero-transmission one-sided 68% bound is \(1-0.32^{1/N}\). The notebook’s Poisson expressions are rare-transmission approximations; repeated inspection and count-dependent stopping need a corresponding sequential procedure if confidence coverage is claimed [52]. The example was not used to normalize a production background result.

4.10 Summary and role in the thesis

The software contributions connect particle transport, readout geometry, reconstructed events, and physical source normalization within a common analysis workflow. Extensions to restG4 and Geant4Lib supplied multithreading, configurable track pruning, delayed-subevent handling, and geometry-name resolution. The published PDP method improved the efficiency of cosmic-particle injection, while the HTCondor tools made independently seeded campaigns and their output provenance manageable at the required scale.

Readout metadata and the browser event viewer provided complementary checks of the correspondence between sensitive volumes, electronic channels, and reconstructed signals. The DAQ, waveform viewer, and high-voltage tools supported detector operation, while the Uproot/fsspec contribution and Python interfaces made the same data accessible to interactive analysis and prototyping.

These tools provide the means to reproduce a calculation; the physical validity of a result still depends on its source definition, retained event information, detector response, and statistical denominator. Chapter 6 applies those requirements to the source inventory, and Chapter 5 tests the shielding and veto observables against simulation and prototype data.

Chapter 5
Shielding and Veto System

Introduction

The current BabyIAXO working baseline assumes an on-surface installation at DESY, where passive shielding must suppress environmental photons without the benefit of underground overburden. The same lead that provides this attenuation does not efficiently moderate fast neutrons and can convert them into secondary neutrons, photons, and charged fragments. The active shield must therefore perform two functions: reject through-going cosmic muons and tag the distributed prompt and post-trigger activity associated with neutron-induced showers.

This chapter presents the physical argument and experimental evidence that led to a three-stage scintillator–cadmium veto surrounding the lead shield. The narrative is organized around the design decisions: why passive shielding is insufficient, how the active stages sample the neutron-induced shower, why three layers were selected, how the waveform information is reduced to veto observables, and what the commissioned IAXO-D0 prototype demonstrates in data. Detailed nuclear-data benchmarks, campaign metadata, full diagnostic scans, and the technical construction of the late-window control analysis are retained in the Appendix.

The division of scope with Chapter 6 is explicit. This chapter addresses veto physics, conditional rejection, calibration-like control acceptance, and prototype validation, including the published IAXO-D0 data cut flow. Chapter 6 provides the source normalization, confidence intervals on source-normalized simulation levels, and prompt/delayed accounting used in the conservative partial source-response model. The common REST-for-Physics/restG4 implementation is described in the software chapter [83–86].

5.1 Design boundary and source inputs

5.1.1 Detector configurations and requirements

Three related detector configurations appear in this chapter and should not be conflated. The optimization simulations use the 59-panel veto geometry developed for the detector line. The experimental validation uses the commissioned 57-panel IAXO-D0 surface prototype. A detector-and-site prediction for BabyIAXO at DESY can be made only after the corresponding contracts are frozen; it is not inferred by rescaling the Zaragoza prototype result.

The design must preserve X-ray-like Micromegas events in the keV region while rejecting surface backgrounds. It must remain compatible with the X-ray beam path, services, mechanical clearances, available scintillator modules, and the synchronized AGET-based readout. The beam pipe prevents perfectly hermetic passive shielding, whereas the neutron-capture timescale requires a readout window long enough to retain post-trigger activity without accepting an excessive number of random coincidences. These constraints make geometry, timing, and analysis inseparable parts of the veto design.

5.1.2 Surface source inputs

The selected design studies use source-specific inputs rather than one generic “cosmic” sample. Production muons use the correlated sea-level parameterization of Guan et al. implemented by the CosmicMuons generator [104]. The neutron layer scans use the outdoor HENSA spectrum in the \(1\,\mathrm{MeV}\)–\(10\,\mathrm{GeV}\) interval [105, 106]. Their nominal input histogram is proportional to \(\sin \theta \cos ^2\theta \), but the inspected projected-source reader applies an additional \(1/\cos \theta \) factor, producing a sampled density proportional to \(\sin \theta \cos \theta \). The input histogram and sampled angular law must therefore be distinguished when interpreting the layer and inclination scans. The campaign normalization and angular-measure audit are documented in Chapter 6; the geometry comparisons here retain their common historical source setting. Historical passive-shield scans and cross-checks use CRY, while EXPACS provides an independent spectral comparison [88, 107, 108].

The HENSA outdoor field includes atmospheric and environment-modified neutrons measured at the surface. It is therefore described below as the HENSA outdoor neutron field, not as a pure cosmic component. It must not be added to the HENSA-minus-CRY environmental residual as if the two were independent source terms. The generator implementation is documented in Section 4.6.5; the source normalization and non-additivity convention are defined in Section 6.5.1.0.

5.2 Limits of passive shielding

5.2.1 Material roles

Lead remains essential because it strongly attenuates environmental photons. Its role for fast neutrons is different. In an elastic collision with a nucleus of mass number \(A\), the maximum transferable fraction of neutron kinetic energy is \(4A/(1+A)^2\), which is unity for hydrogen but only about \(0.019\) for lead. Consequently, lead is a poor moderator, while inelastic and neutron-emission channels produce a secondary shower once the incident energy reaches the MeV range.

Hydrogen-rich plastic scintillator complements the lead by slowing secondary neutrons and converting recoil-proton and charged-particle energy into light. Cadmium is placed only after this moderation step: its large thermal-neutron capture probability converts the slowed component into a gamma cascade near an active panel. The nuclear de-excitation is prompt relative to the capture, but moderation can place the capture and its scintillator response well after the Micromegas trigger. The signal medium itself remains sensitive to compact secondary photons and electrons as well as to nuclear recoils, so the veto must tag the surrounding history rather than identify the primary particle from the Micromegas deposit alone.

The transport-model checks that support this mechanism are summarized in Section 5.3.3 and documented in Appendix A.2.

5.2.2 Lead thickness and penetrations

A parameterized lead-shield scan was performed with idealized \(4\pi \) coverage and with the X-ray beam-pipe opening. The historical CRY samples are used here only to compare geometries under a common source definition; they do not define the final absolute background level. The full per-particle results are retained in Appendix A.11.

The photon response improves by more than four orders of magnitude over the idealized scan and by roughly a factor \(3\times 10^2\) when the pipe opening is included. The neutron response remains within the same order of magnitude and exhibits a broad intermediate-thickness enhancement. The design consequence is robust: thick lead is retained for photon suppression, but increasing its thickness does not replace an active neutron-sensitive system.

5.2.3 Passive neutron moderation

Borated high-density polyethylene (HDPE) was tested as a moderator and absorber while retaining the \(20~\mathrm {cm}\) total lead thickness required for photon attenuation [105]. The scan varied both the HDPE thickness and its position within a Pb/HDPE/Pb stack. Hydrogen slows the neutron population, and the dominant excited-state branch of \(\ce {^{10}B(n,\alpha )^{7}Li}\) releases a \(477.6~\mathrm {keV}\) gamma after capture. The usefulness of this mechanism depends on where moderation and capture occur relative to the lead and the detector.

The most favorable configurations reduce the neutron response by only \(30\)–\(40\%\), corresponding to a suppression factor of order \(1.6\). Practical moderator thicknesses do not thermalize the full MeV–GeV component before secondary production has occurred in the lead and surrounding structures. This result defines the active-veto boundary condition: the lead remains in place, and the active panels are arranged to sample the shower that it produces.

5.3 Neutron-sensitive active veto concept

5.3.1 From surface primaries to taggable secondaries

The integral surface-neutron field is not, by itself, the population that controls the detector response. Low-energy neutrons are abundant in the outdoor spectrum, but the primaries that produce Micromegas-sensitive activity after traversing the shielding are much harder. In the HENSA three-layer diagnostic, 59.68% of the detector-reaching population lies between \(100~\mathrm {MeV}\) and \(1~\mathrm {GeV}\), and a further 31.78% lies between \(1\) and \(10~\mathrm {GeV}\). The historical CRY cross-check exhibits the same qualitative hardening. The comparison in Fig. 5.3 is normalized within each source and detector-reaching sample; it establishes the relevant energy range but is not an absolute source comparison.

Once these fast primaries interact, the lead converts them into a much softer and more numerous secondary population. In the studied 1745 detector-reaching HENSA events, approximately \(9.19\times 10^{4}\) neutrons are produced in lead, \(6.58\times 10^{4}\) leave the lead volume, and \(1.83\times 10^{4}\) leave with momentum directed toward the TPC. Their energy distribution peaks around the MeV scale, where moderation in hydrogen-rich scintillator and subsequent capture become effective. The directionality also shows that the shower is distributed throughout the shield rather than confined to the detector-facing surface.

5.3.2 Tagging the secondary shower

The central design principle is to tag the neutron-induced cascade rather than the incoming neutron. Fast primaries interact in the lead and copper, producing softer neutrons, photons, recoil nuclei, and charged fragments. Plastic scintillator samples the prompt charged component and moderates part of the neutron population. Cadmium sheets between active stages then capture a fraction of the thermalized component and emit gamma cascades close to a neighboring scintillator.

The need to tag this surrounding history is visible directly in the saved-event truth record. In a sample of 879 neutron-induced events with a TPC energy deposit, electromagnetic descendants account for 552 events (62.8%), gas recoils or nuclear fragments for 242 (27.5%), charged-meson descendants for 41 (4.7%), and direct neutron interactions in the gas for only 44 (5.0%). Thus, in almost two thirds of this sample the low-energy TPC activity is produced through the electromagnetic branch of a wider neutron-induced cascade. The classification is used only to establish the mechanism; it is neither an experimental particle label nor a source-normalization factor.

Simplified sandwich scans were used to establish where the active material should sit relative to the lead. The response was evaluated after Birks quenching in the scintillator, so the threshold represents an electron-equivalent visible-energy proxy rather than unquenched deposited energy [109, 110]. The full material-ordering and quenching diagnostics are preserved in Appendix A.7.

The bare scintillator responds most readily to neutrons that can interact directly in the active material. For the harder primaries that dominate Micromegas-triggering events, lead-coupled arrangements retain the useful response because they sample the secondary cascade. This is why the veto surrounds the passive shield instead of replacing it.

5.3.3 Transport-validation envelope

The two transport steps most directly connected to the design conclusion were checked independently. First, a thin-target benchmark of outgoing neutrons from natural lead at \(14.1~\mathrm {MeV}\) was compared with EXFOR data in the measured energy and angular acceptance. The four tested high-precision Geant4 reference lists lie \(8\)–\(9\%\) below the experimental integral and differ from one another by less than 1% in this low-energy benchmark. This agreement supports the secondary-shower interpretation, although it does not by itself validate the full GeV-scale HENSA response.

Second, alternative cadmium de-excitation treatments were replayed through the same detector-response and peak-finding chain. The probability of reconstructing any veto peak remains between 0.719 and 0.742, whereas the conditional fraction above the \(10~\mathrm {MeV}\)-equivalent operating point changes from 0.314 to 0.383. The existence of a neutron-sensitive signature is therefore more stable than its efficiency at a fixed reconstructed-energy threshold. The full cross-section comparisons, outgoing-neutron spectra, cadmium line yields, and response tables are retained in Appendix A.2; the threshold dependence enters the systematic envelope rather than being tuned to data.

5.3.4 Prompt and post-trigger signatures

Here, prompt and post-trigger refer to time relative to the Micromegas trigger, not to the duration of the nuclear de-excitation. Figure 5.8 connects the simulated capture history to reconstructed veto activity.

In the processed three-layer HENSA sample, 98.3% of analysis entries contain a cadmium-sheet capture and 78.9% of all explicit captures occur in cadmium. At event level, however, 23.8% contain a cadmium capture but no reconstructed veto peak. Approximately one quarter contain only prompt or near-trigger activity, while 49.9% contain a late reconstructed peak. Finite light collection, thresholds, timing, and reconstruction therefore prevent a one-to-one mapping between capture and observed veto signature.

The cadmium capture history in the HENSA three-layer simulation provides the characteristic post-trigger timescale relative to the first simulated gas deposit, which is used as a trigger proxy and is distinct from both the physical capture time and the reconstructed veto-peak time. A truncated-exponential fit to the selected post-trigger physical-capture tail gives \(\tau =46.9~\mu \mathrm {s}\). This is a simulation-derived capture-retention study, not a complete acquisition-window optimization: reconstructed thresholds, accidental activity, and dead time are not included in the fitted curve.

Late-window activity alone is not neutron-specific because calibration data contain electronic noise and unrelated environmental coincidences throughout the waveform. The useful observable combines prompt or near-trigger activity with post-trigger energy, peak multiplicity, signal quality, and segmentation. An event-mixing study quantifies the timing information: a late peak alone accepts approximately 52% of the neutron sample and 56% of a neutron-derived time-scrambled control, whereas requiring both prompt and late activity accepts approximately 46% and 14%, respectively. The scrambled control preserves neutron-like peak multiplicity and amplitude while removing alignment to the trigger; it does not measure the apparatus’s accidental-coincidence rate. The improvement comes from the timing context rather than from late activity by itself; the capture-denominator bookkeeping, full trade-off plot, and selection definitions are documented in Appendix A.4. In this chapter, post-trigger or late-window activity always refers to peaks inside the recorded waveform. The term delayed activation is reserved for radioactive-decay descendants occurring beyond the coincidence window, as defined in Section 6.7. No standalone \(m\geq 3\) peak-multiplicity requirement is adopted as an operating point in this thesis. Multiplicity enters the structured and multivariate selectors together with energy, timing, channel occupancy, and signal quality; the final threshold is fixed by calibration-like control acceptance.

5.4 Multilayer optimization

The design scan compares one-, two-, three-, and four-layer cadmium configurations, together with three-layer gadolinium and stainless-steel variants. The HENSA outdoor neutron field is propagated through the full detector-response chain, including quenching, light attenuation, waveform formation, and veto-peak reconstruction. The scan exporter retains every entry in each processed AnalysisTree; it applies no additional one-track, \(2\)–\(7~\mathrm {keV}\), fiducial, or X-ray-topology selection. The denominator is therefore a response-level analysis-entry population, not the conservative reference selection of Chapter 6. All efficiencies in this section are conditional on that exported population.

The distinction between performance quantities is essential. The probability of any reconstructed veto tag tests whether the geometry produces an observable response. Threshold rejection tests a particular visible-energy operating point. The aggregate classifier adds multiplicity and signal-quality information at a fixed calibration acceptance. None of these conditional quantities is an absolute neutron background level.

The any-tag fraction increases from \(0.465\) for one layer to \(0.675\), \(0.741\), and \(0.771\) for two, three, and four cadmium layers, respectively. At a \(10~\mathrm {MeV}\)-equivalent threshold, the corresponding conditional rejections are \(0.150\), \(0.292\), \(0.376\), and \(0.425\). Thus the third layer provides a substantial improvement, whereas the fourth adds \(0.030\) in any-tag probability and \(0.049\) in threshold rejection while increasing the channel count from 59 to 79. The gadolinium variant is similar to cadmium for these aggregate observables, whereas stainless steel provides substantially weaker tagging.

Generated-primary normalization gives a processed-analysis-entry probability of approximately \(2.2\times 10^{-5}\) for each of the one- through four-layer cadmium samples. The active layers improve the conditional tagging response; within the statistical precision of this diagnostic, they do not reduce the population reaching the response-level analysis denominator. The exposure audit and full diagnostic projections are given in Appendix A.8.

Each additional layer also adds channels that can contribute accidental activity. An illustrative overlay model samples the measured calibration-triggered veto activity and scales the number of independent accidental opportunities with the active layer count. It is used to expose the trade-off, not as a final dead-time measurement.

The accidental-overlay model does not, by itself, favor three layers: over the scanned noise range, the four-layer configuration retains the largest simple sensitivity proxy. At the nominal scale, that proxy is \(1.274\) for four layers and \(1.232\) for three layers, while the corresponding calibration-like control acceptances are \(0.860\) and \(0.897\). Three layers are therefore an engineering and channel-count compromise made after most of the conditional tagging gain has been obtained, not a statistical optimum of this simplified model. The small separation between the three- and four-layer sensitivity proxies should be compared with the response and cascade-model variations before assigning a preferred physics operating point. For an expected background of only a few counts, an expected Poisson-likelihood limit with signal and live-time losses is more appropriate than \(S/\sqrt {B}\).

5.5 Prototype geometry and synchronized readout

5.5.1 Geometry and prototype construction

The 59-panel simulated design is organized into Top, Bottom, Left, Right, Front, and Back groups, with three active stages per group. The nominal symmetric arrangement would contain 60 panels, but one short inner-top panel is absent to accommodate mechanical and service constraints. Thin cadmium sheets are placed between neighboring active stages so that moderated neutrons can capture near a scintillator.

The prototype reused NE-110 plastic scintillator bars from a former time-of-flight spectrometer [111]. The bars were cut to \(150~\mathrm {cm}\) and \(65~\mathrm {cm}\), with a \(20\times 5~\mathrm {cm}^2\) cross-section, and coupled to photomultiplier tubes through light guides. The physical prototype used \(1~\mathrm {mm}\) cadmium sheets between neighboring panels and layers, realizing the same capture-stage concept as the simulation [17]. Atmospheric muons provided the gain-equalization reference. For a flat \(5~\mathrm {cm}\) plastic panel, the most probable through-going-muon signal corresponds to approximately \(10~\mathrm {MeV}\) of visible energy; this anchors the \(10\)–\(15~\mathrm {MeV}\)-equivalent region used in the threshold studies [17]. Measurements on the long bars showed that the collected light at the far end can be reduced by approximately a factor of two, so the reconstructed energy is an attenuation- and calibration-dependent proxy rather than a local calorimetric measurement [17].

5.5.2 Electronics and timing

The Micromegas and veto branches each use four AGET application-specific integrated circuits and are synchronized by a common trigger and clock [17, 81]. The circular buffer contains 512 samples, allowing the trigger position and window length to differ between detector branches. For the prototype-like veto configuration, the total acquisition is \(100~\mu \mathrm {s}\) with the Micromegas trigger \(30~\mu \mathrm {s}\) after the start. The trigger-centered convention used below is therefore approximately \([-30,+70]~\mu \mathrm {s}\): near-zero activity provides the prompt tag, while capture-related peaks at positive times contribute to the post-trigger tag only if they occur before the \(+70~\mu \mathrm {s}\) waveform boundary.

The long veto window is a deliberate part of the neutron-sensitive design. It retains prompt muon and shower activity as well as a substantial fraction of the cadmium-capture tail. The window cannot be widened on capture retention alone, because every additional interval also increases random-coincidence and live-time costs.

5.6 Waveform observables and conditional performance

5.6.1 Detector response and reconstructed observables

The simulation is propagated beyond deposited energy to the quantities used in data. Energy deposits are quenched, attenuated according to their propagation distance, converted into channel signals, shaped, digitized, and processed by the REST peak finder. This common representation permits the same peak time, amplitude, multiplicity, and channel-quality definitions to be used for simulated and experimental events. The common reconstruction-process inventory is given in Table C.1, while veto-specific campaign and response settings are documented in Appendix A.6.

Muon-induced events are predominantly prompt, high-amplitude, and track-like across several panels. HENSA neutron-induced events are more heterogeneous: they contain softer prompt activity, a broader post-trigger tail, and less regular channel correlations. These differences motivate aggregate observables rather than a single opposite-panel coincidence.

5.6.2 Calibration-controlled classifier hierarchy

An initial design-facing classifier combined five aggregate reconstructed quantities and established that waveform multiplicity and signal-quality information outperform a single visible-energy threshold. That event-random study is retained in Appendix A.4 as a historical benchmark. The run-disjoint study uses the higher-statistics aligned sample of 20,274 HENSA neutron events and 139,454 experimental calibration events. One independently sampled calibration peak train is concatenated with each simulated neutron peak train. This preserves correlations within the measured activity but does not reproduce peak merging, saturation or baseline shifts that can occur when waveforms overlap before peak finding. The control class is the calibration-triggered activity itself, and every score is treated as an ordering variable rather than an event-by-event neutron probability.

The analysis is organized into three implemented levels of increasing opacity. The level-1 boosted decision tree uses six directly interpretable aggregate observables: total reconstructed veto-energy proxy, peak count, unique panel count, active face count, active layer count, and maximum peak amplitude. The level-2 model adds disjoint waveform-window summaries, face and layer occupancies, amplitude fractions and entropies, opposite-face activity, and face–time and layer–time interactions. The level-3 model replaces these engineered spatiotemporal quantities with a two-channel panel–time representation and combines a shared temporal convolution, a relational panel graph, attentive pooling, and the six level-1 aggregates. No Micromegas energy or topology observable enters any level of this classifier hierarchy. Simulation and prototype channel identifiers are first mapped with separate readout maps to a common \((\text {face},\text {layer},\text {panel})\) coordinate; this prevents identical electronic identifiers in the two readouts from being assigned to different physical panels after noise overlay.

The partition is chronological and run-disjoint. Calibration runs 1335, 1339, and 1342 train the models, run 1345 fixes the score thresholds at nominal 90% and 95% control acceptance, and run 1347 is used once for the held-out evaluation. An overlaid neutron event follows the partition of its sampled calibration event, preventing empirical-noise leakage. The mapped waveform coordinate is divided into pre-control bins 0–189, prompt bins 190–210, early post-trigger bins 211–239, capture bins 240–280, and late-tail bins 281–511. The following hierarchy results retain the original response and feature definition as a historical comparison. A subsequent boundary check rejects peaks outside the stored 512-bin record instead of clipping them to its endpoints; the bounded frozen-model comparison is given in Appendix A.4.1.0. The physical acquisition support and calibrated total-energy response remain unresolved for this flat input, so the comparison does not establish an absolute neutron-veto efficiency.

The full level-2 model improves the held-out rejection by only 0.47 percentage points relative to level 1, with a central 90% paired-bootstrap interval of 0.07–0.82 percentage points, while its AUC difference is consistent with zero. Moreover, the nominal level-1 calibration acceptance varies from 88.2% to 90.9% across the five runs, whereas the full model varies from 84.4% to 90.5%. The added dimensions therefore amplify one run-dependent control shift without producing a material rejection gain. The total-energy removal test retains 79.1% rejection, demonstrating that timing and position contain independent neutron-sensitive information, but permutation tests show that total visible energy remains the dominant nominal input. Level 1 is consequently retained as the reference classifier for this historical response study; the additional levels test information content without establishing a more robust physical operating point.

Capture-delay signature

The small gain from the generic timing vector does not imply that neutron-capture timing is physically uninformative. It answers a narrower question: once total reconstructed veto energy, amplitude, and multiplicity are known, the original broad waveform summaries add little to the global binary classifier. The delayed-capture hypothesis is therefore tested separately, distinguishing the physical capture time from the reconstructed peak time and from an accidental late pulse.

Geant4 truth is used only to establish the expected timescale. For 55,581 positive-delay cadmium captures in the three-layer HENSA sample, the median delay from the first gas deposit is \(25.6~\mu \mathrm {s}\), and a truncated-exponential fit to the \(10\)–\(300~\mu \mathrm {s}\) tail gives \(\tau =46.9~\mu \mathrm {s}\). The cumulative fractions captured after the trigger and no later than \(50\), \(70\), and \(100~\mu \mathrm {s}\) are \(69.7\%\), \(79.7\%\), and \(88.8\%\), respectively, using all records with \(0<\Delta t_{\mathrm {gas}}<2000~\mu \mathrm {s}\) as the denominator. The narrower observable interval \(10<\Delta t_{\mathrm {gas}}\leq 50~\mu \mathrm {s}\) contains \(41.4\%\) of those records; another \(28.3\%\) occur within the first \(10~\mu \mathrm {s}\) and are not part of the delayed window. This truth information fixes the physical interpretation and the candidate window; it is never supplied to an event classifier.

The historical feature construction maps waveform bin \(i\) to an aligned time coordinate through \begin{equation} t_{\mathrm {rel}} = 0.2\,(i-231)~\mu \mathrm {s}. \label {eq:veto-capture-delay-coordinate} \end{equation} The offset 231 aligns prompt populations empirically; it is not an independent calibration of the hardware-trigger position. In this coordinate, bins 0–511 span \([-46.2,+56.0]~\mu \mathrm {s}\), whereas the simulated peak population in the inspected flat neutron input ends at \(+41.6~\mu \mathrm {s}\). Consequently, the nominal capture-like interval below is only partly populated by physical simulated peaks; calibration overlay can still populate its remaining bins. The observable prompt interval is \(-10\leq t_{\mathrm {rel}}\leq 5~\mu \mathrm {s}\), while the capture-like interval is \(10\leq t_{\mathrm {rel}}\leq 50~\mu \mathrm {s}\). The \(5\text{--}10\,\mathrm{\mu s}\) gap separates the nominal prompt and delayed intervals, but does not by itself bound pulse tails or peak-finding leakage. The explicit timing coordinates are the first delayed-peak time, the interval from the last prompt peak to the first delayed peak, and the delayed amplitude-weighted time mean and width. Binary indicators record whether prompt and delayed peaks exist, so the numerical zero assigned to a missing time coordinate cannot be interpreted as a physical zero delay. The capture-like signature then adds prompt and delayed multiplicities and amplitudes, panel, face, and layer occupancies, delayed fractions, and the number of panels that become active only after the prompt interval.

A time-scrambled event-mixing test isolates the importance of the sequence. It draws complete veto-peak trains from other simulated neutron events and circularly shifts them within the acquisition interval, preserving energy, multiplicity, and spatial correlations while destroying their timing relation to the Micromegas trigger. This neutron-derived null tests the timing sequence; it does not bound the experimental accidental rate. The resulting trade-off is summarized in Table 5.5.

The seven delay coordinates alone reject \(49.8\%\) of the held-out neutrons, and the complete 18-variable capture signature rejects \(74.1\%\). Thus, capture timing is informative but is not a universal neutron tag: \(24.2\%\) of the selected events containing a truth-level cadmium capture have no reconstructed veto peak (\(23.8\%\) of all selected events), and late activity also occurs in calibration data. Adding the capture signature to the six level-1 aggregates raises the held-out rejection from \(83.69\%\) to \(84.19\%\), corresponding to 20 additional rejected neutrons among 4035. The paired-bootstrap gain is \(0.50\) percentage points, with a central 90% interval of \(0.20\)–\(0.82\) percentage points, whereas the AUC difference remains compatible with zero. The minimum control acceptance across the five runs decreases from \(88.20\%\) for level 1 to \(86.33\%\) for the combined model. The delay is therefore retained as an important, physically interpretable level-2 signature and as a central input to the sequence model, while the aggregate level-1 BDT remains the nominal selector.

Level-3 spatiotemporal neural model

The level-3 input has shape \(59\times 512\times 2\): for every common semantic panel and aligned waveform bin, the two channels contain summed peak amplitude and peak occupancy. The simulation-only panel absent from the prototype is masked, and no run identifier, raw channel identifier, overlay identifier, TPC quantity, or Geant4 truth enters the network. A shared temporal convolution encodes each panel; two graph blocks exchange information separately between same-face neighbors, adjacent layers, and opposite faces before attentive pooling. Four predeclared variants distinguish a scalar multilayer perceptron, a tensor-only temporal convolution, a tensor-plus-graph model, and the final hybrid with the six level-1 aggregates.

The tensor-only models reject only 71.2% and 72.6% of the held-out neutrons, respectively, showing that the present sparse peak tensor does not replace the global energy summaries. The hybrid reaches 84.1%, only 0.42 percentage points above level 1; the central paired-bootstrap 90% interval is 0.10–0.74 percentage points, while the AUC difference remains compatible with zero. The frozen score is insensitive at the sub-percentage-point level to shifts of up to five waveform bins and to 10% amplitude rescaling in neutron rejection. Masking one representative panel per face–layer cell changes the rejection by at most 0.37 percentage points, but can reduce control acceptance by 1.25 percentage points. Most importantly, the nominal 90% control acceptance falls to 83.4% in calibration run 1339, below the 84.4% minimum of level 2 and the 88.2% minimum of level 1. The neural model therefore confirms the performance ceiling without satisfying the predeclared run-stability gate.

The frozen level-1 model is then applied to the exact 249 conservative-reference HENSA candidates from Section 6.6.3. The three causal-history activation events are removed before prompt scoring and receive no veto credit. For each of the remaining 246 candidates, 200 independent calibration events are overlaid. The mean prompt rejection is 91.14%, leaving 21.8 candidates on average; the central 90% range over accidental overlays is 19–25 survivors. The reproducible first overlay realization leaves 22 candidates, corresponding to \(B_{\mathrm {prompt}}=(3.02^{+1.29}_{-0.98})\times 10^{-7}~\mathrm {counts\,keV^{-1}\,cm^{-2}\,s^{-1}}\) with a two-sided 90% Garwood interval. The full level-2 model leaves 20.6 candidates on average, a reduction of only 1.2 events relative to level 1. The level-3 hybrid leaves 21.0 candidates on average, with a central 90% overlay range of 18–24, and the first realization leaves 20. This is less selective than level 2 and only 0.8 event below level 1, so it does not alter the controlling prompt-background estimate. The delayed-activation channel remains separate at the one-sided saturation bound reported in Section 6.7. The training, readout maps, run partitions, fixed models, candidate identities, and overlay draws are documented in Appendix A.4.

5.7 Experimental validation with IAXO-D0

5.7.1 Published surface cut flow

The commissioned prototype was operated with IAXO-D0 at surface level in Zaragoza for an effective \(52.1~\mathrm {days}\) [17]. The published selection uses a \(2\)–\(7~\mathrm {keV}\) region of interest and a \(9~\mathrm {mm}\)-radius focal region. This should not be confused with the \(10~\mathrm {mm}\) fiducial radius used by the current conservative background-analysis contract.

The prompt selection removes \(201/257=78.2\%\) of the Micromegas-selected events and is the dominant surface-background rejection. The advanced selection removes \(7/56=12.5\%\) of the post-prompt sample; the exact two-sided 90% binomial interval is \(6.0\%\)–\(22.2\%\). The calibration efficiency after all cuts is \(79.4/81.9=97.0\%\) relative to the Micromegas-selection reference. No separate prompt-stage calibration efficiency was reported, so this ratio is not described as retention relative to the prompt veto.

Figure 5.21 replots the reported cut-flow values in a terminology consistent with the present analysis. The stage historically called a “neutron cut” is labeled a neutron-sensitive control selection because the data do not establish the origin of individual rejected events.

The data support the hierarchy expected from the design. Prompt activity provides the large muon-like rejection, and the long waveform supplies an additional handle on non-prompt or multiplicity-rich activity with a small calibration penalty. The seven additionally rejected events do not measure a neutron efficiency because the post-prompt sample contains an unknown mixture of neutron-induced, proton-induced, environmental, activation, and instrumental backgrounds.

5.7.2 Late-window control population

An exploratory thesis extension ranks the feature-complete flattened prototype sample against calibration accidentals, muon simulation, and HENSA-neutron simulation. After removing prompt-muon-like and burst-like events, a frozen score orders the remaining events by their similarity to the neutron-plus-noise template relative to calibration and muon controls. Its threshold is fixed at the upper 1% tail of the clean calibration distribution. The score is deliberately used as a control-population selector rather than as an event-by-event neutron probability; its exact construction, preprocessing, and time-window definitions are documented in Appendix A.5.

The score selects 3877 experimental events, corresponding to 0.50% of the full flattened input and 5.88% of its prompt-suppressed subset. The selected data differ from the calibration control and have passed prompt-muon-like rejection, but they are not quantitatively described by the present HENSA template. In particular, their veto multiplicity, late-window energy, and Micromegas topology differ substantially from the selected neutron-plus-noise simulation. The defensible result is therefore the observation of a calibration-controlled late-window population, not a neutron fraction or a background-model normalization. The detailed template-mismatch table and channel correlations remain in Appendix A.5; the event rasters and Micromegas projections are collected in Appendix A.10.

5.7.3 Limits of experimental neutron identification

The frozen score identifies an experimentally distinct population enriched in neutron-sensitive observables, but it does not identify a sample of neutrons with known purity. At the threshold accepting \(1\%\) of the clean calibration control, \(5.88\%\) of the prompt-suppressed background population is selected. This establishes a difference between the score distributions of background and calibration events. The score also contains Micromegas energy, and its overlapping time windows and run-dependent control populations can produce a difference without a unique new particle component. The comparison therefore does not exclude ordinary accidental or instrumental explanations and does not establish individual event origins.

The principal obstacle is the quantitative mismatch with the available neutron template. The selected data contain a median of 47 reconstructed veto peaks, compared with 9 in the selected neutron-plus-noise simulation, and their median late-window energy proxy is approximately 2.5 times larger. Their Micromegas energy, hit multiplicity, and topology also differ substantially. Consequently, interpreting all selected events as neutrons would contradict the measured observables, while converting the selected count into a neutron rate would import an unsupported template-purity assumption.

Several effects prevent a stronger attribution in the present study. No neutron-source or otherwise tagged neutron data are available for the commissioned configuration. The HENSA production represents an outdoor spectral model rather than a run-matched experimental calibration, and the 59-panel simulation does not reproduce every gap, threshold, gain, unstable channel, and time-dependent condition of the 57-panel prototype. The experimental sample can also contain residual proton- and photon-induced showers, activation products, correlated electronics activity, and other instrumental populations for which complete normalized templates are not available. Finally, a late peak is not neutron-specific: accidental activity is common, and long-lived activation is causally distinct from an in-waveform capture response.

The existing data can strengthen the control result through run- and channel-state matching, matching in Micromegas energy, a veto-only score, and time-shifted or off-time control windows. Score construction and threshold setting should use different runs from the comparison sample. A quantitative neutron fraction would additionally require credible competing templates and independent particle-response constraints, for which tagged neutron data would be particularly useful. Until these conditions are met, the thesis reports a calibration-controlled, neutron-sensitive late-window population rather than an observed neutron count.

5.8 Systematic limitations

The background model also evaluates cosmic-induced random veto activity in a fixed simulated window, as described in Section 6.6.5. That result is distinct from a measured full-system dead-time estimate, which remains configuration dependent. The present chapter therefore reports calibration acceptance for offline selections and does not infer an unmeasured online live-time correction.

Detector inclination during solar tracking was tested separately for muons and HENSA neutrons. Across the simulated \(-25^\circ \) to \(+25^\circ \) range, the processed TPC-response acceptance varies at the few-percent level without a resolved monotonic trend. The scan in Appendix A.3 is conditional on its historical angular input; it does not close the final tracking-exposure dependence before that input is reconciled.

5.9 Summary and outlook

The shielding studies establish a coherent surface-detector strategy. Lead is indispensable for photon attenuation but does not remove the fast-neutron component; instead, it helps create the correlated secondary shower that an active system can tag. Passive borated-HDPE moderation improves selected configurations only modestly and cannot replace the veto.

The historical prototype design uses three scintillator–cadmium stages around the lead shield. The conditional HENSA response increases strongly through the second and third stages and only modestly in the fourth, while additional channels increase mechanical and accidental-veto costs. Generated-primary normalization shows no resolved reduction of the processed analysis-entry population across the one- through four-layer scan; the observed gain is additional reconstructed tagging information.

The IAXO-D0 data validate the two-level analysis logic. Prompt veto activity removes the dominant muon-like population, and late-window or multiplicity-rich waveform observables provide a smaller additional rejection while retaining \(97.0\%\) of the Micromegas-selected calibration efficiency. The simulations establish neutron-sensitive response, whereas the prototype data demonstrate an additional non-prompt rejection handle without identifying the seven rejected events as neutrons. The extended data study similarly isolates a calibration-controlled population enriched in delayed and multiplicity-rich activity, but its mismatch with the HENSA template prevents an experimental neutron count or fraction from being inferred. The present experimental result is additional rejection with unresolved particle attribution. Absolute prompt and delayed background levels are evaluated by the source-normalized analysis in Chapter 6.

Within the historical simulation-based hierarchy, the six-observable aggregate boosted tree provides the reference result. The engineered timing and segmentation model confirms that these observables contain independent neutron-sensitive information, but its nominal rejection gain is only about half a percentage point and it is less stable across one calibration run. The completed neural study reaches the same conclusion independently: explicit temporal convolution and spatial message passing recover the aggregate performance only when the aggregate branch is restored, while the resulting gain is below one candidate and the run dependence worsens. Greater model complexity is therefore retained as a validation study rather than adopted as the nominal selector. The next useful simulations should first close recoil visibility, acquisition timing and source angular support, then propagate cascade and response alternatives through a frozen selector. A March 2026 collaboration design study explores compact three-layer modules with wavelength-shifting fibers and SiPM readout, including boron-loaded material and cadmium options [112]. That geometry should be compared with the historical PMT implementation under a common mechanical envelope and response model; single-bar test efficiency is not a measurement of complete-veto efficiency.

Chapter 6
Background Model

Introduction

As a rare-event search experiment, IAXO requires a detailed background model to distinguish signal candidates from background events. The purpose of the model is to translate measured activities and external particle fluxes into reconstructed, X-ray-like survivor rates in the Micromegas region of interest. This translation is non-trivial because the same source activity can produce different accepted rates depending on geometry, detector response, selection criteria, veto response, and normalization uncertainty.

In this chapter, the signal reference is a compact X-ray conversion reconstructed in the active gas and within the signal fiducial region. A background component is any other physical source that can produce a reconstructed event compatible with that reference. The model uses the IAXO-D0 surface data as an experimental-validation legacy and IAXO-D1 as its argon–isobutane simulation reference; both are Micromegas prototype configurations that inform, but are not, the BabyIAXO detector. It records for each source component whether transport, reconstruction, normalization, and a compatible detector response are available. The work develops the earlier Micromegas background-model studies documented in the theses of Elisa and Cristina [60, 80], which applied the CAST background methodology to earlier detector configurations. The quantitative endpoint of the chapter is the current partial source-response model for the IAXO-D1 argon–isobutane detector configuration. It uses one deterministic Micromegas reference selection and does not credit an unvalidated topology classifier with background rejection. For components whose absolute activity or site source term is still scenario dependent, the tables separate generated-event yields from auxiliary rate scenarios and identify the source or parent-decay denominator needed for an absolute prediction. The final synthesis combines contract-compatible rows, historical response scales, and an explicit closure matrix, but it does not assign zero contribution to omitted sources or form an arithmetic total from incompatible rows. The BabyIAXO xenon–neon detector, optics acceptance, final veto response, and DESY source terms are treated as separate projections rather than folded into the IAXO-D1 argon reference.

Table 6.1 first fixes the energy windows used when comparing these source components and reference samples.

6.1 Scope, analysis contract, and claim levels

A source-by-source model is additive only when its source normalizations, reconstructed-event definition, and selection efficiencies refer to the same analysis contract. Sharing an energy interval is not sufficient: changing the energy estimator, fiducial object, topology classifier, veto requirement, or area normalization changes the response factor that multiplies the source activity or flux. This distinction became important during the present work because several historically valid studies used different selections while being described informally as the same “X-ray cuts.”

The final deterministic thesis reference is identified as background-analysis-v2- conservative-reference. Its machine-readable configuration records the detector configuration, branch definitions, event selection, normalization area, interval convention, veto bookkeeping, and explicit prohibition on topology-rejection credit. Table 6.2 gives the physics-level definition needed to interpret the compatible results in this chapter.

The deterministic reference is the consequence of two explicit negative validation results, not an assumption that topology carries no information. The frozen candidate-v1 BDT retains \(80.22\%\) of untouched simulated \(\ce {^{55}Fe}\) but only \(13.85\%\) of the measured R02756 domain-check sample. A subsequent bounded candidate family reached the nominal \(80\%\) calibration working point, but no candidate passed the independent non-blind background-rejection gate. No v2 candidate was selected and the reserved R03018/R03015 blind block was never opened for selector evaluation. The topology studies therefore remain reproducible diagnostics, while the energy, one-track, and \(10~\mathrm {mm}\) fiducial stages define the thesis partial reference.

The source registry assembled for this chapter contains 30 physical source records, in addition to one source-construction diagnostic and two X-ray control samples. Under the conservative reference, four light-cosmic source rows already have a directly usable deterministic response, 11 physical sources have preserved outputs suitable for reference-selection reprocessing, eight are blocked primarily by an absolute normalization, and seven still require a source or geometry definition. Seventeen named physical sources were absent from the illustrative numerical synthesis. These counts provide a completeness statement: they show that a missing row is an open component, not evidence for a zero contribution.

The following status labels are consequently used throughout the chapter and may coexist for a single source. An analysis-contract-compatible result has been evaluated with the complete deterministic definition above. A legacy or auxiliary result is scientifically useful for mechanism or scale but cannot enter the common sum unchanged. A scenario-normalized result has a simulated response but depends on an adopted activity or site source term. An open component still lacks the response, normalization, or both. Only results that are contract-compatible and use mutually consistent source assumptions are eligible for the partial reference; central estimates, one-sided bounds, and open components remain separate in the present synthesis.

6.2 Simulation and analysis methodology

The background model simulations and the subsequent event reconstruction were carried out with REST-for-Physics [83], using the restG4 and restManager applications described in the software chapter. The Monte Carlo transport stage was defined through source-specific configurations, while the detector-response emulation and event reconstruction were performed with a common analysis chain. This same reconstruction chain is also used for the analysis of experimental data, since the simulated detector response is converted into the same reconstructed event format as real detector acquisitions. This common data model allows the same observables, selection criteria, and background-discrimination procedures to be applied consistently to both simulated and measured events.

6.2.1 Workflow overview

The methodology followed for the background model is summarized in Figure 6.1. The first stage consists of defining a source term and the corresponding detector geometry. The source term depends on the origin of the background contribution under study: radioisotope contamination in a detector component, environmental radiation entering from outside the shielding, or cosmic-ray secondaries. These inputs are then propagated with restG4, which performs the Geant4 transport and stores the event-level truth information.

In a second stage, restManager processes the simulated event through a detector-response chain designed to reproduce the experimental readout observables as closely as possible. This response chain includes both the Micromegas detector readout and the active-veto readout, which are described in REST-for-Physics through dedicated readout definitions. Although both systems are handled within the same analysis framework and are ultimately stored in a common event structure, they represent physically different detector subsystems: the Micromegas readout reconstructs the charge signal produced in the gaseous TPC, while the veto readout reconstructs scintillation signals produced in the surrounding veto modules. Consequently, their channel mapping, signal formation, timing, shaping, and reconstructed observables are treated with subsystem-specific parameters and processes.

The reconstructed output is then used to derive the observables employed for the background studies and for the X-ray-like event selection. In this way, the simulated events can be compared with experimental data at the level of reconstructed quantities, rather than only at the level of idealized energy depositions.

This separation between transport and reconstruction was particularly important in the present work. It allowed the same reconstruction chain to be applied consistently to different background sources, while at the same time making it possible to update detector-response parameters, electronics settings, veto thresholds, or analysis cuts without repeating the full Geant4 transport stage. The same strategy also ensured that simulated events and experimental data were compared using the same reconstructed observables and selection criteria, while preserving the distinct detector-response models required by the Micromegas and veto readout systems.

6.2.2 Source-specific simulations

The Monte Carlo transport stage used a family of source-specific descriptions. Each one defined the source term for one background component, but the structure of the simulations was kept common: a detector geometry, a primary-event generator, the sensitive detector volumes, and the physics lists required for electromagnetic interactions, radioactive decays, and, when needed, hadronic transport. This organization isolates the physical origin of each background contribution while preserving a common interface to the reconstruction chain.

For internal contaminations, the simulated source was defined from the detector volume corresponding to the material under study. This category includes detector materials such as copper, electronics, gas, Kapton, aluminized polyethylene terephthalate (PET; Mylar), shielding elements, and radon or plated-out progeny. The primary positions were sampled uniformly inside the selected volume, or on its surface when the measured contamination was given as a surface activity.

The activity assigned to each source was obtained from radiopurity measurements performed by the collaboration at the Laboratorio Subterráneo de Canfranc. For a mass-specific activity \(a_{m}\) or surface-specific activity \(a_{S}\), the source normalization is \(A_{\mathrm {source}}=a_{m}M\) or \(A_{\mathrm {source}}=a_{S}S\), respectively, where \(M\) or \(S\) is the simulated material mass or surface.

When the measured activity referred to a parent isotope assumed to be in secular equilibrium, the full radioactive decay chain was simulated. In this way, the generated events preserve both the spatial distribution of the contamination in the detector geometry and the correct normalization to the measured activity of the material.

Environmental backgrounds were also considered in the simulation campaign, although their final importance depends on the site-specific radiation field and shielding configuration. At the time when these studies were developed, the experimental layout under consideration assumed that the detector would operate inside a laboratory environment, with at least partial underground overburden. Under those assumptions, radiation from the surrounding laboratory materials, such as concrete gammas and neutrons, was a relevant contribution to evaluate.

These backgrounds were treated as external fluxes incident on the detector and shielding system. When a direct simulation from the laboratory boundaries was inefficient, the source term was factorized into two stages. The calculation first obtained energy and angular distributions for particles emerging from the surrounding materials, then used them as input spectra for the detector-level simulation. This avoided repeating the expensive laboratory-scale transport for each detector-response or selection study.

Under the current outdoor, on-surface BabyIAXO working scenario, cosmic-ray-induced backgrounds are expected to become more prominent than in a deep underground installation. The relative importance of the environmental and intrinsic components cannot nevertheless be ranked until a site-specific source term and conservative-reference responses are available. Nearby telescope structure can also constitute an environmental source term, but its contribution cannot be assessed before its composition and geometry are specified. The environmental studies are therefore retained both as physical response calculations and as cross-checks of the simulation workflow.

Cosmic-ray-induced backgrounds required a separate set of source generators because their normalization and event topology depend strongly on particle type, angular distribution, energy spectrum, and exposed surface of the apparatus. Dedicated configurations were prepared for the main secondary components at surface level: muons, neutrons, protons, gammas, and electrons. Depending on the study, the primary distributions were defined either analytically or from histograms produced with the Cosmic-Ray Shower Library (CRY) [88]. For the largest production campaigns, geometry-aware sampling strategies developed during this work [89] were used to avoid spending most of the computation time on particles whose trajectories would not intersect the detector geometry. The detailed modeling of the cosmic-ray sources is discussed later in this chapter. The relevant point for the present methodology is that, once the transport stage is completed, cosmic-ray and non-cosmic samples are treated with the same detector-response and reconstruction philosophy.

The detector description was derived from detailed IAXO-D0 and IAXO-D1 Micromegas models together with BabyIAXO-oriented shielding, active-veto, and auxiliary-volume variants. Different geometry variants were selected depending on the purpose of each sample. Full geometries including shielding and veto volumes were used for cosmic-ray and shielding studies; reduced geometries were used for isolated material-contamination studies; and chamber-focused geometries were used for X-ray calibration, detector-response validation, or cut-efficiency studies. The active gas volume above the Micromegas readout was the main sensitive region used to compute the detector background rate. Additional sensitive volumes, such as plastic scintillators or neutron-capture layers, were included when the goal was to study veto response, neutron-tagging performance, or the history of particles contributing to a reconstructed event.

The Geant4 transport configuration was kept as uniform as possible across the different source components, so that differences between samples were driven mainly by the source term and geometry rather than by changes in the physics list. Electromagnetic interactions were described with G4EmLivermorePhysics, which is appropriate for low-energy photon and electron transport. Hadronic interactions were handled with the high-precision neutron and binary-cascade models required to describe neutron transport, inelastic interactions, and secondary production in the shielding. For internal-contamination samples, radioactive-decay processes were enabled, including the associated atomic de-excitation mechanisms such as internal conversion, fluorescence, and Auger-electron emission. Production cuts were generally kept at the millimeter scale for charged particles and photons, while the gas volume was assigned a smaller maximum step size to preserve the topology of low-energy depositions in the X-ray region of interest.

6.2.3 Background-model component inventory

The background model was built from independent source components rather than as a single combined Monte Carlo sample. Each component describes one physical origin of background: cosmic-ray secondaries, environmental radiation, intrinsic radioactivity of detector materials, or radon-related activity. For each source, the simulation defines where the particles are generated, which spectrum or decay chain is used, and how the resulting event sample is normalized to an expected rate.

This organization keeps the model modular. A new material-screening result, an updated cosmic-ray flux, or a revised detector geometry can be incorporated by updating only the affected source component. The simulated events from all components are then passed through the same detector-response and reconstruction chain before being compared at the analysis level.

Table 6.3 summarizes the main source components considered in the model. The first four entries correspond to physical background-rate components. The final entry is an auxiliary sample used to define the detector response and the X-ray-like selection efficiency applied when the rate components are combined.

The individual source components are combined only after detector-response emulation, event reconstruction, and event selection. In practice, each simulated sample is first reduced to the number of events that survive the reference selection in the analysis window. That number is then scaled by the appropriate physical normalization: the measured activity of a material, the activity density of a surface contamination, the radon activity in the gas, or the incident particle flux for external and cosmic-ray sources.

Any final background estimate must therefore be assembled from reconstructed events that satisfy the stated selection, rather than from idealized energy depositions. The same source can have a very different impact depending on where the interaction occurs, how the charge or veto signal is reconstructed, and whether the event passes the deterministic energy, track-validity, and fiducial selection criteria. Any additional topology or veto stage changes that response and must be validated and reported separately before its rejection can be credited. Keeping the source generation, detector response, and normalization as separate steps also makes the calculation easier to update as new measurements or improved detector descriptions become available.

6.2.4 Event types and detector-response chain

The transport output is not selected directly from Geant4 truth information. It is converted into detector response, projected onto readout channels, digitized as raw waveforms, and reconstructed into hits and tracks before scalar observables are written to the analysis tree. The framework-level event evolution is defined in Chapter 4, Figure 4.2; the present chapter retains only background-specific response checks and selection consequences.

Truth information is retained for mechanism studies and validation, but it is not available to the experimental selection. At the response stage, energy deposits are assigned to the TPC or veto subsystem and modified by the relevant visible-energy and transport effects. Channel projection and electronics emulation then create the same raw-signal event type used by the acquisition system. After thresholding and signal reconstruction, Micromegas hits are grouped into the two projected track views supplied by the strip readout, while veto peaks retain their reconstructed time, amplitude, channel, and multiplicity information. The detailed event-container walkthrough and representative truth, readout, waveform, and track displays are collected in Appendix C.1.1.

The raw-signal stage provides the most direct comparison between the simulated response and measured waveforms. Figure 6.2 shows such a comparison for an experimental muon candidate and a simulated cosmic-muon event processed through the same raw-signal representation. The two events are not expected to be identical, since they correspond to different physical particles and trajectories. The relevant validation point is instead that the shaped Micromegas and veto pulses have comparable time ordering, widths, and amplitude scales once the detector-response parameters have been applied.

The background model therefore operates on reconstructed observables rather than on ideal deposited energy. The source response depends on whether an interaction survives waveform formation, channel thresholds, hit reconstruction, track building, and the stated analysis contract.

6.2.5 Analysis processes and observables

The common analysis chain is kept in one version-controlled configuration so that simulated and measured events enter the same reconstructed observable space. Simulation-only stages apply the detector-response model before digitization, whereas measured data enter as acquired waveforms. After this input-specific boundary, both follow the same baseline correction, peak finding, hit reconstruction, and topology analysis. Truth observables remain available for validation and mechanism studies but are excluded from the experimental selection.

The response model contains the effects that materially alter the low-energy selection. Lindhard-type ionization quenching is applied to identified gas nuclear recoils, while Birks saturation is applied to highly ionizing deposits in the scintillator [109, 110, 113]. In a representative cosmic-neutron validation sample, the energy-weighted visible energy in the gas changes by only about 0.22% on average because only a small subset of deposits is recoil-like. The corresponding scintillator visible signal is reduced by about 25.7%, so veto thresholds are appreciably sensitive to the Birks and light-collection assumptions. Photon deposits, including capture-gamma deposits, are left unquenched.

Scintillator light is attenuated according to the distance to the effective readout end, and the same path supplies a propagation-time correction. This effective model captures the leading position dependence of the long veto panels without an optical-photon simulation; reflections, surface treatment, coupling, and channel gain are absorbed into calibrated parameters.

TPC ionization is broadened using gas-dependent transverse and longitudinal diffusion coefficients obtained from Garfield++/Magboltz. An empirical hit-smearing stage accounts separately for residual energy-resolution effects not described by diffusion alone, including gain, avalanche, electronics, and calibration broadening. The exact equations, nominal constants, validation sample, and implementation inventory are retained in Appendix C.1.2.

Waveform formation uses separate sampling, shaping, trigger, and calibration settings for the TPC and veto branches. The Micromegas scale is anchored to the reconstructed \(5.9~\mathrm {keV}\) \(\ce {^{55}Fe}\) peak, while the veto scale is aligned to the measured through-going-muon response panel by panel. The resulting time-structured waveforms are processed with the same channel masks, noise corrections, peak definitions, and readout mapping used for data rather than treated as deposited-energy sums.

The final TRestAnalysisTree observables include reconstructed energy, valid-track counts, fiducial position, hit and width summaries, projection balance, and veto timing and multiplicity. These reconstructed quantities, not source identity or transport truth, define the selections and source-response factors used below.

6.2.6 Reference samples for selection and normalization

In addition to source-specific background simulations, dedicated reference samples were used to characterize the response to X-ray-like events and to validate the selection criteria. These samples are not background components: their purpose is to define the signal acceptance of the reconstruction and to provide a controlled reference against which background events can be selected or rejected. They therefore occupy a central position between the detector-response model and the final source-normalized background table.

Two classes of signal-like simulation samples were used for this purpose. The first class consists of \(\ce {^{55}Fe}\)-like calibration simulations. The dominant manganese \(K_{\alpha }\) line at \(5.9\,\mathrm {keV}\) lies inside the axion-search energy interval and produces compact photoelectric conversions in the gas. This sample is used to validate the response near the standard calibration energy and to compare the simulated reconstructed spectrum with measured calibration data, as discussed in Section 3.6.1. The same sample also exposes fluorescence-induced, multi-site topologies that fail the one-track requirement. A representative reconstruction is retained with the supplementary selection diagnostics in Figure C.5.

The second class consists of uniform low-energy X-ray simulations, in which primary photons are generated over a flat 0–12 keV energy range. This sample maps the selection efficiency across the full low-energy region rather than only at the \(\ce {^{55}Fe}\) line. The full sample-role and configuration map is given in the appendix. In summary, source-specific simulations provide the rejection diagnostics, while measured calibration data provide the accidental-veto model.

The production campaign keeps the calibration and background samples gas-matched. For the candidate-v1 study summarized below and the cosmic diagnostics retained in Appendix B.9, the \(\ce {^{55}Fe}\), muon, and neutron samples were reconstructed with the same argon–isobutane detector-response settings used by the IAXO-D1 simulation chain. Equivalent \(\mathrm {Xe}\)-\(\mathrm {Ne}\)-\(\mathrm {iC}_{4}\mathrm {H}_{10}\) calibration productions are also part of the broader BabyIAXO program, but they are combined only with background samples reconstructed with the same gas, pressure, drift field, and readout configuration. Keeping the reconstruction stage identical is essential: the efficiencies must be expressed in terms of the same observables that are later applied to the background components. In practice, the most relevant reconstructed quantities are the fiducial or readout-plane energy, the number of reconstructed hits, the spread of the charge cloud in the readout plane, the balance between the two strip directions, and the track observables produced after hit clustering.

The deterministic Micromegas reference selection is \begin{equation} C_{\mathrm {ref}} = C_{E} \cap C_{\mathrm {one\text {-}track}} \cap C_{\mathrm {fid}} , \label {eq:background-xray-cut-definition} \end{equation} where \(C_{E}\) selects the reconstructed energy region of interest, \(C_{\mathrm {one\text {-}track}}\) requires one valid maximum track in each strip projection, and \(C_{\mathrm {fid}}\) requires the maximum-track center to lie within \(10~\mathrm {mm}\) of the readout center. The stages are applied in that order: energy, one-track reconstruction in both projections, and the \(10~\mathrm {mm}\) fiducial criterion. Learned topology selections are evaluated only as diagnostics and are not factors in \(C_{\mathrm {ref}}\). The full signal efficiency must be defined in bins of true incident photon energy, \begin{equation} \varepsilon _{\mathrm {ref}}(E_{\mathrm {true}}) = \frac {N_{\mathrm {reconstructed}}(E_{\mathrm {true}}\mid C_{\mathrm {ref}})} {N_{\mathrm {generated}}(E_{\mathrm {true}}\mid \text {defined signal acceptance})}. \label {eq:background-xray-efficiency} \end{equation} The denominator must include generated photons that fail to interact, reconstruct, or enter the analysis tree. The distinction between this complete-denominator efficiency and the conditional topology response of the legacy retained-event sample is formalized with the detailed response tables in Appendix C.1. The \(\ce {^{55}Fe}\) sample provides a complementary check at the calibration energy: it tests whether the Monte Carlo response produces the same compact event population, reconstructed peak position, and peak width observed in measured calibration data.

Machine-learning study of an X-ray-like topology cut

The topology study tested whether reconstructed Micromegas shape information could add rejection after the deterministic energy, one-track, and fiducial requirements. Its principal candidate, background-analysis-v1, is a boosted decision tree trained on gas-matched simulated \(\ce {^{55}Fe}\) and cosmic-background samples using only reconstructed charge-width, hit-multiplicity, skewness, energy-sharing, and projection-balance observables. Reconstructed energy, source identity, particle type, transport history, and other simulation-only information are excluded from the feature vector. The working point was frozen at 80% acceptance of an untouched simulated \(\ce {^{55}Fe}\) partition before comparison with measured calibration data.

The BDT was compared with binned log-odds, sequential interval cuts, and lower-capacity models. These comparisons established that topological information is present in the reconstructed variables, but they do not establish a transferable rejection factor. The exact feature vector, score definitions, smoothing choices, thresholds, random seeds, grouped evaluation, and complete method survey are documented in Appendix C.1. The main chapter retains the two tests that determine whether any learned rejection may enter the background model: simulation-to-data transfer of the frozen candidate and independent run-disjoint validation of a bounded repair family.

The complete method-development comparison is given in Appendix Table C.4. It motivated the multivariate study but is not an independent production-rate evaluation and supplies no rejection credit to the conservative reference.

The complete run-block closure and candidate-v1 gate audits are given in Appendix Tables C.5 and C.6, respectively. The decisive results are summarized here. On the untouched August–September block, the calibration-anchored BDT retained \(34814/43726=79.62\%\) of calibration events but also accepted \(21/97=21.65\%\) of background candidates. For the transfer test, the same simulation-trained model and its frozen threshold are applied to measured R02756 without retraining. It retains \(9224/11499=80.22\%\) of untouched simulated \(\ce {^{55}Fe}\) events but only \(8889/64162=13.85\%\) of the measured calibration, so it fails detector-domain transfer. The same model accepts \(35/172=20.35\%\) of the simulated production-holdout cosmic candidates. This cosmic value and the wider \(61/294=20.75\%\) group-safe cross-fit result are diagnostics, not experimentally validated background acceptances.

Figure 6.3 contains the decisive promotion test. The classifier orders the untouched simulated X rays above many simulated production-holdout cosmic candidates, but the measured \(\ce {^{55}Fe}\) population moves predominantly below the same frozen boundary. The failure is therefore one of detector-domain transfer, not merely a choice of operating threshold. The supporting observable ECDFs, grouped importance/domain-shift comparison, and physically consistent response slices are retained in Appendix Figs. C.6, C.7, and C.8, respectively.

A post-failure ablation study found no feature subset or lower-capacity model that met the joint signal-transfer and group-safe cosmic-rejection screen. Because this study was designed after observing R02756, it remains development evidence and cannot validate a successor selector. Its exact gates, candidate definitions, and outcomes are retained in Appendix C.1.

A final bounded repair family was then predeclared on independent 2025 IAXO-D1 argon runs before the reserved R03018/R03015 blind block was opened. Exactly three candidates were allowed: a calibration-anchored logistic model, a robust signal-distance score, and a transparent five-feature interval box. Their thresholds were fixed on R02997 and evaluated on the independent R02998 calibration and R02993/R02994 background samples. Table 6.4 gives the resulting promotion test; the detailed run-quality and exclusion record is provided in the appendix.

The decision was deterministic: the result records selected_candidate=null and blind_input_opened=false. The R03018/R03015 block therefore remains unopened for selector evaluation, and the failed non-blind result was not followed by retuning. The logistic candidate reproduced the nominal \(80\%\) signal working point, but failed promotion decisively: its \(50/83\) background acceptance demonstrates that the tested feature representation does not provide transferable rejection under the independent run conditions. Consequently, the conservative thesis reference assigns no learned topology-rejection credit.

The frozen candidate-v1 response was also evaluated versus energy with a uniform-X-ray argon production. Its conditional and incident-chain topology efficiencies are retained in the appendix because the selector fails the measured-signal domain gate and therefore cannot define the thesis signal efficiency. The companion saveAllEvents production is nevertheless important: it retains every generated photon, including non-interactions and reconstruction failures, and supplies the complete incident denominator needed for the reference-selection reference.

The same complete ledger also permits the reference-selection efficiency required by the conservative reference to be evaluated without a new transport campaign. Table 6.5 stops the cut flow after the energy, one-track, and \(10~\mathrm {mm}\) fiducial requirements. It is therefore independent of both failed topology studies.

The conservative incident-reference efficiency peaks at \(30.01\%\) in the \(4.5\)–\(5.0~\mathrm {keV}\) bin. Integrated over the flat generated spectrum in the \(2\)–\(7~\mathrm {keV}\) true-energy interval, \(102144/417091=24.49\%\) of the incident photons pass the conservative reference, with a 90% confidence interval of \(24.38\)–\(24.60\%\). This is the thesis reference response for the specified calibration-like illumination, rather than a final axion efficiency. An optics-weighted BabyIAXO efficiency must additionally use the Xe–Ne detector response, the telescope point-spread function and spectrum, and separately measured veto/live-time losses.

The two independent validation routes lead to the same conclusion. Candidate-v1 fails simulation-to-data transfer, and the bounded 2025 family fails the non-blind background gate despite recovering the nominal calibration working point for one candidate. Shared reconstructed branch names do not establish detector-domain closure, and no learned topology-rejection factor is credited in the conservative reference. The feature-level domain diagnostics, historical selector comparisons, run-block studies, and candidate-v1 response tables remain in Appendix C.1. Any future learned selector will require new run-group-independent evidence; it is not a prerequisite for the deterministic thesis reference.

The veto stage follows three accounting rules established in Chapter 5. For an uncorrelated X-ray signal, veto loss is accidental and the survival probability is \begin{equation} \varepsilon _{\mathrm {sig}}^{\mathrm {veto}} = 1 - P_{\mathrm {acc}}(C_{\mathrm {veto}}), \label {eq:background-veto-accidental-survival} \end{equation} where \(P_{\mathrm {acc}}\) must be measured from an appropriate noise overlay or data control. For prompt-correlated backgrounds, a validated reconstructed veto selection may be credited separately. For delayed activation, the initiating shower is outside the Micromegas-trigger coincidence window and no prompt-veto rejection is credited. The uniform-X-ray production does not yet include an accidental overlay, and the current source frames do not match the calibration-noise domain of the design classifier; both therefore remain pre-veto in the conservative reference.

The final source contribution is obtained by combining the raw source normalization with the event-level survival of the X-ray-like selection and the source-appropriate veto treatment. For a source \(i\), the most general expression is a weighted sum over reconstructed events, \begin{equation} R_i^{\mathrm {selected}} = \sum _{j \in i} w_{ij}\, I_j(C_{i}^{\mathrm {selected}}), \label {eq:background-rate-after-cuts} \end{equation} where \(w_{ij}\) contains the source normalization and any geometrical, spectral, live-time, activity, surface, or phase-space weight assigned to event \(j\), and \(I_j\) equals one when the event satisfies \(C_{i}^{\mathrm {selected}}\). The source-specific selection \(C_{i}^{\mathrm {selected}}\) includes \(C_{\mathrm {ref}}\) and, when applicable, the reconstructed-veto survival criterion. For delayed-activation components, it includes no correlated prompt-veto rejection. A separately measured accidental-veto or live-time survival factor may still apply to the delayed channel. For an unweighted prompt sample generated directly from the physical source distribution, Eq. 6.4 reduces to \(R_i^{\mathrm {raw}}N_i(C_i^{\mathrm {selected}})/N_i^{\mathrm {generated}}\); the delayed case uses \(C_i^{\mathrm {selected}}=C_{\mathrm {ref}}\) with respect to the correlated prompt veto. Depending on the source component, the raw normalization is derived from a material activity, a measured environmental flux, a cosmic-ray flux model, or an experimental live-time normalization.

For one fully specified and mutually exclusive source hypothesis \(\mathcal {H}\), the total predicted background rate in the region of interest is then \begin{equation} R_{\mathrm {tot}}^{\mathrm {selected}} = \sum _{i\in \mathcal {H}} R_i^{\mathrm {selected}}, \label {eq:background-total-rate-after-cuts} \end{equation} with analogous sums before cuts and after X-ray-like cuts alone. Alternative gas scenarios and alternative descriptions of the same neutron field are never included together in \(\mathcal {H}\). Likewise, an aggregate HENSA row cannot coexist with its prompt and delayed subchannels, whereas the two disjoint prompt and delayed subchannels may each appear once. This three-stage presentation is useful because it separates the physics source model from the detector selection:

1. the raw rate before analysis cuts tests the source normalization and geometry;
2. the rate after the deterministic Micromegas reference tests whether the component produces a valid low-energy, one-track event in the central fiducial region;
3. the rate after the reference plus a source-appropriate veto tests the residual background after the active-shielding strategy is applied, without assigning prompt-veto rejection to delayed activation.

The background tables are organized, for each source component, around the number of simulated events, the number of analyzed events, the X-ray-like selection efficiency, the veto survival fraction, the raw normalized level, and the residual level after all selection stages. This structure allows transport samples to be reused when only reconstruction or selection changes. The source tables presently include candidate-v1 results and earlier snapshots such as fe55-shape1014-ld165-td063-bin234-v1. The latter detector-response nickname does not identify a unique event selector: the audit found transparent interval cuts, legacy BDTs, energy-binned cuts, and both \(10\) and \(15~\mathrm {mm}\) fiducial objects under related labels. Each table therefore states its actual analysis treatment. Only rows explicitly marked as compatible with background-analysis-v2-conservative-reference enter the thesis partial reference; candidate-v1 and legacy rows remain diagnostic or await reprocessing.

Monte Carlo statistical uncertainties use 90% counting intervals [114, 115]. Ordinary equal-weight counts receive central Garwood intervals. Rows with zero, one, or two survivors are reported as one-sided upper bounds corresponding to \(2.303\), \(3.890\), or \(5.322\) equivalent Poisson events, respectively; each bound is propagated through the same source and area normalization. Unequal-weight strata are treated separately before combination, and legacy rows without the required bookkeeping remain auxiliary. The complete interval convention is documented in Appendix C.1.3.

6.3 Measurement inputs and normalization strategy

The measurements used in this chapter do not constitute a single background data set. They enter the model in three distinct ways. Material-screening measurements provide activity normalizations for intrinsic radioactivity. Environmental and cosmic-field measurements define source terms for particles entering the detector from outside. Detector background data provide validation samples and operational constraints for the reconstruction, veto response, radon handling, and residual event interpretation. This separation is important because a measured activity, a measured external flux, and a measured detector rate constrain different parts of the calculation.

6.3.1 Material screening and radiopurity inputs

Radiopurity screening provides the activity normalization for the intrinsic-background part of the model. The measurements summarized here are collaboration inputs, principally from the Zaragoza detector and radiopurity teams and from work performed at the Canfranc Underground Laboratory (LSC); they are not claimed here as an original contribution of this thesis. They are nevertheless essential to the simulation chain, because every activity limit or measured contamination level must ultimately be translated into an expected event rate in the Micromegas region of interest.

The screening strategy follows the low-background Micromegas program developed for CAST, TREX-DM, and the IAXO prototypes [16, 116, 117]. Material samples are measured mainly with ultra-low-background high-purity germanium (HPGe) detectors at LSC, where the underground overburden suppresses the cosmic-ray component of the counting background. The relevant gamma-emitting isotopes and decay-chain segments include \(\ce {^{40}K}\), \(\ce {^{60}Co}\), the \(\ce {^{232}Th}\) chain, and the \(\ce {^{238}U}\)/\(\ce {^{235}U}\) chains. For the background model, the outcome of these measurements is a set of specific activities, or upper limits, assigned to detector volumes such as the Micromegas readout, field cage, cathode, chamber, shielding, calibration hardware, cables, and electronics. Upper limits are retained explicitly because many selected materials are sufficiently clean that no statistically significant peak is observed in the screening spectrum.

The IAXO-D1 screening compilation draws principally on the TREX-DM and Micromegas material-screening campaigns [78]. Most material activities in the present model are upper limits and must therefore be interpreted as conservative bounds on their background contributions rather than as measured central values. The activity assumptions for \(\ce {^{39}Ar}\) in the gas, \(\ce {^{210}Pb}\) in the lead shielding, and \(\ce {^{40}K}\) in the readout are identified separately in the source-specific tables.

The radiopure-electronics program is another collaboration input that affects the material inventory close to the detector. E. Picatoste reported the status of the Micromegas radiopure electronics at the 21st IAXO Collaboration Meeting, including the production and testing of front-end flex circuits, limandes, and FEC/BEC interconnect elements intended to reduce the amount of non-radiopure material inside the shielded volume [76]. This work is relevant for the background model because the electronics are geometrically close to the gas volume and can therefore contribute through compact low-energy deposits or through secondary radiation produced in nearby materials. For this reason, the final detector model must distinguish between material located inside the radiopure boundary and services or back-end electronics that are farther away or shielded differently.

Radiopurity measurements alone do not determine the low-energy background, because the detector response depends on where the isotope is located, on the geometry between the source and the gas volume, and on the subsequent reconstruction cuts. The procedure used in the model is therefore to simulate each relevant isotope–volume pair with Geant4, process the surviving events with the same analysis chain used for experimental data, and only then scale the accepted rate by the measured activity or upper limit. The corresponding intrinsic-contamination simulations are described in Section 6.4 as part of the full production inventory.

6.3.2 Environmental and cosmic source measurements

External source terms are constrained by measurements and generators in a different way from material screening. For surface cosmic-ray backgrounds, CRY, analytic muon parameterizations, EXPACS, and HENSA measurements define the incident particle spectra used in the detector simulations. For laboratory environmental radiation, NaI and HENSA measurements provide local gamma and neutron fields that can be propagated through the detector geometry. These inputs are source terms, not detector backgrounds by themselves: they become a predicted Micromegas rate only after transport, detector response, reconstruction, and the X-ray-like selection.

The Zaragoza laboratory measurements and HENSA-based neutron spectra are therefore used as source-term anchors for the simulations discussed in Section 6.5. They are especially useful for testing the response of the shielding and veto system to realistic neutron fields. However, the corresponding absolute rates remain site dependent. A future DESY-specific characterization of the gamma field, ground and nearby materials, local structures, and neutron environment is needed before the same source inventory can be converted into a BabyIAXO site prediction.

6.3.3 Detector background data and operational constraints

Detector data are used primarily to validate the reconstruction and to constrain operational background mechanisms. The surface-veto validation uses the published IAXO-D0 prototype data set [17]; the HENSA-driven simulations are used to study the neutron response of the selected three-layer design-study geometry; and environmental gamma or material-produced neutron studies are retained as source-specific checks until their DESY normalization is fixed. This separation avoids mixing measured detector performance, simulated source transport, and site-dependent absolute fluxes into a single number without stating the assumptions behind it. The historical response scale in Appendix B.6 is therefore built from explicit scenario choices and upper bounds rather than from an implicit combined fit to detector data.

The LSC IAXO-D1 data sets also show why the material model must be complemented by operational background studies. The detector was operated inside a 20 cm lead shield with a calibration source, nitrogen or radon-free-air flushing inside the shielding, and evolving gas recirculation and buffer configurations [78, 118, 119]. Those measurements showed that changes in gas handling and radon suppression can affect the alpha and low-energy backgrounds substantially, even when the solid materials have been selected for radiopurity. Consequently, the background model separates intrinsic material radioactivity from radon-related and surface-contamination components, rather than absorbing all observed low-energy events into a single material-activity term.

6.4 Intrinsic background

6.4.1 Gas-borne and radon-related contamination

The IAXO Micromegas detector is designed to operate with either an argon-based gas mixture or a xenon–neon-based gas mixture. Because the active gas is the interaction medium, its isotopic composition and any gas-borne radioactive contaminants must be treated separately from the solid detector materials. Common gas impurities such as oxygen and water affect electron attachment, gain stability, and energy calibration, but their concentrations and natural isotopic composition do not make them relevant radioactive-background sources. The radiological gas model is therefore dominated by two classes: intrinsic radioisotopes in the gas itself and radon-related activity introduced by emanation, leaks, or recirculation.

For argon mixtures, the relevant intrinsic isotope is \(\ce {^{39}Ar}\), a beta emitter with \(Q_{\beta }=565~\mathrm {keV}\) and \(T_{1/2}=269~\mathrm {y}\). Natural atmospheric argon has a measured \(\ce {^{39}Ar}\) specific activity of \(1.01\pm 0.08~\mathrm {Bq}\,\mathrm {kg}^{-1}\) of natural argon [120]. The absolute rate therefore scales with the gas inventory and with the choice of atmospheric or underground argon; low-radioactivity underground argon has been measured to suppress \(\ce {^{39}Ar}\) by a factor \((1.4\pm 0.2)\times 10^{3}\) relative to atmospheric argon [121]. \(\ce {^{39}Ar}\) beta decays generally produce extended ionization tracks rather than compact few-keV X-ray-like clusters, and legacy selectors consequently predict strong rejection. The conservative reference nevertheless credits no learned topology-rejection factor until this source is rescored with a detector-domain-validated selection.

\(\ce {^{85}Kr}\) provides a second gas-borne beta-decay scenario for argon-based operation when krypton traces remain in gas distilled from air. Its half-life is \(10.7~\mathrm {y}\), with \(Q_{\beta }=687~\mathrm {keV}\), and its activity can vary strongly between gas batches and handling histories. The GERDA collaboration measured a \(\ce {^{85}Kr}\) specific activity of \((0.36\pm 0.03)~\mathrm {mBq}\,\mathrm {kg}^{-1}\) in an atmospheric liquid-argon batch, while also noting the broader atmospheric and experiment-dependent variability of this isotope [122]. The \(\ce {^{85}Kr}\) simulation is therefore treated as a scenario component normalized by an assumed gas activity, not as a fixed property of the detector materials.

Radon must be handled differently from ordinary material-chain activity. As a noble gas, \(\ce {^{222}Rn}\) can escape from surrounding materials or gas-system components and break secular equilibrium with the parent uranium chain. Its concentration in the detector volume is consequently an operational quantity, set by emanation, leaks, flushing, recirculation, and gas purification rather than by the bulk activity of a single detector material. The most relevant isotope for this model is \(\ce {^{222}Rn}\), with \(T_{1/2}=3.82~\mathrm {d}\). It acts first as a uniform gas source, but its daughters can become surface sources after ion drift or plate-out.

The separation between the radon components is important because each component has a different normalization. \(\ce {^{218}Po}\), the first short-lived daughter of \(\ce {^{222}Rn}\), is often positively charged after production and can drift toward the cathode under the detector field. Long-lived \(\ce {^{210}Pb}\), with \(T_{1/2}=22.3~\mathrm {y}\), can then remain on detector surfaces and is not generally in equilibrium with the instantaneous radon activity. For this reason, and following the surface-contamination concern motivating dedicated \(\ce {^{210}Pb}\) screening with Micromegas detectors [123], the model treats gas \(\ce {^{222}Rn}\), cathode \(\ce {^{218}Po}\), cathode \(\ce {^{210}Pb}\), and vessel or surface \(\ce {^{210}Pb}\) as separate source hypotheses. The source taxonomy is summarized in Table 6.7.

The gas and radon simulations resolve the detector response for distinct source locations. They use the fe55-shape1014-ld165-td063-bin234-v1 argon–isobutane reconstruction, including the maximum-track energy and 10 mm fiducial definition. Table 6.8 retains the source-filtered and reconstructed counts; the last column is an auxiliary transparent-topology diagnostic and receives no rejection credit.

For source activity \(A_s\), the physical response is \[ B_s=\frac {A_s}{\Delta E\,A_{\mathrm {fid}}} \frac {N_{\mathrm {sel},s}}{N_{\mathrm {parent},s}}. \] Here \(N_{\mathrm {parent},s}\) counts generated parent decays before event filtering, with the simulated chain segment specified. The preserved count table does not establish that denominator. The earlier conversion using stored entries is therefore not retained as a per-becquerel result; subsequent analyses require an explicit generated-parent ledger, and chain subevents retain their common parent identity for uncertainty estimation.

The activity inputs can nevertheless be stated independently of detector acceptance. The 235.62 cm³ active volume at 1.4 bar, 20 °C, and \(99\%\) argon corresponds to approximately 5.35 × 10⁻⁴ kg of argon. Table 6.9 separates the literature benchmarks from operational radon and surface-contamination hypotheses.

Surface contamination requires an implantation-depth or plate-out distribution as well as an activity. Short-lived daughters need not remain at the original gas-decay position, and long-lived \(\ce {^{210}Pb}\) is not in equilibrium with the instantaneous radon concentration. Existing alpha and gas-handling controls can constrain these source classes without fitting each activity independently to the sparse X-ray background data. Representative ionization topologies are shown in Appendix C.3.

6.4.2 Detector materials

The detector materials are selected and screened with particular attention to components close to the active gas volume, where low-energy photons or charged particles can reach the Micromegas readout with little additional attenuation. For the background model, the most relevant material classes are:

• Copper: the main chamber and local shielding material, also present near the readout plane and in some electronics structures.
• Lead: the passive shielding material. General-purpose lead can contain substantially larger \(\ce {^{210}Pb}\) activity than the copper chamber, so the detector-facing lead layers are treated explicitly.
• Stainless steel: a structural material for supports, platform elements, and beamline connections. It is minimized near the sensitive volume and treated mainly as a geometry- and screening-dependent source.
• Kapton: a polymer used in the Micromegas readout plane and flex structures. Its radiopurity is important because it is close to the charge-collection region.
• PTFE: an insulating and low-outgassing polymer used in detector components close to the sensitive gas volume.
• Aluminized PET: the thin entrance-window/cathode material above the central region where focused axion-induced X-rays are expected to convert.
• Front-end electronics materials: mixed PCB and component materials that must be close to the detector for signal integrity, but are difficult to represent with a single homogeneous radiopurity value.

The radiopurity program follows the low-background Micromegas experience from CAST and related detector developments, but the relevant activity vector is still component specific. High-purity germanium measurements at the Canfranc Underground Laboratory provide activities or upper limits for many candidate materials, including auxiliary components such as epoxies and glues. These screening inputs define source scenarios for the material response. A screening upper limit can set a conservative activity scenario, but its product with a simulated acceptance is not automatically a confidence bound on the total background. Uranium- and thorium-chain segments must be normalized independently unless secular equilibrium is demonstrated; an early-chain assay does not determine the late-chain or surface activity. For the copper and lead components, auxiliary standalone decay-transport simulations were also produced to verify the source construction before running the full detector-level background simulations. These diagnostics score photons and electrons as they escape the material volume, retaining their energy, exit angle, and parent depth. Each material/isotope configuration contains \(2\times 10^{8}\) generated decays, split into independently seeded simulation shards; the uncertainty bands in the figures are the corresponding Poisson statistical uncertainties after combining the shards. The plots are therefore used as transport and source-depth checks, not as standalone background-level estimates.

Copper parts

Electroformed copper has very high chemical purity, but the relevant background source is its residual radioactive content and activation history rather than its elemental purity alone. The copper source inventory includes \(\ce {^{60}Co}\), \(\ce {^{40}K}\), \(\ce {^{238}U}\), and \(\ce {^{232}Th}\). Among these, \(\ce {^{60}Co}\) is especially important because it can be produced by cosmic-ray activation. Its activity depends on the exposure history of the copper, and a surface experiment does not benefit from the long underground cooling periods available in some low-background facilities. The dedicated HENSA inventory in Section 6.7 observes 124 \(\ce {^{60}Co}\) products in \(1.39\times 10^{6}\) simulated neutrons. The same study finds more frequent production of shorter-lived copper isotopes; detector coupling determines their relative selected-event yields, while half-lives determine the time dependence.

In the detector-level simulations, copper is treated as a volumetric source of photons and electrons produced by the decay of the isotopes present in the material. The relevant detector-level question is not the MeV-scale spectrum of particles escaping the copper by itself, but the much smaller subset that reaches the gas, deposits energy in the 1–10 keV signal region, and survives the topology selection. The auxiliary decay-transport simulations therefore serve mainly as a consistency check on the source construction: photons can emerge from deeper inside the copper, while escaping electrons are concentrated close to the material surface. This behavior is shown in Figure 6.4, where the photon and electron escape spectra are shown together with the parent-depth distributions.

The production threshold and tracking step are distinct numerical controls. A 1 mm range cut is converted to a material-dependent secondary-production energy threshold; the configured 1 keV conversion floor does not by itself demonstrate accuracy at the 2 keV analysis threshold. Likewise, a 0.05 mm gas step limit does not replace a production-cut convergence test in copper, lead, the window, or gas. Selected-event yields and low-energy spectral shapes must be compared with tighter region-specific cuts before the material response is assigned a numerical convergence uncertainty.

6.4.3 Telescope and X-ray optics contamination

The telescope-side materials form a separate intrinsic-background source because they are not part of the Micromegas chamber, but they lie on the same optical axis as the focused solar-axion signal. Radioactive decays in the X-ray optics, telescope pipe, or nearby telescope support materials can therefore contribute photons that enter the detector through the magnet-facing aperture rather than through the surrounding shielding. This geometry is qualitatively different from the front-end electronics or shielding sources: most charged secondaries and off-axis photons are absorbed far from the gas volume, while a small fraction of gamma rays emitted into the telescope acceptance can travel along the bore and interact in or near the detector.

The current iaxo-simulations scaffold represents this source with a telescope-side generator volume, telescopePipeGeneratorVolume, and transports the emitted photons through the detector geometry using the standard REST detector-response machinery. It is nevertheless kept separate from the better-constrained intrinsic-background studies because the geometry is an optics-side approximation rather than a screened BabyIAXO optics model, and because the larger production has not yet been reduced with a fully clean, contract-specific analysis output for all files. The first rate-pilot production was generated for the \(\ce {^{238}U}\) and \(\ce {^{232}Th}\) decay chains. To make the calculation tractable, photons were emitted inside a \(15^{\circ }\) cone pointing toward the detector. This is an angular-biasing shortcut, not a physical collimation assumption. The pilot rates in Table 6.10 are therefore corrected by the isotropic-cone factor \[ f_{\Omega } = \frac {1-\cos (15^{\circ })}{2} = 1.70\times 10^{-2}, \] so that the quoted quantity is the contribution from that cone per becquerel of an isotropic telescope-side activity. The unsampled angular complement is not constrained: scattering in the pipe or shielding can redirect photons initially emitted outside the cone. A full isotropic prediction requires a complementary angular sample or a demonstrated bound on that contribution. A larger production has transported \(\ce {^{238}U}\), \(\ce {^{232}Th}\), and \(\ce {^{40}K}\) photon source terms, but it has not yet yielded a response-chain-consistent telescope-side result. The telescope-side component therefore remains open until the preserved transport output is reprocessed with a validated response snapshot and the deterministic reference selection.

The pilot establishes a detector-coupled transport path and the normalization of its restricted angular support. The event display in Figure 6.5 confirms that the simulated source can populate the detector through the intended telescope-side path, while the event counts in Table 6.10 guide statistical allocation within the sampled cone; they do not establish the contribution from ungenerated angles. Because the larger production has not yet been reprocessed with a clean, response-chain-consistent analysis output for all files, the telescope-side contribution is not folded into the current source-response budget or the historical response scale in Appendix B.6. The final conclusion on the X-ray optics contribution will depend on reprocessing the preserved raw outputs, replacing the generator approximation with the adopted optics-material activity model, and applying the deterministic energy, one-track, and fiducial reference selection. Any source-appropriate veto correction must be validated and reported separately; no BDT or other topology rejection is credited in the present thesis reference.

6.4.4 Front-end electronics

The front-end electronics constitute a special intrinsic-background source because they must be placed close to the Micromegas readout in order to preserve signal quality, while at the same time containing materials that are harder to radiopurify than bulk copper, kapton, or PTFE. This contribution was therefore treated separately from the generic copper and readout-plane contaminations. The simulation described here corresponds to the four front-end cards represented in the IAXO-D1 detector model, without including the flat cables or other service elements. The activity model follows the component-level radiopurity study of the BabyIAXO electronics, used here as a collaboration input rather than as an original measurement of this thesis [76, 124].

The simulated source regions were the four electronics-card bodies located near the Micromegas readout. For each card and each isotope, radioactive decays were generated uniformly inside the corresponding card volume and transported with the same Geant4 physics configuration used for the rest of the intrinsic-background model. The isotopes included in the present production were \(\ce {^{40}K}\), \(\ce {^{60}Co}\), \(\ce {^{137}Cs}\), the \(\ce {^{232}Th}\) chain, the \(\ce {^{235}U}\) chain, and the \(\ce {^{238}U}\) chain. The activities assigned to the four cards are summarized in Table 6.11. The optional contribution from the 10 \(\Omega \) resistors was not included in the nominal normalization because those components were not part of the original low-background board design considered in the reference electronics study.

The normalization was performed at the level of generated decays. For each isotope–card pair, the event weight was defined as \[ w_{i,c} = \frac {A_{i,c}}{N^{\mathrm {gen}}_{i,c}}, \] where \(A_{i,c}\) is the activity assigned to isotope \(i\) in card \(c\), and \(N^{\mathrm {gen}}_{i,c}\) is the number of generated decays in that production. This choice is important because only a small fraction of the decays produce a stored detector event, and normalizing to saved or reconstructed entries would bias the rate estimate. The production consisted of 24 isotope–card groups, corresponding to the six isotopes or decay chains in Table 6.11 for each of the four cards. In total, \(8.48\times 10^{9}\) decays were generated and \(2.71\times 10^{4}\) detector events were available for the analysis stage. The \(\ce {^{235}U}\) chain is the least efficient source in this detector model, and several \(\ce {^{235}U}\) jobs produced no saved detector event; those jobs were nevertheless retained in the normalization denominator.

The rates are expressed in the background units used throughout this chapter, \(\mathrm {counts\,keV^{-1}\,cm^{-2}\,s^{-1}}\), using the circular signal fiducial area \(r<1~\mathrm {cm}\) for the area normalization. This production predates the conservative thesis reference. Its historical post-cut branch applies the energy-binned X-ray topology cuts implemented by the electronics analysis, not the grouped cross-fitted BDT defined above; the BDT wording retained in some generated plot labels is legacy nomenclature. The result is therefore an auxiliary card-response estimate pending conservative-reference rescoring. In this window, before the legacy X-ray cuts are applied, the electronics-card contribution is \(4.54\times 10^{-8}~\mathrm {counts\,keV^{-1}\,cm^{-2}\,s^{-1}}\). The weighted sum of the few post-cut events is \(4.38\times 10^{-10}~\mathrm {counts\,keV^{-1}\,cm^{-2}\,s^{-1}}\), but this is a normalization diagnostic rather than a reported residual level because several constituent rows have at most two survivors.

The post-cut electronics comparison is limited by one or two survivors for several isotope chains. For \(\ce {^{238}U}\), one observed event corresponds to the normalization diagnostic \(3.56\times 10^{-10}~\mathrm {counts\,keV^{-1}\,cm^{-2}\,s^{-1}}\), but the reported result is the one-sided bound \(B_{\ce {^{238}U}}<1.40\times 10^{-9}\) at 90% confidence. The activity vector and component-level study still identify the ceramic capacitors as an important \(\ce {^{238}U}\)-bearing source, but the sparse legacy selection does not support a precise ranking of the surviving isotope contributions.

These results should be interpreted as the card-only electronics contribution for the current detector model and activity vector. They do not yet include flat cables, possible connector materials, or a detailed separation of the individual board components within each card volume. Those refinements are relevant for a future BabyIAXO background model because the activity is not uniformly distributed among components: the \(\ce {^{238}U}\) activity is concentrated mainly in ceramic capacitors, while resistors, diodes, and chips contribute different isotope mixtures. The card-only production provides a useful first estimate of scale, but its legacy selection and incomplete service-material geometry prevent the result from establishing that front-end electronics are subdominant in the conservative partial inventory.

6.4.5 Shielding

The lead shielding surrounds the detector and is the most massive component in the passive-shielding model. Most electromagnetic emissions from contaminants in the bulk lead are absorbed before reaching the detector. The relevant electromagnetic contribution therefore comes mainly from activity near the detector-facing surface, where photons or electrons can escape the lead and enter the copper and gas region. Neutrons produced in lead by spontaneous fission of \(\ce {^{238}U}\) or by \((\alpha ,n)\) reactions are treated separately because their penetration length and rejection mechanisms are different from those of charged electromagnetic secondaries.

The shielding model considers \(\ce {^{40}K}\), \(\ce {^{232}Th}\), \(\ce {^{238}U}\), \(\ce {^{235}U}\), and \(\ce {^{210}Pb}\). Among them, \(\ce {^{210}Pb}\) is the most distinctive lead contaminant because its activity depends strongly on the age and handling history of the lead. Its half-life, \(T_{1/2}=22.3~\mathrm {y}\), is short enough that old or underground-stored lead can have substantially reduced activity. Very low activity lead, including archaeological lead in some experiments, is therefore most valuable in the innermost shielding layers, where it has the largest effect on the detector-facing source term.

Figure 6.6 shows the segmented shielding geometry used for the detector-level production. The highlighted source region corresponds to the innermost lead layer, a \(10~\mathrm {mm}\)-thick lead shell and the part of the shield most likely to contribute to the Micromegas background. Supplementary escape-particle diagnostics in Appendix B.3 show surface-dominated emission, but do not bound the selected-event contribution from deeper lead. The 10 mm shell is therefore the scope of this result; successive depth shells are needed to demonstrate convergence of a full-lead electromagnetic prediction.

The present \(\ce {^{210}Pb}\) production generated decays in this innermost lead layer and normalized them to the activity assumption \(80~\mathrm {Bq\,kg^{-1}}\times 187.416~\mathrm {kg}=1.50\times 10^{4}~\mathrm {Bq}\). Its processed output uses a legacy readout-energy, \(15~\mathrm {mm}\) reconstructed-hit-centroid, and older topology-BDT definition. It is retained as a shielding-response estimate but is not compatible with the \(10~\mathrm {mm}\) maximum-track-centered contract. The completed sample corresponds to 262.5 days of this activity; the production bookkeeping is reported in Appendix B.3. After detector response and readout analysis, 1883 events remain in the fiducial \(2\)–\(7~\mathrm {keV}\) energy window. Only 196 of them have the reconstructed-hit centroid inside the \(15~\mathrm {mm}\)-radius signal region, and two events pass the full TPC/X-ray selection. This geometric check suppresses events that contribute a small reconstructed energy component to the fiducial readout region while the reconstructed charge distribution is actually centered outside the expected axion-window footprint. Because only two events survive, the \(\ce {^{210}Pb}\) shielding contribution is quoted as a one-sided 90% confidence upper bound, \[ B_{\ce {^{210}Pb}\ \mathrm {shield}} < 6.65\times 10^{-9}~ \mathrm {counts\,keV^{-1}\,cm^{-2}\,s^{-1}} . \] The bound uses the one-sided Poisson upper mean \(5.322\) for two observed events; it is not the upper endpoint of a central two-sided interval. This snapshot does not assign an independent prompt-veto rejection to \(\ce {^{210}Pb}\), because the current processed files do not contain scintillator-sensitive observables for this source.

The control production in which the detector-facing copper box was replaced by air gives five final TPC/X-ray survivors, corresponding to \(B=\left (7.15^{+7.88}_{-4.33}\right )\times 10^{-8}~\mathrm {counts\,keV^{-1}\,cm^{-2}\,s^{-1}}\) for the same \(\ce {^{210}Pb}\) activity. The higher central response is consistent with attenuation by the copper box, but five control survivors and two nominal survivors do not determine a precise suppression factor.

Additional electromagnetic shielding productions were generated for the activity assumptions \(A(\ce {^{238}U})=3.3\times 10^{-4}~\mathrm {Bq\,kg^{-1}}\), \(A(\ce {^{232}Th})=1.0\times 10^{-4}~\mathrm {Bq\,kg^{-1}}\), and \(A(\ce {^{40}K})=1.2\times 10^{-3}~\mathrm {Bq\,kg^{-1}}\). These activities are several orders of magnitude below the adopted \(\ce {^{210}Pb}\) activity, and their normalized detector-level contributions after the full TPC/X-ray selection are correspondingly small, as shown in Table 6.14.

Neutron production in the shield, for example by \(\ce {^{238}U}\) spontaneous fission or by \((\alpha ,n)\) reactions, is not included in Table 6.14. It is treated as a separate penetrating component because its source volume is the full lead shield rather than only the detector-facing electromagnetic layer, and because the rejection mechanism follows the neutron cascade and veto logic discussed in the external-neutron section. The dedicated full-lead \(\ce {^{238}U}\) spontaneous-fission neutron campaign has completed its transport and detector-response processing; its detector-level normalization is kept separate from the electromagnetic table while the \((\alpha ,n)\) source term is being defined.

6.5 Environmental background

Environmental components are photons and neutrons produced by the ground, structures, and materials near the detector; atmospheric cosmic-ray secondaries are treated separately in Section 6.6. For BabyIAXO, the current working scenario is an outdoor, on-surface DESY location [15, 67]. The results in this section are detector-response estimates using the available laboratory source terms and are not a final DESY environmental-background budget.

6.5.1 Environmental source model

Environmental radiation refers here to external photons and neutrons produced by the surroundings of the detector, rather than by radioactivity inside the detector materials themselves. This component must be separated from the intrinsic material background discussed above and from the cosmic-ray background discussed later, and it must be carried with an explicit maturity status because its absolute normalization remains site dependent. The first environmental simulations in this work were developed for an enclosed laboratory configuration in which nearby concrete walls, floor, and ceiling were plausible dominant sources of MeV photons and radiogenic neutrons. Those studies remain useful because they established the external-source workflow and the relevant angular distributions, but they are no longer the nominal site model for BabyIAXO. Under the current outdoor, on-surface DESY working scenario, the external field will depend on the ground, local structures, nearby materials, and the cosmic-ray component at the selected location. The results below should therefore be read as detector-response estimates normalized to the best presently available laboratory source terms, not as a final DESY environmental-background budget.

Concrete-emission source study

The historical concrete study modeled the natural radioactivity of construction materials through the main gamma-emitting families: \(^{40}\)K, \(^{232}\)Th, \(^{235}\)U, and \(^{238}\)U. For each isotope, decays were generated uniformly in a \(1~\mathrm {m}\)-thick concrete slab with effectively infinite transverse size. The auxiliary Geant4 simulation recorded particles that escaped through the surface facing the detector, including their type, kinetic energy, production depth, and exit angle. Only a small fraction of the decay products leave the material, so this two-stage approach avoids repeating the expensive transport through bulk concrete for every detector-response study.

The concrete calculation is not used as the final BabyIAXO source geometry, but it motivated two features that remain in the current detector-level simulations. First, it provides representative MeV-scale photon spectra and event topologies for environmental radioactivity. Second, it shows that the exit-angle distribution of escaping photons is close to the \(\sin (2\theta )\) law expected for particles crossing a surface from an approximately isotropic external field, with a small skew toward lower angles due to attenuation at large path length. The detailed concrete spectra and decay-chain diagrams are retained in Appendix B.1, while the older detector-level gamma and neutron diagnostics are collected in Appendix B.2.

External-field generator and normalization

The current detector-level environmental simulations use a compact spherical generator around the closed-pipe detector geometry, as sketched in Figure 6.7. Particles are launched from a sphere of radius \(R=5~\mathrm {m}\), with incidence angles sampled according to \(\sin (2\theta )\). For an isotropic scalar fluence rate \(\Phi \), the generated-primary rate is given by the projected area of the enclosing sphere, \begin{equation} R_{\mathrm {gen}} = \pi R^{2}\Phi . \label {eq:environmental-sphere-normalization} \end{equation} The angular projection is already included in this expression, so no additional mean-cosine factor is applied when converting the simulated events into a rate. The resulting events are transported with restG4 and then processed with the same detector-response and X-ray-like selection chain used for the other background components.

The background level is computed from the number of selected events \(N_{\mathrm {sel}}\), the number of generated primaries \(N_{\mathrm {gen}}\), the generated-primary rate \(R_{\mathrm {gen}}\), the energy-window width \(\Delta E\), and the signal fiducial area \(A_{\mathrm {fid}}=\pi (1~\mathrm {cm})^{2}\): \begin{equation} B = \frac {N_{\mathrm {sel}}}{N_{\mathrm {gen}}} \frac {R_{\mathrm {gen}}}{\Delta E\,A_{\mathrm {fid}}}. \label {eq:environmental-background-level} \end{equation} This area convention matches the central \(r<1~\mathrm {cm}\) signal region used for the X-ray-like comparison. If the older full-readout convention of \(36~\mathrm {cm}^{2}\) is used instead, the quoted values should be scaled down by a factor \(\pi /36\).

Environmental gammas

The environmental-gamma source represents the non-cosmic MeV photon field produced by natural radioactivity in the surrounding laboratory materials. In the present calculation, photon energies are sampled from the EnvironmentalGammas distribution, \(p(E)\propto E^{-3/2}\exp [-E/(1.5~\mathrm {MeV})]\), over \(0.25\)–\(10~\mathrm {MeV}\). The absolute rate is obtained from the Zaragoza NaI comparison in Figure 6.8. The simulated NaI response is matched to the measured deposited-energy integral between \(0.25\) and \(2.75~\mathrm {MeV}\), \(97.08~\mathrm {s}^{-1}\), which gives \(2.0039\times 10^{4}\) generated photons per measured NaI count. For this fixed spectral template, the resulting generator rate is \(1.945\times 10^{6}~\mathrm {s}^{-1}\), equivalent to a fluence of \(2.48~\mathrm {cm}^{-2}\mathrm {s}^{-1}\) under the adopted \(5~\mathrm {m}\)-radius source convention. Matching one NaI deposited-energy integral fixes the amplitude of the chosen template; it does not uniquely determine the incident spectrum. Alternative line-plus-continuum spectra can reproduce that integral while producing different low-energy leakage through the shielding. The auxiliary result also excludes incident photons below 0.25 MeV, above 10 MeV, and the open telescope path. A DESY-specific prediction requires spectral or radiation-map constraints and tests of those omitted regions.

The detector-level production used the closed-pipe geometry with the gas as the only sensitive detector, so that the result estimates the Micromegas background rather than the veto noise response. The campaign generated \(5.41\times 10^{10}\) photons and stored 83 gas-sensitive events. The 79 non-empty transport files were then post-processed with the standard detector-analysis chain. After the X-ray-like cuts, no event remains in the \(2\)–\(7~\mathrm {keV}\) reference window, so the quoted environmental-gamma contribution is a finite-statistics upper bound.

Environmental neutrons

The environmental-neutron treatment evolved during the background-model development. The first diagnostic simulations used a literature-based radiogenic-neutron spectrum for concrete, approximated by an evaporation-like distribution centered around the MeV scale [125]. Those simulations are still useful for illustrating how MeV neutrons can produce low-energy Micromegas deposits through capture gammas and secondary electromagnetic particles, but they are not used as the current normalization. The relevant physical sources of ambient neutrons are instead grouped as follows. First, radiogenic neutrons are produced by \((\alpha ,n)\) reactions in light elements and by spontaneous fission of uranium-series contaminants in concrete, soil, and shielding materials; these processes populate the fast component at the MeV scale. Second, the same radiogenic neutrons, together with cosmic-ray neutrons that scatter in the hall, floor, shielding, and nearby structures, can moderate down to epithermal and thermal energies. This moderated population produces the low-energy peak in the HENSA-derived environmental spectrum, near \(5\times 10^{-8}~\mathrm {MeV}\), while the fast radiogenic and room-return component gives the broader structure around \(1~\mathrm {MeV}\). Third, any remaining site-specific albedo or structure-scattered neutron field is absorbed into the measured HENSA residual rather than assigned to a separate analytic source.

For the present estimate, the neutron source term is the positive HENSA-minus-CRY residual below \(10~\mathrm {MeV}\). Figure 6.9 shows the Zaragoza indoor and outdoor residuals used for the detector-level production, together with one representative DESY indoor and outdoor HENSA spectrum based on the BERT unfolding. The full subtraction diagnostic, including the measured HENSA spectra, the normalized CRY component, and the signed residuals, is provided in Appendix B.2, Figure B.10. This residual is a model-dependent decomposition of the measured scalar fluence, not a separately measured radiogenic field. Unfolding, cosmic-model, moderation, and angular uncertainties all enter the subtraction; replacing negative bins by zero biases a noisy residual upward. Correlated unfolded bins must therefore be propagated before the difference is used as a quantitative site comparison. The corresponding Zaragoza integrated fluxes are \(3.61\times 10^{-3}~\mathrm {cm}^{-2}\mathrm {s}^{-1}\) for the indoor spectrum and \(5.81\times 10^{-3}~\mathrm {cm}^{-2}\mathrm {s}^{-1}\) for the outdoor spectrum; the DESY BERT indoor and outdoor residuals give \(5.38\times 10^{-3}\) and \(4.99\times 10^{-3}~\mathrm {cm}^{-2}\mathrm {s}^{-1}\), respectively. The Zaragoza residuals are propagated with the same spherical-source normalization of Equation 6.6 and the same \(\sin (2\theta )\) incidence law used for the environmental-gamma production. This construction overlaps the full outdoor HENSA field used later as the nominal cosmic-neutron source. The two must not be added: an additive site model must choose either the full HENSA field or a matched decomposition into a CRY cosmic component plus the HENSA-minus-CRY residual. The environmental residual is therefore retained here as a diagnostic site-transfer decomposition rather than as an additional neutron term beside the full HENSA source.

The processed residual-neutron statistics combine the original sparse residual pass with the closed-pipe \(300\times 3~\mathrm {h}\) extension completed on 14 May 2026. After detector reconstruction, 703 indoor-residual events and 626 outdoor-residual events are available for the selection study. The final X-ray-like selection is still limited by one indoor event and zero outdoor events, so the last rows of Table 6.15 should still be interpreted with finite-statistics confidence intervals rather than as precise rate measurements.

Current detector-level results

Table 6.15 and Figure 6.10 summarize the current detector-level environmental-background estimates in the \(2\)–\(7~\mathrm {keV}\) reference window. The selections are applied progressively: first the fiducial reconstructed energy window, then a basic topology preselection, and finally the legacy X-ray-like cuts used for this environmental-response comparison. These rows have not yet been rescored with background-analysis-v2-conservative-reference and are therefore auxiliary site-transfer estimates rather than entries in the partial inventory.

The NaI-normalized environmental-gamma sample has no event after the legacy X-ray-like selection, giving the exposure-limited bound \(B_{\gamma }<5.28\times 10^{-6}~\mathrm {counts\,keV^{-1}\,cm^{-2}\,s^{-1}}\) at 90% confidence. Because this bound is above the intended background scale and the selector is legacy, the result does not establish that environmental gammas are negligible. The indoor residual-neutron sample has one selected event and is reported as \(B_{\mathrm {indoor}\,n}<9.34\times 10^{-8}~\mathrm {counts\,keV^{-1}\,cm^{-2}\,s^{-1}}\) at 90% confidence. The outdoor residual-neutron sample is presently only an upper limit after cuts, \(B_{\mathrm {outdoor}\,n}<9.79\times 10^{-8}~\mathrm {counts\,keV^{-1}\,cm^{-2}\,s^{-1}}\) at 90% confidence. The main systematic limitation for both source components remains the site normalization: the gamma field should ultimately be replaced by a DESY-specific measurement or radiation map, and the residual-neutron spectra should be revisited once the selected BabyIAXO site and its boundary conditions are fixed.

6.6 Cosmic-ray background

The surface operation of BabyIAXO makes cosmic-ray secondaries a central part of the external-background model. The relevant components are muons, neutrons, protons, gamma rays, and electrons/positrons. They are treated as separate source components because their spectra, angular distributions, detector-facing rates, and veto signatures are physically different. Muons are the dominant penetrating charged component at ground level and are expected to be controlled mainly by the prompt active veto. Neutrons are the most subtle component: they are neutral, penetrate shielding efficiently, and can produce low-energy Micromegas deposits through hadronic cascades, capture or de-excitation photons, electromagnetic descendants, and delayed activation products. Cosmic gamma rays, electrons/positrons, and protons are expected to be subdominant, but they are included to close the surface-cosmic source inventory and to test whether non-muon, non-neutron atmospheric secondaries can populate the \(2\)–\(7~\mathrm {keV}\) Micromegas region after detector-response processing.

The source-yield comparison uses the deterministic energy, one-track, and \(10~\mathrm {mm}\) maximum-track-center definition for Guan muons, the three light CRY components, and both timing channels of the HENSA outdoor-neutron field. The 249 selected neutron histories are joined to their transport ancestry, separating 246 prompt/non-delayed candidates from three delayed activation events. A higher-statistics historical sample supplies supplementary mechanism diagnostics. The learned topology selector is not credited, while deterministic reconstruction and fiducial acceptance remain conditional on the simulated detector response. Campaign exposure and source-angle conventions must close independently before these yields become absolute rates. Appendix B.8 records the preserved generated and selected event counts.

6.6.1 Cosmic source components and normalization

Cosmic-ray source terms are normalized at the level of generated primaries rather than at the level of saved or reconstructed events. For an incident component with generated-primary rate \(R_{\mathrm {gen}}\), the detector-level background level after a selection is computed as \begin{equation} B = \frac {N_{\mathrm {sel}}}{N_{\mathrm {gen}}}\, \frac {R_{\mathrm {gen}}}{\Delta E\,A}, \label {eq:background-cosmic-normalization} \end{equation} where \(N_{\mathrm {gen}}\) is the number of generated primaries, \(N_{\mathrm {sel}}\) is the number of reconstructed events surviving the selection, \(\Delta E=5~\mathrm {keV}\) for the \(2\)–\(7~\mathrm {keV}\) reference window, and \(A\) is the detector area associated with that selection. This convention keeps the physical source normalization independent of the detector-response filtering and of the number of events saved by restG4. For the current cut-flow tables, the pre-fiducial rate stages use the full \(6\times 6~\mathrm {cm}^{2}\) readout area, \(A=36~\mathrm {cm}^{2}\), because no central-radius requirement has yet been applied. Beginning with the fiducial column, the normalization area is the \(10~\mathrm {mm}\)-radius axion-window region, \(A_{\mathrm {fid}}=\pi (1~\mathrm {cm})^{2}\).

For the muon sample, integration of the Guan parametrization over 0.2–5000 GeV and the downward hemisphere, with \(2\pi \sin \theta \) applied once, gives a scalar fluence rate of \(1.7223\times 10^{-2}~\mathrm {cm}^{-2}\mathrm {s}^{-1}\) [104]. Its conversion to generated primaries requires the projected generation surface of each campaign. The historical cut-flow calculation used \(\pi (5~\mathrm {m})^{2}=78.54\,\mathrm{m}^{2}\), whereas a read-only check of one preserved May 17 campaign file records 9.93 m². These surfaces cannot be interchanged: the former reproduces the previously quoted 65.2 h muon exposure, but does not establish the exposure of every archived file. The results below therefore report selected-event yields per generated primary; no absolute muon bound is inferred from either unverified surface choice. The local Guan source configuration also emits only negative muons. Although penetrating energy loss is similar for the two charges, stopping negative-muon capture changes neutron and activation production, so a charge-composition check is required before interpreting the sample as the complete \(\mu ^{\pm }\) field.

The neutron energy distribution originates from the outdoor HENSA unfolding extending to 10 GeV [126]. The production configuration restricts incident neutrons to energies above 1 MeV; lower-energy descendants are transported, but lower-energy incident neutrons are a separate source contribution. HENSA constrains an energy-dependent scalar fluence, not an angular distribution. The assumed downward law \(p(\theta )=3\sin \theta \cos ^{2}\theta \) must therefore be distinguished from the measured spectrum and from a horizontal crossing distribution. The historical Cosmics adapter divides histogram bins by the cosine of the zenith-bin center. Applied to a scalar-fluence histogram without compensating encoding, this changes the continuous angular law to \(2\sin \theta \cos \theta \) and increases its integral by a factor of \(3/2\). Consequently, an angular correction requires event weights or new transport; dividing every surviving background level by \(3/2\) would ignore the angle dependence of shielding and veto response.

An explicit source-construction check separates bin-integrated fluence from densities in \(\ln E\) or \(\log _{10}E\), encodes the inverse-cosine adapter, and preserves the input and output hashes. For an isotropic scalar field \(\Phi =\int I\,\mathrm {d}\Omega \), the sphere crossing rate is \(\pi R^{2}\Phi \); a horizontal plane instead receives \(A\int _{\mathrm {down}}I\cos \theta \,\mathrm {d}\Omega \). The new generator-only geometric check reproduces the plane/sphere crossing ratio within \(0.26\) standard deviations in \(10^{5}\) trials. An independent check of the installed REST source reader restores every candidate histogram bin within \(9\times 10^{-15}\) relative precision and samples \(10^4\) neutrons both with and without the 1 MeV restriction. The sampled restricted-range acceptance, 0.51496, agrees with the histogram integral, 0.51409, and the unrestricted mean \(\langle \cos \theta \rangle =0.7504\pm 0.0019\) agrees with the declared angular law. This verifies the declared sampling convention, without replacing the missing archived-source provenance or validating the physical HENSA angular field. The preliminary DESY unfolding also retains pressure, solar-modulation, noise-selection, and unfolding-prior uncertainties [127]. For gamma rays, protons, and electrons/positrons, CRY is used as the current surface-cosmic source model.

6.6.2 Gamma-ray, electron, and proton mechanisms

Dedicated CRY configurations were prepared for surface photons, electrons/positrons, and protons. These components are retained to close the surface-cosmic source inventory and to test different routes to a low-energy Micromegas deposit. Cosmic gamma rays are neutral at generation, so they contribute to the Micromegas only after Compton scattering, pair production, or an electromagnetic shower in the shielding or detector materials. Electrons and positrons are charged and can produce prompt veto activity, but they also radiate bremsstrahlung photons that initiate secondary electromagnetic deposits. Protons are charged hadrons; if the primary or a charged secondary reaches the scintillator system it tends to give a prompt high-ionization veto response, while the hadronic cascade itself remains a useful control sample for neutron-like secondary production.

Truth-history classification confirms that gamma- and electron-induced TPC deposits are overwhelmingly electromagnetic: in the higher-statistics gamma diagnostic, secondary electrons or positrons dominate \(98.8\%\) of events with a non-zero Micromegas signal. The proton response is more mixed, combining electromagnetic descendants with proton recoils, charged cascade particles, neutrons, and nuclear fragments. The detailed classification, detector-response cut flow, and representative event displays are retained in Appendix B.9. These diagnostics support the mechanism interpretation, but none supplies topology or veto-rejection credit to the conservative reference.

6.6.3 Current cosmic-ray cut flow

Table 6.17 reports the selected-event yield per generated primary after the common energy, one-track, and fiducial requirements. This quantity isolates the reconstructed response from the unresolved conversion of incident phase space to physical exposure. The samples use the \(\ce {^{55}Fe}\)-tuned reconstruction; agreement of that response with the relevant detector data remains a separate uncertainty even though no learned topology rejection is credited.

No muon event survives the fiducial requirement in the \(3.17\times 10^9\)-primary sample. The corresponding event-yield upper bound is \(7.25\times 10^{-10}\) per generated muon at 90% confidence. The track-position diagnostic in Appendix B.9 explains this rejection, but a bound in physical background units requires the campaign-specific area and source normalization described above. Further muon production should follow that normalization check and a charge-composition control. The absence of a delayed ancestor in the audited muon survivors is not evidence that muon-induced activation is identically zero.

The legacy prompt-veto overlay applied to the 246 prompt neutron candidates leaves 22 entries in its first fixed draw, with a central 90% population range of 19–25 across 200 overlays. These counts illustrate sensitivity to accidental activity; they do not establish a physical-window-corrected neutron rejection efficiency. The acquisition-window and calibrated-energy qualifications in Chapter 5 apply before such a veto factor can enter the physical background model. The full historical topology/veto cut flow remains an auxiliary diagnostic in Appendix B.9.

6.6.4 Cosmic-ray event classes and veto survival

The source-by-source background rates do not fully describe how cosmic-ray events appear after reconstruction. For the background model, however, the role of the detailed event-history studies is deliberately limited: they diagnose why any future validated survival treatment must remain source and timing-channel dependent. The detector-level interpretation of prompt muon tags and late-window neutron-sensitive observables, together with the comparison with experimental IAXO-D0 veto data, is given in Chapter 5. The truth-history classification used to support that interpretation is presented in Fig. 5.6 of Chapter 5.

The relevant distinction is that cosmic-ray sources do not survive the analysis for the same physical reason. Muon-induced events usually carry a prompt, high-amplitude, multi-panel scintillator signature. Their residual contribution after the prompt veto is therefore expected to be dominated by atypical cases: inefficient regions, unstable or disabled channels, weak prompt deposits, or secondary particles produced by the muon in the surrounding materials. Neutron-induced events are less direct. The neutron-history study in Fig. 5.6 shows that the largest class of TPC-depositing neutron events is produced by electromagnetic descendants rather than by a primary neutron scattering elastically in the gas. This explains why a neutron-initiated event can look X-ray-like in the Micromegas while still leaving late-window, multiplicity-rich, or spatially diffuse veto activity in the scintillator–cadmium system. There is also a delayed-activation tail in which the neutron produces an unstable residual nucleus and the low-energy TPC event occurs only when that product decays. This channel is not mitigated by tightening the veto selection, because the correlated scintillator activity belongs to the original neutron interaction rather than to the later Micromegas trigger. The dedicated discussion in Section 6.7 quantifies this effect under the conservative reference and retains the larger legacy sample only as a mechanism diagnostic. The apparent reduction of the delayed channel by the legacy Micromegas topology selector is not credited in the conservative result.

This separation keeps the background-model chapter focused on the source inventory and rate construction. The veto observables enter here as reconstructed selections and efficiencies, not as truth-level labels. Consequently, each rate should be read under the explicitly documented Micromegas selector and source-dependent veto treatment. A conservative-reference prediction is the target of the registry, not an assumption applied retrospectively to the legacy rows. The event-history diagnostics remain essential, but their detailed presentation is retained in Appendix B.5, where truth-level mechanisms are kept separate from the source-normalized rate accounting presented here.

6.6.5 Cosmic-induced veto activity and random coincidences

The same surface-cosmic simulations can also be used to estimate the rate of veto activity that is unrelated to an otherwise signal-like Micromegas trigger. This contribution is not a background level in the Micromegas region of interest. It supplies an accidental-veto input for estimating the chance coincidence of unrelated activity with an X-ray-like event. The relevant quantity is therefore the visible veto-trigger rate, defined here as the rate of simulated cosmic events with at least one reconstructed rawPeaksVETO peak after the full detector-response chain. This definition includes the same quenching, light attenuation, waveform shaping, digitization, baseline correction, and peak threshold used for the background cut flow. Events with no reconstructed veto peak are not counted as veto-noise triggers, because they would not be observable as veto activity in the analysis.

Dedicated veto-noise productions were generated for muons, neutrons, gammas, protons, and electrons/positrons, with the TPC and veto scintillators treated as sensitive volumes. The normalization uses the equivalent physical time of each generator sample, while the numerator counts only events with at least one reconstructed veto peak. Approximating each visible event as a point trigger with independent Poisson arrivals gives the probability of at least one trigger in a window \(\Delta t\): \begin{equation} P_{\mathrm {cosmic\,veto}}(\Delta t) = 1 - \exp \!\left (-R_{\mathrm {veto}}\Delta t\right ), \label {eq:background-cosmic-veto-accidental} \end{equation} where \(R_{\mathrm {veto}}\) is the event rate, not the rate of individual peaks. For a correlated peak train of finite duration, the probability that any peak overlaps a randomly placed window also depends on the train timing; the point-trigger approximation does not capture that effect. Table 6.18 summarizes the current rate estimate.

The muon component dominates the accidental-veto rate because the surface muon flux is large and almost every saved muon event produces a reconstructed veto peak. The other components are much smaller, although gamma, electron/positron, and neutron primaries still produce visible veto-trigger rates at the level of tens of hertz in the present detector-facing geometry. The proton rate is lower after normalization to the generated physical time, despite the large fraction of proton events with visible veto activity.

Table 6.18 gives point-trigger occupancies, not rejection or dead-time probabilities for the published veto logic. They approximate signal loss for a rule that rejects any visible activity only when the point-trigger treatment is adequate; an operational efficiency requires the full peak or waveform timing, coincidence logic, and measured channel state.

Peak multiplicity, energy sharing, and panel occupancy are retained as supporting detector-topology diagnostics in Appendix C.2, Figures C.14 and C.16; they do not enter the absolute rate normalization. In particular, no \(m\geq 3\) peak-multiplicity requirement is applied to the rates or accidental occupancies reported here. Multiplicity is a diagnostic input to the separately calibrated multivariate veto selections described in Chapter 5, not a frozen standalone operating criterion.

Appendix Figure C.15 converts the visible veto-trigger rates into accidental probabilities over the full coincidence-window range. For short windows of order \(10~\mu \mathrm {s}\), all non-muon components remain below the percent level. At 100 µs, the corrected muon-induced occupancy is \(3.59\%\), while the other components remain below \(1\%\). At 1 ms, the muon occupancy reaches \(30.7\%\). This behavior is a useful reminder that the veto selection has two different effects: it rejects correlated cosmic backgrounds, but it also introduces an accidental live-time or signal-efficiency cost that depends directly on the chosen time window and on the visible veto-trigger rate.

6.7 Neutron-induced activation background

The selected veto geometry, including the cadmium sheets placed between plastic-scintillator stages, is defined in Chapter 5; that chapter also establishes the lead-cascade, moderation, prompt-recoil, and cadmium-capture mechanisms. For the background model, their principal consequence is an accounting rule: a prompt veto selection cannot be applied indiscriminately to every neutron-induced event.

The outdoor HENSA field is therefore partitioned into prompt, non-delayed histories and delayed-activation histories. In the latter, a neutron activates a nucleus in the detector or shielding and the Micromegas signal is produced by a later radioactive decay. The original interaction may produce veto activity, but the decay can occur long after the recorded coincidence window and therefore cannot receive prompt-veto credit. The delayed channel remains a separately normalized residual unless a validated Micromegas selection removes it.

The delayed-decay label is assigned from the saved Geant4 event history by following the parent chain of the gas energy deposits and requiring a RadioactiveDecay step more than \(100~\mu \mathrm {s}\) after the primary neutron interaction. The diagnostic cut flow, activation-product distribution, and representative delayed and prompt no-veto survivor displays are retained in Appendix B.5. For the rate model, the controlling point is that prompt-veto rejection cannot be assigned to the delayed branch.

The archived HENSA productions already transport the full hadronic and radioactive-decay chain, including the residual nucleus, its decay time, and the detector response of its descendants. The conservative-reference history audit therefore reuses the exact 249 detector-level candidates in Table 6.17 rather than introducing a second transport sample. For each candidate, every track depositing energy in the TPC gas is followed through its causal ancestry. Only a radioactive decay in that ancestry is classified as activation; an unrelated delayed decay elsewhere in the same simulated event is insufficient. The \(100~\mu \mathrm {s}\) boundary matches the subevent separation used in the production and is beyond the prompt coincidence regime considered for the neutron-sensitive veto. It is an analysis boundary between detector timing channels, not a definition of nuclear activation.

That detector-coupled audit is complemented here by an unbiased production inventory. The inventory calculation retained every primary and every residual-nucleus track, irrespective of whether the event later deposited energy in the TPC. One hundred independently seeded jobs generated \(1{,}390{,}753\) incident neutrons and inspected \(1.236\times 10^{8}\) Geant4 tracks. The historical 693.496 s exposure was parsed from a restG4 summary that divided by the full spectral integral without the configured energy-range acceptance. It is therefore not used here as a physical irradiation time. The inventory instead reports yields per generated neutron; converting these to production rates requires the corrected, campaign-specific source ledger. The residual-nucleus ledger contains \(2.876\times 10^{6}\) direct or secondary products and keeps them separate from \(1.447\times 10^{5}\) radioactive-decay descendants, thereby avoiding double counting a parent and its simulated daughter chain.

Table 6.19 summarizes representative products with operationally relevant half-lives. These are production counts, not selected background events. In particular, the campaign produced 124 \(\ce {^{60}Co}\) nuclei, corresponding to a central yield of \(8.92\times 10^{-5}\) products per generated neutron. This supports an isotope-level comparison within the simulated incident phase space; source-field and hadronic-model uncertainties remain separate from the counting precision. However, \(\ce {^{60}Co}\) is not the most frequently produced radionuclide: \(\ce {^{64}Cu}\) is produced approximately 24 times more often, and several lead, cadmium, and veto-material products also have larger yields. The background relevance of \(\ce {^{60}Co}\) depends on both production and detector coupling, while its long half-life determines buildup and persistence during cooldown.

For a constant production rate \(P_i\), zero initial inventory, retention in the production volume, and subsequent source-off cooldown, the activity of isotope \(i\) is \begin{equation} A_i(t_{\mathrm {irr}},t_{\mathrm {cool}}) = P_i\left (1-\exp [-\lambda _i t_{\mathrm {irr}}]\right ) \exp [-\lambda _i t_{\mathrm {cool}}], \qquad \lambda _i=\frac {\ln 2}{T_{1/2,i}}. \label {eq:background-neutron-activation-buildup} \end{equation} At saturation, \(A_i=P_i\), independently of the half-life. Decay-chain feeding requires a coupled Bateman calculation; for a well-mixed flowing gas, removal adds \(qN_i/V\) to the loss rate, where \(q\) is the volumetric flow and \(V\) the active volume. Initial cosmogenic contamination must be included as an initial inventory rather than counted again in the ongoing production term.

The decay-response calculation then generates each radionuclide at rest and uniformly within its observed production volume in the exact IAXO-D1 geometry. Repeated veto logical volumes are represented by six deterministic, approximately uniformly spaced physical placements. The complete radioactive chain, low-energy electromagnetic transport, atomic relaxation, REST detector response, and standard reconstruction are applied before the same conservative \(2\)–\(7~\mathrm {keV}\), one-track, and \(10~\mathrm {mm}\) fiducial selection used in Table 6.17. No prompt-veto rejection is applied.

The broad response screen includes every isotope–volume pair with at least 20 direct products, every pair in the gas or a detector-adjacent volume irrespective of its observed yield, and a set of long-lived priority products. It represents 194,581 of the 197,681 direct radioactive products in the inventory, or 98.4%, through 332 logical pairs and 769 physical source placements. Twelve \(\ce {^{10}C}\) source jobs in distant scintillator volumes terminated inside the Geant4 radioactive-decay transport; the remaining 757 jobs, covering 330 logical pairs, completed normally. This missing branch represents 156 production tracks and is retained as a small, explicitly unmodeled tail rather than assigned zero background.

The short screen generated \(4{,}676{,}940\) radioactive decays. Of these, 322 produced a saved TPC event, 321 entered the reconstructed feature tree, 75 satisfied the \(2\)–\(7~\mathrm {keV}\) and full-readout requirements, 50 also had one track in each projection, and none satisfied the final \(10~\mathrm {mm}\) fiducial requirement. This result shows that detector coupling, rather than radionuclide production, controls the required decay statistics. The component-wise bounds from the screen were therefore used only to allocate a high-multiplicity follow-up to the pairs that dominated continuous-saturation and five-year-plus-cooldown scenarios. Finite irradiation and cooldown scenarios are obtained by weighting each source response with Eq. 6.10.

The follow-up comprised 3,000 jobs allocated by the five-year-plus-cooldown ranking, 1,750 jobs allocated by the saturation ranking, 500 jobs covering every observed \(\ce {^{60}Co}\) production volume, and 450 jobs covering every observed \(\ce {^{58}Co}\) production volume. Every job completed successfully. Together with the broad screen, these campaigns generated \(1.035\times 10^{9}\) radioactive decays, of which 79,007 produced a saved TPC event, 78,678 entered the reconstructed feature tree, 17,433 passed the energy and full-readout requirements, 9,441 also passed the one-track requirement, and 73 satisfied the final fiducial selection. The selected sample contains 54 \(\ce {^{60}Co}\) decays and 19 \(\ce {^{58}Co}\) decays; no other screened isotope survived the complete selection.

The observed decay responses can be combined with production counts without assigning an unverified physical exposure. Define the selected-event yield per generated incident neutron as \[ y_{\mathrm {sel}}=\sum _{i,v}\frac {N_{i,v}^{\mathrm {prod}}}{N_{\mathrm {gen}}}\, \epsilon _{i,v}, \] where \(\epsilon _{i,v}\) is the simulated decay-selection response for isotope \(i\) in volume \(v\). The central saturation yields are \(4.47\times 10^{-11}\) for \(\ce {^{58}Co}\) and \(5.63\times 10^{-11}\) for \(\ce {^{60}Co}\) per generated incident neutron. Their sum is a production-volume model result for the sampled phase space, not an upper limit on every activation product. Once the incident rate is established, the corresponding background level follows from \(B=R_{\mathrm {gen}}y_{\mathrm {sel}}/(\Delta E A_{\mathrm {fid}})\).

\(\ce {^{58}Co}\) dominates the finite irradiation scenarios through five years followed by a 30-day cooldown. \(\ce {^{60}Co}\) supplies approximately 56% of the modeled saturation yield because of the product of production yield and detector coupling, and its 5.27 yr half-life makes that activity persist during cooldown. Coverage of 98.4% of produced radioactive nuclei does not imply the same coverage of accepted background: a rare product near the gas can couple more efficiently than a common product far away. The omitted isotope-volume tail and the six-placement approximation therefore require response-weighted bounds. The component-wise statistical envelopes are not a joint 90% interval. Bonferroni-adjusted isotope intervals are conditional on valid production and response marginals; cascade correlations and pilot-directed allocation must be included before asserting unconditional coverage.

The detector-coupled ancestry study provides a complementary result that preserves the actual production positions of the selected histories. Three of the 249 candidates are delayed activation: two \(\ce {^{64}Cu}\) decays following capture in copper and one \(\ce {^{41}Ar}\) decay following capture in argon. The remaining 246 histories are prompt or non-delayed, as shown in Table 6.17. For the separate delayed-channel bound, a predeclared one-sided 90% construction gives a selected-event-yield limit of \(1.40\times 10^{-9}\) per generated incident neutron under the simulated decay and selection assumptions. This conditional bound does not cover an ungenerated low-energy incident field or an unmodeled isotope response.

Both selected products are effectively saturated after 30 days of continuous irradiation in the retained-inventory model; after one day, their combined response reaches 82% of saturation. Longer-lived cobalt contributions are characterized by the dedicated volume study rather than inferred from their absence among three rare selected histories. Delayed activation remains a distinct source class with no prompt-veto rejection credit.

The higher-statistics legacy HENSA-neutron response audit is summarized in Table 6.23. The table reports the prompt non-delayed residual and delayed-activation upper limit as separate channels. The delayed branch is evaluated after the fiducial \(2\)–\(7~\mathrm {keV}\) and full TPC/X-ray topology selections, but without crediting any prompt veto rejection. The non-delayed branch uses the complete prompt selection chain: fiducial \(2\)–\(7~\mathrm {keV}\) readout energy, veto ML, X-ray BDT, and reconstructed-hit fiducial containment. In the photon-evaporation HENSA-neutron sample, the delayed component has no surviving events after the full Micromegas topology and reconstructed-hit fiducial selections, so it is retained as a separate \(90\%\) confidence upper bound.

Under the stricter legacy full Micromegas topology and reconstructed-hit fiducial-containment requirement, the delayed-activation component has no survivor. It is nevertheless kept as a separate upper-limit component because the prompt veto cut cannot be credited for rejecting it. The legacy response scale is therefore reported as two statements: \(B_{\mathrm {prompt}}=\left (2.63^{+1.37}_{-0.98}\right )\times 10^{-8}\) and \(B_{\mathrm {delayed}}<3.79\times 10^{-9}~\mathrm {counts\,keV^{-1}\,cm^{-2}\,s^{-1}}\), without combining them into a nominal 90% interval. These historical rate values retain their original source normalization and selector assumptions; neither has been promoted to an absolute current bound. The generated-event yields above provide the exposure-independent comparison.

6.8 Cosmic and activation background status

The quantitative cosmic result is the source-yield inventory in Table 6.17. Its six leaf channels retain the deterministic reference selection and their generated-primary denominators. The prompt-neutron overlay remains a conditional legacy veto diagnostic: the stored observables do not permit the full calibrated-energy feature to be recomputed in a corrected physical time window. No absolute post-veto background rate is credited, and delayed activation receives no prompt-veto rejection. The higher-statistics results in Table 6.23 are retained only for mechanism interpretation and historical accounting.

6.9 Status and uncertainty roadmap

The quantitative endpoint of this chapter is a partial IAXO-D1 argon source-response model under the deterministic contract in Table 6.2. It includes an incident-photon-denominator signal response, generated-primary cosmic yields, a separate time-dependent activation model, a 30-source provenance registry, and explicit statistical reporting conventions. Absolute source-rate promotion requires matched campaign ledgers and detector-response validation. A closed total additionally requires compatible intrinsic, material, environmental, and telescope-side responses with detector-specific normalization and complete source support. The BabyIAXO Xe–Ne detector, telescope optics, final veto, and DESY source terms constitute a separate projection and are not mixed with the IAXO-D1 reference.

The selector-incompatible historical response scale is retained in Appendix B.6. It identifies the physical mechanisms and normalization assumptions retained from the earlier source studies; invalid parent-decay conversions are omitted, and incompatible scenarios and selections are not summed. The scientifically defensible endpoint is therefore the conservative IAXO-D1 partial inventory together with the explicit open-component dispositions, not a single BabyIAXO background level.

The next quantitative step does not depend on finding another topology classifier. Work that can proceed without new physics input includes conservative-reference reprocessing of seven preserved source samples, source-specific validation of the prompt-neutron veto response, and regeneration of the partial inventory from machine-readable outputs. Closing the absolute IAXO-D1 inventory then requires detector-specific choices or measurements for the sixteen normalization-blocked sources and physical definitions for the seven source-model or geometry rows. The detailed analysis and source-model roadmap is retained in Appendix B.7; veto-specific uncertainties remain in Chapter 5. The BabyIAXO Xe–Ne, optics, final-veto, and DESY-site calculation must be constructed afterward as a separate contract rather than as an implicit correction to the argon reference. For each included source, the collaboration table should record the input normalization, geometry and configuration hashes, exposure or number of primaries, analysis identifier, surviving level, statistical interval, systematic uncertainty, and inclusion status. The registry and conservative contract make that extension auditable and prevent an omitted or incompatible component from being silently interpreted as zero.

Summary and Conclusions

This thesis develops the tools and physical interpretation needed to model backgrounds in the IAXO Micromegas detector program. Its main contributions are a simulation and reconstruction workflow, a study of the shielding and active veto for surface operation, and a source-resolved background inventory for IAXO-D1 in argon–isobutane. The IAXO-D0 measurements provide an experimental benchmark for the veto strategy. Together, these contributions support the future BabyIAXO calculation, whose xenon–neon response, optics, site environment, and final geometry must be evaluated explicitly.

From radiation transport to detector observables

The software work connects source generation, Geant4 transport, detector response, and reconstruction through REST-for-Physics and restG4. Versioned geometry generation enables comparisons of shielding thickness, veto layers, detector orientation, and channel layouts. The production and analysis tools make those comparisons practical at large simulation volumes while preserving the connection between physical inputs and reconstructed events. The published cosmic-ray injection method improves the efficiency of transporting particles toward a bounded detector geometry. Its application requires a precise distinction between directional intensity, horizontal-plane crossings, and scalar fluence; the geometric optimization does not remove that normalization requirement.

Common processing is valuable because it exposes disagreements in the quantities actually used for selection. It does not, by itself, establish agreement between simulation and data. The thesis therefore records the retained event representation, source denominator, reconstruction settings, and validation status for each response. Preserved transport can support further response studies when the required deposits, times, particle identities, and track information remain available. This is particularly important for nonlinear quenching corrections and for radioactive decays that share an incident parent but occur in separate time windows.

Surface backgrounds and the active veto

The neutron studies explain why increasing passive shielding alone is insufficient for a surface helioscope. High-energy neutrons interact in lead and generate secondary showers whose photons and charged particles can deposit X-ray-like energies in the gas. In the saved-history sample, electromagnetic descendants account for 62.8% of neutron-induced TPC events, whereas direct neutron interactions in the gas account for 5.0%. These are conditional fractions for the simulated source and geometry. They motivate tagging the surrounding shower and capture activity rather than attempting to identify the incident neutron solely from its TPC deposit.

The scintillator–cadmium design combines prompt shower detection with delayed neutron-capture signals. The simulated probability of any reconstructed veto tag increases from 0.465 with one layer to 0.741 with three and 0.771 with four. The diminishing increment supports three layers as a practical engineering choice, subject to the specified source and response assumptions. It does not establish a global sensitivity optimum: additional channels also affect threshold stability, accidental activity, cost, and operation. At sufficiently low expected background counts, these choices must be compared through a counting likelihood with signal acceptance and live time included.

The capture-time study identifies a post-trigger physical tail with a characteristic time of approximately 46.9 µs. A cumulative fraction of captures in a truth-time interval is distinct from the fraction of reconstructed pulses retained in a finite waveform. This distinction matters for the classifier comparison: the historical flat sample includes a small population of peaks outside the declared acquisition window. Removing their timing and multiplicity contributions leaves the nominal six-observable classifier decisions unchanged in the bounded frozen-model check, but changes decisions in a model that omits the total-energy feature. The stored total-energy scalar cannot be fully corrected without calibrated pulse or waveform information. Consequently, the hierarchy quantifies discrimination in the available response sample; it does not determine an absolute neutron efficiency or a universal ceiling on the benefit of a more complex model.

The measured IAXO-D0 result is stronger and more specific. In 52.1 d of surface data, the prompt veto removes \(201/257=78.2\%\) of the Micromegas-selected events. The advanced prompt/post-trigger selection removes a further \(7/56=12.5\%\), leaving a background level of \((8.56^{+2.30}_{-1.91})\times 10^{-7}\) counts keV⁻¹ cm⁻² s⁻¹ at 90% confidence. The complete veto retains 97.0% of the Micromegas-selected calibration sample. This establishes additional background rejection beyond the prompt selection. It does not identify the seven rejected events as neutrons, nor validate the later simulated classifier hierarchy on the same physical population. A neutron-efficiency measurement would require a matched source or an independently constrained mixture of backgrounds.

Background inventory and detector-response validation

The IAXO-D1 inventory separates the physical source strength from the probability that an incident particle produces a selected event. Its reference selection requires a reconstructed energy of 2–7 keV, one valid track in each projected view, and a reconstructed track center within 10 mm of the detector center. No learned topology rejection is credited. The retained energy, tracking, and fiducial requirements nevertheless depend on diffusion, charge sharing, gain, noise, and clustering; their efficiency remains part of the physical response to be validated.

The topology-transfer studies demonstrate why this distinction is necessary. The frozen candidate accepts 80.22% of an untouched simulated \(\ce {^{55}Fe}\) sample but only 13.85% of the measured R02756 transfer sample. A separate repair family reaches its nominal calibration working point for one candidate while retaining \(50/83=60.24\%\) of the independent background candidates. No candidate meets the declared validation requirements, and the reserved blind samples remain unopened. These negative results prevent simulated discrimination performance from being counted as an experimentally supported reduction of the background. Further classifier development is optional; validation of the deterministic response remains necessary.

The uniform-X-ray simulation provides the incident-photon denominator for the reference response, including losses before successful reconstruction. The selection accepts 24.49% of the flat 2–7 keV incident sample under its specified illumination and response model. This number is a simulation result for IAXO-D1, rather than an axion-spectrum-weighted BabyIAXO efficiency. The latter requires a response resolved in incident energy and position, folded with the solar spectrum and optical image. Absorption, geometric acceptance, and reconstruction losses already contained in that response must not be applied a second time.

The source audit identifies specific conditions needed to convert simulated yields into absolute background levels. Muon exposure requires the production geometry and the same angular and flux conventions as the source integral. The HENSA neutron field requires a consistent scalar-fluence measure, energy support, and generated-primary ledger. Gas and radon contributions require generated decay counts and a declared decay-chain convention; saved detector entries are not a substitute for that denominator. The remaining source records are therefore retained with explicit inclusion status instead of being assigned zero contribution or combined into a nominal total.

Neutron-induced activation

Activation is treated separately because the subsequent radioactive decay can fall outside the prompt veto window. A production inventory of \(1{,}390{,}753\) generated neutrons is coupled to broad and targeted decay-response simulations totaling \(1.035\times 10^{9}\) decays. The selected dedicated response contains 54 \(\ce {^{60}Co}\) and 19 \(\ce {^{58}Co}\) events. These counts establish simulated decay acceptances for the sampled materials and spatial distributions; an absolute production rate additionally requires the incident-neutron exposure to be validated. Coverage of most produced nuclei does not guarantee coverage of the accepted low-energy background, because rare products can have a larger detection probability.

The time dependence also separates isotope production from detector response. For constant production without feeding, the activity approaches the production rate at saturation, while the half-life controls the approach to saturation and the subsequent cooldown. Thus, the long half-life of \(\ce {^{60}Co}\) explains its persistence but does not itself increase its saturation activity. The final activation prediction must combine spatial production yields, decay acceptances, irradiation history, and the contribution of unmodeled products. No prompt-veto rejection is assigned to this delayed component.

Priorities for completing the prediction

The existing measurements are sufficient for useful response tests without expanding the experimental data set. The first priority is to recover immutable production metadata and close the source integrals before increasing Monte Carlo statistics. Small controlled simulations should then test production-cut convergence, gas and scintillator quenching, thermal-neutron treatment, capture cascades, and the effect of retaining full cosmic-shower correlations. The same frozen reconstruction and selection should be applied to each variation so that changes in accepted yield have a physical interpretation.

The next priority is to replay the preserved detector information with a consistent waveform window and calibrated pulse energies, and to validate energy migration, tracking, fiducial acceptance, and accidental-veto losses against the available runs. Independent calibration runs should test any response tuning; the final blind blocks should remain reserved for a predeclared evaluation. Only after these checks should larger campaigns target the source components whose statistical uncertainty materially affects the result. Zero-survivor samples should be planned and reported as limits with their generated exposure, rather than as negligible backgrounds.