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Abstract

The International Axion Observatory (IAXO) is designed to search for solar axions through magnetic conversion into X-rays. We developed simulation and background-reduction methods for its Micromegas detectors and BabyIAXO, the intermediate stage of IAXO.

We extended the REST-for-Physics and restG4 software packages to model radiation transport and detector response, including microscopic ionization, electron drift, amplification, and charge collection with Heed/Garfield++. We evaluated cosmic, environmental, and intrinsic background sources for the IAXO-D1 Micromegas prototype in argon–isobutane. Disagreements between simulated and measured observables and selection acceptance limit the use of simulation-trained classifiers on data; further response validation is required. Absolute rates require source activities and incident particle fluxes.

To reject high-energy neutrons and their showers in lead, we studied a plastic-scintillator–cadmium veto combining prompt activity with delayed capture signals. The simulations favor three layers under the assumed source and detector response. Neutron-induced activation is evaluated separately, without applying prompt-veto rejection to delayed decays.

In 52.1 d of surface data from the IAXO-D0 Micromegas prototype, the veto reduces the background in the 2–7 keV interval to \((8.56^{+2.30}_{-1.91})\times 10^{-7}\) counts keV⁻¹ cm⁻² s⁻¹ at 90% confidence, retaining 97.0% of the Micromegas-selected calibration sample. Additional rejection beyond the prompt veto is observed without identifying individual events as neutrons. Predicting the BabyIAXO background also requires its xenon–neon response, optics, final geometry, and radiation fluxes and material activities at DESY.

Resumen

El International Axion Observatory (IAXO) está diseñado para buscar axiones solares mediante su conversión magnética en rayos X. Desarrollamos métodos de simulación y reducción de fondo para sus detectores Micromegas y para BabyIAXO, la etapa intermedia de IAXO.

Ampliamos los paquetes de software REST-for-Physics y restG4 para simular el transporte de radiación y la respuesta del detector, incluyendo ionización microscópica, deriva, amplificación y colección de carga con Heed/Garfield++. Evaluamos fuentes de fondo cósmicas, ambientales e intrínsecas para el prototipo Micromegas IAXO-D1 con argón–isobutano. Las discrepancias entre los observables simulados y medidos y la aceptación de la selección limitan el uso de clasificadores entrenados con simulación en datos; todavía se requiere validar la respuesta. Las tasas absolutas requieren actividades de las fuentes y flujos de partículas incidentes.

Para rechazar neutrones de alta energía y sus cascadas en el plomo, estudiamos un veto de centelleador plástico y cadmio que combina actividad rápida con señales retardadas de captura. Las simulaciones favorecen tres capas bajo los supuestos de fuente y respuesta del detector. La activación neutrónica se evalúa por separado, sin aplicar el rechazo del veto rápido a las desintegraciones retardadas.

En 52.1 d de datos en superficie del prototipo Micromegas IAXO-D0, el veto reduce el fondo en el intervalo de 2–7 keV a \((8.56^{+2.30}_{-1.91})\times 10^{-7}\) counts keV⁻¹ cm⁻² s⁻¹ al 90% de confianza, conservando el 97.0% de la muestra de calibración seleccionada por Micromegas. Se observa rechazo adicional respecto al veto rápido, sin identificar los sucesos individuales como neutrones. Predecir el fondo de BabyIAXO también requiere su respuesta en xenón–neón, óptica, geometría final y los flujos de radiación y actividades de los materiales en DESY.

Contents

Introduction

The Standard Model of particle physics provides a 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 experiment must align a strong magnet with the Sun, focus any converted photons onto a small detector area, and identify a possible excess of keV X-rays above a 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 the IAXO experiment [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 studies the IAXO-D0 and IAXO-D1 Micromegas prototypes to inform the BabyIAXO detector design. 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.

The central experimental task is to identify the sources of X-ray-like background, evaluate how reconstructed observables reject these events, and measure the X-ray acceptance of the resulting selection. This requires following an interaction through charge collection, waveform reconstruction, and event selection. The relevant observables include energy, position, track multiplicity and shape in the TPC, together with prompt signals, delayed activity and panel multiplicity in the veto. They connect the detector measurements to the background prediction.

In this thesis, we address this task through three studies. First, we present methods for comparing measured and simulated events, including our contributions to REST-for-Physics, its Geant4 interface restG4, detector-response models, and large Monte Carlo production. Second, we study cosmic-ray backgrounds, particularly neutrons, and a multilayer plastic-scintillator–cadmium veto. We cover its optimization, waveform observables, construction, commissioning, and comparison with data. Third, we build a background inventory by source for IAXO-D1 in argon–isobutane using material radioactivity, environmental measurements, cosmic-ray models, and detector-response simulations. Predicting the BabyIAXO background additionally requires its xenon–neon response, focusing optics, final veto, and radiation fluxes and material activities at DESY.

These studies mainly use REST detector-response processes. We also developed a complementary model coupling Geant4, Heed, and Garfield++ to the same experimental readout and native REST reconstruction. Its refined version follows electrons through a local Micromegas field and assigns their anode arrivals to readout channels. We report numerical checks of this refined model separately from calibrated comparisons of earlier versions with data, examining reconstructed observables and selection acceptance.

The background simulations use these reconstructed observables whenever a detector-response calculation is available. This treatment is especially important for surface operation, where muons, high-energy neutrons, and secondaries produced in the shielding can leave X-ray-like deposits despite the passive shielding [17].

The chapters follow the progression from the physics motivation to detector technology, simulation methods, and background studies. Chapter 1 connects the axion and axion-like-particle motivation, the strong \(\mathrm {CP}\) problem, and the main experimental search methods to the solar helioscope technique and the IAXO experiment. The solar signal, conversion probability, helioscope figure of merit, and role of BabyIAXO establish the detector requirements and the experimental context of this work. Chapter 2 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. It closes by following detector signals to the X-ray candidates used in the analysis. Chapter 3 defines the common reconstructed observables, TPC baseline and multivariate selection method before comparing selection acceptance or applying the analysis to the veto and background studies. It also describes the simulation and reconstruction framework, detector-response chain, data production, visualization, and related software developments. Chapter 4 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 5 applies the common selection to the IAXO-D1 argon source-response model, including intrinsic, environmental, cosmic, and neutron-induced activation contributions, 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
Axion Searches and the IAXO Experiment

The absence of observed charge-conjugation and parity (\(\mathrm {CP}\)) violation in quantum chromodynamics (QCD) motivates the axion, a hypothetical particle associated with a mechanism that relaxes the effective QCD angle to zero. Its weak interactions and possible nonthermal production also make it a candidate for cold dark matter [8–10]. Axion-like particles (ALPs) extend the search to pseudoscalars whose masses and couplings need not satisfy the QCD-axion relation.

Stellar interiors can produce these particles, and laboratory magnetic fields can convert them into photons. Solar helioscopes use this combination to search for an excess of X-ray events during solar tracking. The progression from the CERN Axion Solar Telescope (CAST) to the International Axion Observatory (IAXO) and its intermediate stage, BabyIAXO, sets the efficiency and background requirements for the Micromegas studies developed in this thesis [13, 14, 18].

This chapter follows that progression from the particle motivation and search methods to solar production, magnetic conversion, and the IAXO experiment.

1.1 Axions and Axion-Like Particles

1.1.1 The Strong CP Problem and the QCD Axion

The strong \(\mathrm {CP}\) problem arises from an allowed interaction whose strength is not explained by the Standard Model. The most general QCD Lagrangian contains the following term, which violates parity and the combined charge-conjugation and parity symmetry, denoted \(\mathrm {CP}\):

Here, \(G_{\mu \nu }^{a}\) is the gluon field-strength tensor and \(\widetilde {G}^{a,\mu \nu }=\varepsilon ^{\mu \nu \lambda \rho }G_{\lambda \rho }^{a}/2\) is its dual. The remaining quantities are the strong coupling \(\alpha _{\mathrm {s}}\) and the quark mass matrix \(M_q\). The physical angle \(\bar {\theta }\) combines the bare QCD angle \(\theta \) with a phase from the quark masses. It describes a source of \(\mathrm {CP}\) violation distinct from the Cabibbo–Kobayashi–Maskawa phase observed in the weak interaction.

The neutron electric dipole moment (nEDM) tests this interaction experimentally. The 2020 measurement found a value consistent with zero and set the following upper limit [19]:

Hadronic calculations give \(d_n/\bar {\theta }\) of order \(10^{-16}\,e\,\si {cm}\), with a coefficient that depends on the calculation method [10, 20, 21]. The measured limit therefore requires \( |\bar {\theta }|\lesssim \mathcal {O}(10^{-10}) \). The Standard Model permits this small value but provides no symmetry that requires it once the quark masses are complex. The unexplained difference between this bound and a dimensionless angle of order unity constitutes the strong \(\mathrm {CP}\) problem. Proposed solutions include imposing fundamental \(\mathrm {CP}\) symmetry or modifying the light-quark sector. The Peccei–Quinn (PQ) mechanism instead makes the angle dynamical, linking its smallness to the existence of a new particle [8, 10].

In this mechanism, a global \(U(1)_{\mathrm {PQ}}\) symmetry is spontaneously broken at a scale \(f_a\) [1, 2]. The resulting pseudo-Nambu–Goldstone field \(a(x)\) couples to QCD through the anomaly of this symmetry. The effective interaction replaces the fixed angle in Eq. 1.1 by a field-dependent quantity:

Nonperturbative QCD generates a potential whose minimum satisfies \(\langle a\rangle /f_a=\bar {\theta }\). As the field relaxes to this minimum, the effective strong \(\mathrm {CP}\) angle vanishes. Fluctuations about the minimum constitute the axion [3, 4].¹

The curvature of this potential also determines the axion mass. Its relation to the PQ scale follows from the QCD topological susceptibility. Chiral and lattice calculations give [22, 23]

Equation 1.4 connects the solution of the strong \(\mathrm {CP}\) problem to the experimental difficulty of detecting the axion. A larger PQ scale produces a lighter axion with weaker interactions. Laboratory measurements excluded axions with \(f_a\) near the electroweak scale, while invisible-axion models with \(f_a\gg v_{\mathrm {EW}}\) remain viable. The searches discussed below therefore require sensitivity to particles that interact only weakly with the apparatus.

1.1.2 Interactions and Axion-Like Particles

The coupling to gluons removes the effective strong \(\mathrm {CP}\) angle, while interactions with photons, electrons, and nucleons provide ways to produce and detect axions. Their strengths depend on the particle model. For helioscopes, the photon coupling is especially useful because it connects production in a stellar plasma to conversion in a laboratory field. The corresponding interaction and its QCD-axion coupling are

Here, \(F_{\mu \nu }\) and \(\widetilde {F}^{\mu \nu }\) are the electromagnetic field-strength tensor and its dual. The constant \(\alpha \) is the electromagnetic fine-structure constant, and \(E/N\) is the electromagnetic-to-color anomaly ratio of the PQ current. The term \(1.92(4)\) describes the model-independent contribution from mixing with neutral mesons [10, 22]. The coupling \(g_{a\gamma }\) has dimensions of inverse energy. Together with Eq. 1.4, this expression ties the photon coupling to the axion mass for a given anomaly ratio. Different QCD-axion models therefore occupy a band in the \((m_a,g_{a\gamma })\) plane.

Figure 1.1 illustrates the two uses of this interaction in a solar helioscope. In the Primakoff process, a photon scatters in the microscopic Coulomb field of a charged particle and produces an axion. Thermal photons in the solar plasma can supply this source. In the laboratory, an axion traversing a macroscopic transverse magnetic field mixes coherently with the photon state over the field length. This conversion produces the X-rays sought by the detector [10, 24, 25]. A buffer gas can match the photon and axion momenta, keeping conversion amplitudes in phase along the magnet (Section 1.3).

The axion–photon coupling also allows spontaneous decay into two photons. In natural units, \(\hbar =c=1\), the 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 lifetime increases rapidly as the mass and coupling decrease. For the illustrative values \(m_a=1\,\mathrm{meV}\) and \(g_{a\gamma }=1\times10^{-14}\,\mathrm{GeV}^{-1}\), it is approximately \(4\times10^{34}\,\mathrm{yr}\). Decay is negligible on laboratory, solar-system, and cosmological timescales for this benchmark, so magnetic conversion provides the relevant detection process.

QCD axions and ALPs can be produced or absorbed through their electron coupling, which we write in pseudoscalar form as \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} Here, \(m_e\) is the electron mass. The electron coupling \(g_{ae}\) is dimensionless and depends on the model through \(C_e\).² Electron and nucleon couplings affect solar production, stellar energy loss, and interactions with a detector. When production and detection involve different couplings, a measurement constrains their product unless a model or an independent result fixes one of them.

The Kim–Shifman–Vainshtein–Zakharov (KSVZ) and Dine–Fischler–Srednicki–Zhitnitsky (DFSZ) constructions provide reference models for these interactions [27–30]. In the simplest KSVZ construction, a new heavy quark generates the anomaly; an electrically neutral heavy quark gives \(E/N=0\). DFSZ models couple Standard Model fermions through an extended Higgs sector, with \(E/N=8/3\) in the commonly used benchmark. These choices define useful lines in the mass–photon-coupling plane, but other anomaly ratios give different QCD-axion couplings.

ALPs extend the search beyond this mass–coupling relation. They are light pseudoscalars that can arise from approximate global symmetries, hidden sectors, or string compactifications without solving the strong \(\mathrm {CP}\) problem [31–34]. Their masses and couplings are independent parameters. The production and conversion processes in Figure 1.1 can therefore be used to search for both QCD axions and sufficiently light ALPs. The measured coupling limit can be interpreted either within a QCD-axion model or in the more general ALP parameter space.

1.1.3 Cosmological and Astrophysical Context

The axion field can also supply a cosmological population of particles. In the vacuum-misalignment mechanism, the field is initially displaced from the minimum of its potential after PQ symmetry breaking. When the expansion rate falls to approximately \(3H(T_{\mathrm {osc}})\simeq m_a(T_{\mathrm {osc}})\), it begins coherent oscillations. Here, \(H(T)\) is the Hubble expansion rate and \(T_{\mathrm {osc}}\) is the temperature at the onset of oscillations. Their energy density subsequently redshifts approximately as nonrelativistic matter, allowing nonthermal axions to form cold dark matter [9, 35].

The amount of dark matter produced in this way depends on the initial field and the cosmological history. If PQ symmetry breaking occurs before inflation and is not restored afterward, the observable Universe inherits one initial misalignment angle. Isocurvature constraints then connect the axion model to the scale of inflation. If the symmetry breaks after inflation, different regions begin with different angles, and axion strings and domain walls can contribute to the abundance. These alternatives allow different mass ranges and do not require axions to account for all dark matter.

Thermal production leads to a different cosmological signature. Sufficiently light and long-lived thermal axions contribute a hot relic component that affects the cosmic microwave background and the growth of large-scale structure. The inferred limits depend on the thermal history, the axion couplings, and the cosmological data sets used in the analysis [10, 36]. Their interpretation therefore requires a specified model.

Stars provide both potential axion sources and tests of their interactions. Axions that escape from a stellar interior carry away energy, changing the evolution predicted for the star. 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 [36, 37]. Comparisons of observed stellar populations or evolution with models including this energy loss constrain the relevant couplings. Each bound depends on the object, observable, and stellar-model uncertainties. Some observations have also been interpreted as cooling anomalies, providing targets for laboratory searches, although their significance does not establish evidence for axions.

The Sun offers a source whose interior is constrained by helioseismology and neutrino measurements. Its predicted axion emission can be tested directly by a helioscope, connecting stellar-production models to the experimental searches discussed next.

1.2 Experimental Searches

The source of the axions determines how an experiment can search for them. Photon-coupling searches use Galactic dark matter, particles produced in the laboratory, or emission from the Sun [10, 38, 39]. These sources lead to different apparatus, mass coverage, and assumptions.

Haloscopes search for nonrelativistic Galactic axions by converting them into photons in a magnetic field. Microwave cavities enhance the signal at resonance and scan axion masses by tuning their resonant frequency. Other technologies aim to extend the accessible mass range. The inferred coupling depends on the assumed local axion density and velocity distribution; a smaller axion fraction of the halo weakens the corresponding limit.

Light-shining-through-wall experiments produce ALPs from laser photons in one magnetic region and search for regenerated photons in a second region after an opaque barrier. Both production and regeneration occur in the laboratory, making the result independent of stellar-source and cosmological-abundance assumptions [40]. The combined probability scales as \(g_{a\gamma }^{4}\). The Any Light Particle Search II (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 \(0.1\,\mathrm{meV}\) [41].

Helioscopes use the solar plasma as a source of relativistic axions. A transverse laboratory magnetic field converts a small fraction into X-rays, which can be focused onto a detector. The signal is an excess correlated with solar tracking. This search depends on the solar-production and photon-conversion couplings and on the solar model, while requiring no local dark-matter axion population. CAST demonstrated this technique; IAXO and BabyIAXO extend the same approach [13, 14, 42].

Other experiments probe interactions with matter and remain sensitive when the photon coupling is suppressed. Low-threshold detectors search for axion absorption through electron couplings. The Cosmic Axion Spin Precession Experiment (CASPEr) uses nuclear magnetic resonance and spin-precession observables to probe oscillating axion-induced moments and fields, while ARIADNE searches for an axion-mediated spin-dependent force [38, 43]. Together with photon-coupling searches, these methods test different interactions and source assumptions.

Figure 1.2 places the photon-coupling searches in the mass–photon-coupling plane. It compares measured limits with design projections and the QCD-axion model band introduced above.

The haloscope searches reach benchmark QCD-axion sensitivity in selected mass intervals, whereas helioscopes test solar production over a broader range. The haloscope boundary is an envelope of measurements with different mass coverage and analysis assumptions, rather than a joint likelihood [10, 44]. The digitized CAST boundary provides an approximate representation of its mass dependence; Section 1.4.1 gives the published low-mass result. The BabyIAXO and IAXO projections show the reach expected under their published design assumptions [13, 14]. The stellar boundary provides another comparison: it uses the ratio of asymptotic-giant-branch to horizontal-branch populations in globular clusters and depends on the treatment of convective mixing [45]. Its astrophysical interpretation differs from the direct searches.

The solar-helioscope approach is the experimental setting of this thesis. The next section develops the solar spectra, conversion probability, and statistical sensitivity that determine how the magnet, optics, and detector contribute to the expected signal.

1.3 Solar Axions and the Helioscope Technique

1.3.1 Solar Axion Production and Energy Spectrum

The solar plasma can produce axions through interactions with photons and electrons. In the Primakoff process, thermal photons convert into axions in the electromagnetic fields of charged plasma constituents. The axion–electron coupling permits additional production through atomic axio-recombination and axio-deexcitation, electron–ion and electron–electron bremsstrahlung, and Compton-like scattering. These atomic, bremsstrahlung, and Compton contributions are collectively known as the ABC channels [26]. Figure 1.3 connects these production mechanisms to the common magnetic-conversion step used for detection.

The production mechanism determines which coupling combination can be measured. For Primakoff axions, production and detection each contribute a factor \(g_{a\gamma }^{2}\), giving a signal rate proportional to \(g_{a\gamma }^{4}\). For ABC axions, the rate is proportional to \(g_{ae}^{2}g_{a\gamma }^{2}\). A helioscope therefore constrains \(\lvert g_{a\gamma }\rvert \) through the Primakoff component and \(\lvert g_{ae}g_{a\gamma }\rvert \) through the ABC component. An independent constraint or a model relation is needed to separate the two couplings in the latter case.

The energy distributions determine the useful detector band. Figure 1.4 compares the benchmark Primakoff and ABC spectra.

The Primakoff spectrum peaks at a few kiloelectronvolts, within the reference Micromegas analysis interval of approximately 1–10 keV. The ABC spectrum is softer, making sub-kiloelectronvolt thresholds particularly useful for detectors such as GridPix and cryogenic sensors [47]. At the stated coupling, integration of the Primakoff tabulation over 0.01–20 keV gives a total flux \(\Phi _a=3.46\times10^{11}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}\) and a mean energy of \(4.14\,\mathrm{keV}\).

These tabulated spectra illustrate the relevant energy scales and relative rates. The solar-model and opacity inputs are not specified for the Primakoff tabulation used here, so an absolute signal prediction requires a separately defined solar model and its uncertainties. The comparison in Ref. [46] finds a Primakoff-flux difference of approximately 5% between solar models, in addition to the uncertainty within each model. At lower energies, longitudinal-plasmon conversion in solar magnetic fields supplies another \(g_{a\gamma }\)-dependent component and may dominate below approximately \(200\,\mathrm{eV}\), depending on the solar-field profile [48]. The continuum spectra shown here thus cover the few-kiloelectronvolt study developed in this thesis, while searches at substantially lower thresholds require a broader description of the solar source.

1.3.2 Axion–Photon Conversion in a Helioscope

A helioscope converts the solar flux into a signal correlated with the direction of the Sun. Axions entering its magnetic aperture can convert into X-rays through the inverse Primakoff effect. The optics concentrate these photons at the focal plane, while the tracking platform keeps the conversion region aligned with the Sun. The production and detection chain is summarized in Figure 1.3.

The conversion probability depends on whether the axion and photon waves remain in phase along the magnet. For a homogeneous transverse field \(B_\perp \) of length \(L\), neglecting photon absorption and using natural units \(\hbar =c=1\), it 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 factor \(\mathcal {F}\) describes the loss of coherence caused by the momentum mismatch \(q\): \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}

For a relativistic axion of energy \(E\) in vacuum, \(q \simeq m_a^2/(2E)\). When \(qL \ll 1\), the waves remain approximately in phase, \(\mathcal {F}\simeq 1\), and the conversion probability grows as \(B_\perp ^2L^2\). Increasing the axion mass increases the mismatch and suppresses this coherent enhancement.

A buffer gas changes the photon momentum at fixed energy, which is described by an effective mass \(m_\gamma \). The mismatch becomes \(q \simeq \lvert m_a^2-m_\gamma ^2\rvert /(2E)\), which vanishes near \(m_a=m_\gamma \); the vacuum expression follows by setting \(m_\gamma =0\). Equations 1.8 and 1.9 remain valid with this substitution when absorption is negligible. A quantitative gas-scan prediction must also account for photon absorption and density gradients [49–51].

For X-ray energies well above the atomic resonances of a low-\(Z\) gas, the effective photon mass is set by the 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 total electron density, including the bound electrons of a neutral buffer gas, and \(m_e\) is the electron mass. In the ideal-gas approximation at fixed temperature and composition, this density is proportional to pressure. A quantitative helium scan instead uses the appropriate equation of state and the density profile along the bore [50, 51]. Changing the density selects the resonant mass \(m_a\simeq m_\gamma \). Figure 1.5 shows the narrow interval restored at each density. A higher-mass search therefore divides the available tracking exposure among overlapping pressure settings, as in the CAST campaigns discussed below.

The detected spectrum combines the solar flux, conversion probability, magnetic aperture, efficiencies, and tracking exposure. For one detection line, the differential yield in true photon energy is \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}

The detector energy response relates the true photon energy \(E\) to the reconstructed energy. The instrumented aperture is \(A\), the optics and detector efficiencies are \(\epsilon _o\) and \(\epsilon _d\), and the effective tracking exposure is \(\epsilon _t t\). For a selected focal region, \(\epsilon _o\) includes the fraction of the solar image contained within that region. A multi-line helioscope sums the yields calculated with the field, aperture, and response of each line. This expression identifies the physical quantities that must be improved together to increase the accepted axion signal.

1.3.3 Buffer-Gas Scans and Mass Coverage

A vacuum campaign observes a broad interval of sufficiently small axion masses with the same magnet configuration. A buffer-gas campaign scans successive narrow mass intervals by varying the gas density. At each setting, the experiment records the tracking exposure and the gas conditions that determine the conversion probability. The CAST helium campaigns established this method of extending a helioscope search beyond the vacuum coherence range [50, 51].

The spacing between settings must preserve overlap between neighboring conversion resonances. For a fixed photon energy and homogeneous magnet, the argument of the coherence factor depends on \(m_a^2-m_\gamma ^2\). Its central maximum therefore spans a fixed interval in squared mass, while the corresponding interval in \(m_a\) becomes narrower at higher mass. In the ideal-gas approximation at fixed temperature, equal density or pressure increments give equal increments in \(m_\gamma ^2\). The actual settings must be obtained from the gas equation of state and the density along the bore, rather than from a uniform pressure-to-mass conversion alone. The range covered by a campaign consequently depends on both its accessible densities and the spacing chosen between them.

Figure 1.6 illustrates the relation between overlap and exposure using five density settings near \(m_a=0.10\,\mathrm{eV}\). The upper panel shows the conversion response of each setting. The lower panel combines their contributions for equal tracking exposures. For a homogeneous field with negligible absorption and unchanged optics and detector response, this exposure-weighted coherence factor is \begin{equation} \mathcal {R}_{\mathrm {scan}}(m_a,E) =\sum _j\frac {T_j}{T_{\mathrm {scan}}} \mathcal {F}\!\left ( \frac {\lvert m_a^2-m_{\gamma ,j}^2\rvert L}{2E} \right ), \qquad T_{\mathrm {scan}}=\sum _jT_j. \label {eq:helioscope-scan-response} \end{equation} Here, \(T_j\) is the effective tracking exposure at setting \(j\). The normalization compares the scan with an experiment that remains fully coherent at the trial mass throughout \(T_{\mathrm {scan}}\). Although each individual curve reaches unity at resonance, a trial mass benefits mainly from the exposure spent at nearby settings. Their weighted sum therefore retains the cost of dividing a finite observing time across a mass interval.

A real search integrates these responses over the solar spectrum and the energy-dependent acceptance in Eq. 1.11. Lower-energy photons lose coherence over a smaller squared-mass interval, so a spacing adequate at one energy need not give the same coverage over the full detector band. Photon absorption and density gradients further change the height and width of the conversion response. In CAST, the density profile varied with the gas conditions and magnet inclination, requiring a calculation of the effective conversion length [51]. These effects determine the signal expected at every trial mass and must remain associated with the exposure accumulated under each condition. If the density changes during a tracking run, the expected signal is obtained by integrating the time-dependent conversion probability over that exposure.

Events from neighboring settings can contribute to the same trial-mass likelihood, with their individual conversion probabilities and backgrounds. The gas-setting index is therefore part of the observing-condition index in Eq. 1.16 below. Spreading a fixed exposure across more settings extends coverage but reduces the time available near any one mass. This explains why the projected vacuum and buffer-gas reaches of BabyIAXO correspond to separate campaigns with specified exposure assumptions [14].

1.3.4 Experimental Figure of Merit

An increase in signal yield improves sensitivity only in relation to the background collected over the same exposure. In the background-dominated regime, this balance is summarized by the helioscope figure of merit (FOM) [13, 18]: \begin{equation} f = f_M f_{DO} f_T. \label {eq:helioscope-fom} \end{equation}

The magnetic, detector–optics, and tracking contributions 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}

The magnetic factor contains the total instrumented aperture \(A\) and its effective transverse field \(B_{\mathrm {eff}}\). For a uniform field, \(B_{\mathrm {eff}}=B_\perp \); for a nonuniform magnet, the coherent-limit quantity \(B_{\mathrm {eff}}^2L^2A\) represents \(\int _A\lvert \int _0^L\mathbf {B}_\perp \,\mathrm {d}\ell \rvert ^2\mathrm {d}A\). The detector–optics factor balances the detector efficiency \(\epsilon _d\) and optics throughput \(\epsilon _o\) against the areal background level \(b\) and selected focal area \(a\). The focal image includes both the optics point-spread function and the finite angular extent of the solar source. The final factor accounts for the tracking fraction \(\epsilon _t\) and elapsed run time \(t\).

Figure 1.7 distinguishes the two areas entering the FOM. The aperture \(A\) controls the axion flux entering the conversion region, while the selected focal area \(a\) sets the detector region over which background is counted. Optics connect these areas by concentrating the converted photons, with a signal efficiency that depends on the fraction of the focal image retained.

A larger magnetic aperture increases the converted flux, while efficient optics concentrate that signal onto a small detector region and reduce the number of background events admitted with it. Longer daily tracking increases the useful exposure. Since the Primakoff rate is proportional to \(g_{a\gamma }^{4}\), these gains translate into an approximate coupling sensitivity \(\lvert g_{a\gamma }\rvert \propto f^{-1/4}\). The small exponent makes coordinated improvements to all three terms especially valuable.

1.3.5 Sensitivity at Low Background

The background-dominated FOM applies when the conversion is coherent and the count distribution can be approximated as Gaussian. Its original derivation takes approximately ten or more expected background events as a guide [18]. The IAXO targets can yield only a few events, requiring an explicit treatment of Poisson statistics. For a uniform background over an energy interval \(\Delta E\) and total selected focal area \(a\), the expected count is \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. For illustration, the full-IAXO targets in Table 1.1, an energy window of 2–7 keV, and \(3\,\mathrm{yr}\) of elapsed operation give \(\mu _b=2.84\) when \(\epsilon _t=0.5\). Three years of effective tracking exposure instead gives \(5.68\) events. The difference comes from the exposure definition. This estimate uses the run duration in the conceptual-design study [14] but omits its energy-dependent acceptance and allocation of exposure among gas settings.

At a fixed trial axion mass, a Primakoff search can retain the energy, position, and observing-condition dependence through 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} The index \(\ell \) identifies the detection line and observing condition, including gas density, while \(k\) identifies a reconstructed-energy and focal-position bin. The signal expectation \(S_{\ell k}\) at reference coupling \(g_0\) folds the solar flux and conversion probability with the optics and detector response. The expected background is \(B_{\ell k}\), and auxiliary measurements or simulation constraints enter through \(\mathcal {L}_{\mathrm {aux}}\) and nuisance parameters \(\boldsymbol {\nu }\). The response must therefore describe energy migration, focal containment, and selection efficiency as well as the total detected yield.

The statistical consequence can be isolated in a single counting region with known background mean \(\mu _b\). For \(n\) observed events and a prior uniform in the nonnegative signal mean \(s\), 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} For a fixed Primakoff response, this prior is uniform in \(g_{a\gamma }^{4}\), as in the CAST analysis [42]; other interval constructions can give different bounds [52]. Zero observed events give \(s_{95}=-\ln (0.05)=3.00\). The expected limit is obtained from the integer outcomes \(n\sim \operatorname {Pois}(\mu _b)\). At \(\mu _b=2.84\) and \(5.68\), their medians are three and six events, giving \(s_{95}=5.48\) and \(6.91\). At fixed response and exposure, the corresponding coupling limits are approximately 16% and 23% higher than the zero-background value. Figure 1.8 shows this transition across a wider range of expected background counts.

In the background-dominated regime, fixed spectra and efficiencies give \(g_{a\gamma }^{\mathrm {lim}}\propto b^{1/8}T^{-1/8}\). When the median outcome is zero events, further background reduction leaves the median counting limit unchanged, whereas increasing the accepted exposure gives \(g_{a\gamma }^{\mathrm {lim}}\propto T^{-1/4}\). A veto or event-topology requirement must therefore be assessed through both its background rejection and its signal acceptance. This is the connection between the detector studies in this thesis and helioscope sensitivity. The published projections discussed below provide the design benchmarks; an absolute BabyIAXO prediction would additionally require the full solar, magnet, optics, exposure, and detector inputs.

1.4 From CAST to IAXO

1.4.1 CAST as the Reference Helioscope

CAST established the main elements of the modern helioscope [12]. Its repurposed Large Hadron Collider (LHC) test dipole provided two parallel bores, instrumented at both ends with low-background X-ray detectors. From 2002 to 2006, a conventional time projection chamber (TPC) covered both sunset bores; at sunrise, one bore used a Micromegas detector and the other a pn-CCD (charge-coupled device) behind an X-ray telescope [53–55]. The telescope concentrated the expected signal onto a smaller detector area, demonstrating the reduction in background counts described by the detector–optics FOM.

Detector upgrades progressively improved the background performance. Following degradation of the TPC, shielded Micromegas detectors replaced the sunset system and the original sunrise Micromegas. Microbulk fabrication, radiopure materials, event-topology discrimination, and increasingly complete passive and active shielding reduced the accepted background. In 2014, a purpose-built slumped-glass X-ray telescope was installed on a sunrise bore, focusing photons onto a shielded microbulk Micromegas detector. This optics–detector assembly, known as the IAXO pathfinder, tested the combination of focusing and low-background detection proposed for IAXO [42, 56].

CAST extended its mass coverage through the three operating regimes shown in Figure 1.9. Evacuated bores retained coherence for \(m_a\lesssim 0.02\,\mathrm{eV}\). The first buffer-gas campaign used \(\ce {^4He}\) at \(1.8\,\mathrm{K}\), scanning 160 density settings to cover 0.02–0.39 eV. The pressure increments were approximately \(0.08\,\mathrm{mbar}\), reaching \(13.4\,\mathrm{mbar}\); the saturated-vapor pressure limited the attainable \(\ce {^4He}\) density. Subsequent \(\ce {^3He}\) campaigns reached higher densities at the same temperature and covered 0.39–1.17 eV. In both gas phases, adjacent settings were chosen to overlap their narrow coherence intervals [49–51].

CAST demonstrated long-term solar tracking, low-background X-ray detection, and the advantage of focusing under operating helioscope conditions. 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 \(m_a\lesssim 0.02\,\mathrm{eV}\) [42].³ This limit provides the measured reference for the optics, Micromegas detectors, and background-control methods developed for BabyIAXO.

1.4.2 Why a Dedicated Helioscope Is Required

The CAST magnet constrained the next improvements: its total aperture was small, the available geometry limited optics and detector integration, and the tracking window was short. A purpose-built helioscope can optimize these quantities together. Table 1.1 compares the published design benchmarks for CAST, BabyIAXO, and IAXO.

The principal magnetic gain comes from the larger aperture, despite a lower representative field than CAST. Focusing optics on every line, lower background targets, and longer tracking provide additional gains. The resulting strategy improves \(f_M\), \(f_{DO}\), and \(f_T\) together in a dedicated instrument [13, 18, 57].

1.4.3 The IAXO Experiment

IAXO applies this coordinated design to solar axions and ALPs [13, 57, 58]. In the low-mass region, its design projections improve the background-limited signal-to-noise ratio over CAST by approximately four to five orders of magnitude. The corresponding coupling sensitivity is near \(\lvert g_{a\gamma }\rvert \sim 3\times10^{-12}\,\mathrm{GeV}^{-1}\), about a factor of 20 below the current CAST limit, for the assumed exposure and background performance [58]. The softer solar component also offers sensitivity to production through \(g_{ae}\) beyond previous laboratory searches. Figure 1.10 places the projected reach alongside measured exclusions and QCD-axion benchmarks.

The projected curves depend on the exposure, efficiency, background, and magnet assumptions of their respective studies. They provide performance targets for the subsystems below and have not been recalculated using the March 2026 engineering parameters. The experimental stages considered here are BabyIAXO and IAXO; IAXO+ represents an optimistic extension of the research-and-development studies rather than a separately approved stage.

Magnet

The 2014 reference design uses an approximately \(20\,\mathrm{m}\)-long superconducting toroid with eight coils and eight bores of approximately \(60\,\mathrm{cm}\) diameter [13]. A useful bore field of about \(2.5\,\mathrm{T}\), together with the large aperture, increases the integrated magnetic conversion relative to CAST. The peak winding field is approximately \(5.4\,\mathrm{T}\). The accessible bores define eight parallel optics–detector lines and can operate in vacuum or with buffer gas for higher-mass scans.

The final IAXO magnet design remains under development beyond the BabyIAXO stage. Recent studies retain the large multi-bore concept and also consider high-temperature-superconductor alternatives, with possible changes to the field and cryogenic implementation [58].

X-ray Optics

Grazing-incidence X-ray optics are assigned to every line in the reference IAXO design [13, 60]. The benchmark in Table 1.1 assumes a selected focal area of approximately \(0.15\,\mathrm{cm}^{2}\) per line. The useful signal fraction depends on the energy-dependent mirror throughput and on how much of the extended solar image lies within that area.

The focal region must be chosen together with its signal containment: reducing \(a\) is beneficial only while retaining enough converted photons. This tradeoff is expressed by the detector–optics factor in Eq. 1.14.

Solar Tracking and Operation

Elevation and azimuth drives carry the magnet, optics, and detectors together, allowing solar tracking for up to approximately half of each day in the reference IAXO concept, or \(\epsilon _t\simeq 0.5\) [13]. The moving structure must support the cold mass and maintain alignment from each bore to its focal plane. Reproducible pointing also allows tracking data to be compared with off-Sun measurements, which constrain the background entering the signal search.

The IAXO experiment is designed for surface operation, where the detector and its surrounding shielding must control the environmental background. The specific BabyIAXO site scenario has evolved during this work, affecting the cosmic-ray conditions assumed in the background simulations described below.

1.5 BabyIAXO and Detector Requirements

1.5.1 BabyIAXO as an Intermediate Experiment

BabyIAXO is the intermediate helioscope between CAST and the full IAXO experiment [14, 58, 59]. Its two detection lines will bring the magnet, cryogenics, optics, detectors, tracking, alignment, gas handling, and data acquisition into one operating instrument. Commissioning them together tests the integration and operating procedures needed for IAXO, while the experiment has its own physics reach.

The 2021 conceptual design assumes \(1.5\,\mathrm{yr}\) of effective exposure for each of the vacuum and buffer-gas campaigns. Under those assumptions, the projected vacuum sensitivity is \(\lvert g_{a\gamma }\rvert \simeq 1.5\times10^{-11}\,\mathrm{GeV}^{-1}\) for \(m_a\lesssim 0.02\,\mathrm{eV}\). A subsequent buffer-gas scan would extend the mass coverage and probe the KSVZ benchmark approximately over 0.06–0.25 eV [14]. Figure 1.11 shows the integrated apparatus studied in the later engineering work.

1.5.2 Magnet Engineering

The 2021 concept uses a common-coil dipole: two parallel flat racetrack coils carry opposite currents around two \(10\,\mathrm{m}\)-class bores [14]. The March 2026 engineering model specifies two \(11\,\mathrm{m}\)-long free bores of \(0.70\,\mathrm{m}\) diameter and an aluminum-stabilized NbTi/Cu Rutherford-cable conductor operated at \(6\,\mathrm{kA}\) [61]. At this current, the calculated mean transverse bore field is \(2.1\,\mathrm{T}\), the peak cable field is \(4.7\,\mathrm{T}\), and the three-dimensional magnetic FOM is approximately \(290\,\mathrm{T}^{2}\,\mathrm{m}^{4}\). These values were retained in the public June 2026 status presentation [62]. The field model in Figure 1.12 distinguishes the useful bore field from the larger field in the conductor.

Each bore accommodates a complete detection line on a scale representative of IAXO. The magnet therefore tests the aperture, cryogenic integration, and detector interfaces needed for the final IAXO design.

On August 11, 2026, the University of Bonn announced that the German Research Foundation (DFG) had approved funding for construction of the BabyIAXO magnet system. Its EUR 6 million cost is shared by the DFG (EUR 3 million), North Rhine-Westphalia (EUR 2.4 million), and the participating universities (EUR 0.6 million) [63].

1.5.3 Optics and Detector Lines

The optics design has also evolved from the 2021 baseline, which paired a custom NuSTAR-derived segmented-glass telescope with an available XMM-Newton flight-spare telescope [14]. At the 23rd IAXO Collaboration Meeting in March 2026, BRAVO-SUN and XRISM-derived components were also under consideration, together with a co-mounted telescope configuration [64]. The final combination remained under development. A public June 2026 comparison quoted focal areas of approximately \(0.2\,\mathrm{cm}^{2}\) for the custom telescope and 0.3–0.7 cm² for XMM [62]. Each selected configuration requires its own throughput and focal-containment calculation, so these areas describe different lines and selections.

1.5.4 Evolution of the DESY Site Scenario

The environmental background depends on the material surrounding the installation. When the background-model and veto-simulation studies began, the reference site was the HERA South Hall on the DESY campus. This underground accelerator hall offers a different cosmic-ray environment from a surface installation because the overburden, access shafts, and local structures can alter the incident particle field. The early simulations accordingly treated the cosmic component as site dependent, accounting for openings and shielding rather than assuming deep-underground conditions.

Collaboration studies in 2025 and 2026 moved the working baseline toward an outdoor location on the DESY campus (Figure 1.13). The reported motivations were simpler civil works, reduced demands on DESY infrastructure, lower expected cost, and earlier site activation [65]. At the March 2026 collaboration meeting, the DESY directorate had encouraged continued site exploration and the preparation of cost and schedule plans. Formal approval, the exact position, and the site elevation remained under study [15].

We adopt the March 2026 surface scenario for the background studies without assuming protection from hall overburden. Studies performed with HERA South conditions are identified separately. The surface source must still be transported through the local environment: the ground, housing, platform, and magnet can attenuate primary particles and produce or redistribute secondaries. Consequently, an outdoor spectrum alone does not establish an upper bound on every contribution at the detector. A final site prediction requires consistent source normalization and the surrounding geometry.

Sea-level muons and neutrons, including secondary production in the passive shielding, motivate an active veto around the detector. Chapter 4 evaluates plastic-scintillator modules with cadmium neutron-capture layers for this purpose. Their effectiveness must be judged together with the X-ray acceptance, following the sensitivity considerations introduced above.

1.5.5 Surface Backgrounds and Rejection Methods

The small axion-conversion probability requires efficient X-ray detection, stable operation, and a low rate of events that can imitate the signal. At a surface installation, particles arrive from the atmosphere and the surrounding ground and structures, while radioactive decays also occur inside the detector assembly. Their initial energies can be much higher than the 1–10 keV signal band. Only a small part of that energy may reach the gas, however, and secondary photons can produce the same ionization as a converted axion photon. The relevant background is therefore the rate of accepted deposits in the signal region, rather than the incident particle flux alone [14, 17].

Radioactive impurities in the readout, vessel, electronics, and shielding emit photons and charged particles, while radon and its progeny add decays in the gas or on nearby surfaces. Because these sources can lie inside the shield, reducing them requires radiopure materials and control of the gas environment. Dense shielding instead attenuates environmental gamma rays, although joints, services, and the X-ray entrance limit its coverage. Photons that reach the inner detector can produce deposits in the analysis interval through Compton scattering and fluorescence [14].

Cosmic-ray muons can cross the gas directly or interact in the surrounding materials. The first case often produces an extended ionization track that can be distinguished from a compact X-ray deposit. The second can produce electromagnetic showers, fluorescence photons, and neutrons, some of which reach the detector without the primary muon crossing its active volume. An active veto provides information about that primary particle outside the gas. Measurements with the BabyIAXO Micromegas prototype demonstrate why this external information complements the event topology measured by the TPC [17]. Its rejection efficiency depends on geometric coverage, the scintillator response, and the time interval used to associate the veto signal with the detector event.

Neutrons introduce another set of mechanisms. Elastic scattering can transfer energy to nuclei and leave a compact deposit resembling an X-ray event, while inelastic interactions and capture can release photons. Neutrons may originate in the environment or be produced by cosmic particles interacting in the apparatus and shielding. An energetic atmospheric neutron can also produce further neutrons in the lead shielding before a secondary reaches the gas. Moderation and capture layers change this transport, and a neutron-sensitive veto can tag associated activity. The capture photons must nevertheless be transported through the surrounding geometry [17]. Neutron activation can additionally produce later decays that are not correlated with a prompt veto signal; Chapter 5 treats this contribution separately. Adding shielding material therefore changes both attenuation and secondary production; its benefit must be assessed for the final detector selection [17].

These sources require complementary measurements and rejection methods. Calibration data determine how efficiently X-rays survive the detector selection, while background data and transport simulations identify deposits that remain after it. Off-Sun observations constrain the background used in the helioscope search, provided changes in pointing, operating conditions, and detector response are accounted for. A compact secondary photon may survive a topology requirement, and an accidental veto coincidence may remove a genuine signal event. The resulting balance between accepted signal and residual background connects the source mechanisms in Figure 1.14 to the sensitivity discussion in Section 1.3.5. Chapters 4 and 5 evaluate that balance for the configurations studied in this thesis.

1.5.6 Detector Requirements

The focal-plane detectors must detect X-rays efficiently in the reference 1–10 keV band while suppressing events that can mimic the signal. The conceptual background targets are \(1\times10^{-7}\,\mathrm{counts}\,\mathrm{keV}^{-1}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}\) for BabyIAXO and \(1\times10^{-8}\,\mathrm{counts}\,\mathrm{keV}^{-1}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}\) for IAXO [13, 14]. At a surface installation, radiopure construction, passive shielding, event-topology discrimination, and an active veto all contribute to approaching these targets [17].

Microbulk Micromegas are the principal gaseous detectors considered here. CAST and IAXO-D0 demonstrated the radiopurity, topological discrimination, stable operation, and compatibility with focused soft X-rays needed for this application.

The following chapter begins with the formation and collection of the ionization charge produced by an X-ray, then develops the Micromegas detector and its experimental operation.

Chapter 2
Micromegas X-ray Detectors for BabyIAXO

Introduction

The BabyIAXO Micromegas detectors measure the soft X-rays emerging from the helioscope optics. For photons in the 1–10 keV region, the detector must provide an energy measurement and identify a localized conversion in the region illuminated by the optics. At surface level, cosmic rays and radiation from the surroundings and detector materials can also deposit energy in the gas. The distribution and timing of the collected charge, together with the activity recorded by the surrounding veto panels, provide the information needed to distinguish X-ray candidates from these backgrounds.

This chapter follows the signal from the entrance window to the calibrated strip waveforms. It explains how photons interact in the gas, how the primary electrons drift and multiply, and how the microbulk Micromegas readout measures the resulting charge. The IAXO-D0 and IAXO-D1 prototypes then provide the concrete setting for the gas, high-voltage, acquisition, and calibration procedures used in the thesis. Their detector response and experimental performance establish the basis for the reconstruction and simulations in Chapter 3 and the background studies in Chapter 5.

2.1 Signal Formation in a Micromegas TPC

A time projection chamber (TPC) measures ionization charge after it drifts through a gas volume toward a segmented readout. In the shallow BabyIAXO TPC, the microbulk Micromegas readout amplifies this charge and collects it on two sets of orthogonal strips. The detector therefore records the deposited charge, its two-dimensional distribution, and the relative timing of the strip pulses. These measurements describe both the energy and the shape of an event: a soft X-ray usually produces a localized ionization cloud, whereas many background interactions produce a longer track, several separated deposits, or activity coincident with the veto.

Figure 2.1 shows the stages that produce the signal. An interaction creates electron-ion pairs in the gas, and the drift field transports the electrons toward the readout while the ions move more slowly toward the cathode. The electron cloud spreads during this transport. The electrons that reach the Micromegas amplification region then generate avalanches, producing a charge large enough for the electronics to measure. The following sections connect each stage to the energy, position, and timing information recorded by the detector.

2.1.1 Entrance-Window Transmission and Gas Conversion

An X-ray emerging from the optics must cross the entrance window before it can interact in the detector gas. The window separates the helioscope vacuum from the gas and must combine mechanical strength with sufficient transmission at low energy. For the aluminized Mylar window used in this detector family, absorption in the polymer film and its metallic coating reduces the number of photons reaching the sensitive volume. This loss is largest at the low-energy end of the signal region.

Photon attenuation through a uniform material of thickness \(x\) follows

Here, \(I_0\) and \(I(x)\) are the incident and transmitted intensities, and \(\mu \) is the linear attenuation coefficient at the photon energy. The equivalent expression \(\mu =\rho \mu _m\) relates it to the material density \(\rho \) and mass attenuation coefficient \(\mu _m\). The transmission of successive layers is the product of their individual transmissions. Figure 2.2 applies this relation to the aluminum coating and Mylar film and shows how the polymer determines most of the attenuation in the few-kiloelectronvolt region.

Once a photon has crossed the window, it must interact before leaving the gas volume. For a path length \(\ell _{\mathrm {gas}}\) in a uniform gas, the probability of interaction is \(1-\exp [-\mu _{\mathrm {gas}}(E)\ell _{\mathrm {gas}}]\). The probability that an incident photon crosses the window and interacts along that path is therefore

where \(T_{\mathrm {win}}(E)\) is the window transmission and \(\mu _{\mathrm {gas}}(E)\) is the gas attenuation coefficient. In the signal region, photoelectric absorption dominates these interactions and converts the photon energy into ionization. Increasing gas density or path length raises the conversion probability, while the choice of gas changes its energy dependence. The window support introduces a further geometric loss that depends on the illuminated area.

These probabilities describe photon transport before a signal is reconstructed. Some interactions release fluorescence photons that escape, so an interaction need not deposit the full incident energy. Charge collection, the electronic trigger, and event selection introduce additional losses after the conversion. The full detector efficiency must include these effects and the illuminated geometry; the window and gas probabilities alone do not give the acceptance of the final X-ray selection.

2.1.2 Ionization in Gases

For a soft X-ray that interacts in the gas, photoelectric absorption releases a photoelectron that loses energy through excitation and ionization. The resulting electron-ion pairs form the initial charge cloud. The atomic vacancy subsequently relaxes through Auger emission or fluorescence. If a fluorescence X-ray escapes the sensitive volume, the collected charge corresponds to a smaller deposited energy and an escape feature appears in the calibration spectrum. This feature is particularly visible in argon-based \(\ce {^{55}Fe}\) calibrations.

The attenuation coefficients in Figure 2.3 show why noble gases provide the main conversion medium. Their photoelectric absorption is stronger than that of the molecular gases added in small concentrations as quenchers. The quencher contributes less to X-ray conversion but is needed for stable charge amplification, as discussed below.

The strong \(Z\) dependence of the photoelectric cross section in this energy range favors noble gases with greater absorption. The detected spectrum also depends on fluorescence escape and reabsorption, so gas choice affects both the conversion efficiency and the calibration features. Other electromagnetic processes are included in the background simulation, which transports photons and charged particles over a wider energy range than the soft X-ray signal considered here.

Charged particles produce ionization along their path rather than at a single photon-conversion site. Stopping power, multiple scattering, and secondary radiation determine the spatial distribution of this charge, which is typically broader and more elongated than that of an X-ray with an energy of a few kiloelectronvolts. Neutral particles can instead generate nuclear recoils or secondary photons and charged particles in the gas or surrounding materials. These different interactions motivate the combination of radiation transport and detector-response reconstruction used in the background model.

2.1.3 Nuclear-Recoil Ionization and Quenching

Neutrons can produce nuclear recoils in the detector gas. As a recoil slows, it transfers energy to atomic motion and to electronic excitation and ionization. The charge signal measures the resulting ionization, so the recoil energy and its electron-equivalent energy need not coincide. For an electron calibration with reference mean pair-creation energy \(W_e\), we define \begin{equation} \label {eq:nuclear-recoil-electron-equivalent-energy} E_{\mathrm {ee}}=W_e\langle N_{\mathrm {ion}}\rangle , \qquad q_{\mathrm {ion}}(E_{\mathrm {R}})=\frac {E_{\mathrm {ee}}}{E_{\mathrm {R}}}. \end{equation} The ionization yield depends on the ion species, energy and gas [69].

Lindhard theory describes the partition between electronic energy and atomic motion over the slowing recoil [70]. For an elemental self-recoil, the conventional parameterization is \begin{equation} \label {eq:lindhard-electronic-fraction} Q_{\mathrm {L}}=\frac {k g(\epsilon )}{1+k g(\epsilon )}, \quad \epsilon =11.5 E_{\mathrm {R}}Z^{-7/3}, \quad k=0.133Z^{2/3}A^{-1/2}, \end{equation} where \(\epsilon \) is the dimensionless reduced recoil energy, \(E_{\mathrm {R}}\) is expressed in keV, and \(A\) and \(Z\) are the mass and atomic numbers. The function \(g\) is parameterized as \begin{equation} \label {eq:lindhard-reduced-stopping} g(\epsilon )=3\epsilon ^{0.15}+0.7\epsilon ^{0.6}+\epsilon . \end{equation} Figure 2.4 illustrates the energy dependence for argon and relates one recoil energy to the predicted primary charge.

Electronic energy includes excitation as well as ionization. Identifying \(Q_{\mathrm {L}}\) with \(q_{\mathrm {ion}}\) is therefore an approximation for the gas response [69]. The expression contains no pressure, mixture or drift-field parameter, so the charge yield for Ar/isobutane 99/1 at 1.4 bar requires separate validation. The example shows how this approximation reduces the primary charge used to predict the waveform amplitude and reconstructed energy.

For a recoil born and stopped in one gas volume, we evaluate the factor at its initial kinetic energy \(E_0\) and distribute the visible energy over the stored deposits: \begin{equation} \label {eq:nuclear-recoil-visible-deposits} E_{\mathrm {ee},i}=Q_{\mathrm {L}}(E_0,A,Z)E_{\mathrm {dep},i}, \qquad \langle N_e\rangle =\frac {\sum _i E_{\mathrm {ee},i}}{W_e}. \end{equation} Complete histories with local energy closure and no resolved secondary tracks are required. Deposit positions and times provide the initial charge distribution for electron transport, amplification and waveform reconstruction. Escaping or branching recoils require a different treatment. The proportional allocation remains an approximation; gas-specific yield, charge fluctuations and spatial ionization structure require independent validation before final neutron-background predictions.

2.1.4 Electron Transport and Amplification

An electron-recoil energy deposit \(E\) creates a mean number of electron-ion pairs determined by the mean energy \(W\) required per pair:

The primary-charge fluctuations are commonly expressed through the Fano factor \(F\) [71]:

For electron recoils, these fluctuations are smaller than Poissonian and contribute to the intrinsic energy resolution. For nuclear recoils, the electron-equivalent energy defined in Section 2.1.3 determines the corresponding mean primary charge.

The drift field carries the electrons toward the mesh. In the mobility approximation, their mean velocity is \(\vec {v}_d=-\mu _e\vec {E}\), with the positive mobility \(\mu _e\) depending on field, density, and gas composition. Transport properties are often compared through \(E/p\), where \(p\) is pressure, or \(E/N\), where \(N\) is the gas number density; the latter also accounts for temperature-dependent density changes. The gas tables used in the developed response model are described in Section 3.4.1.

Collisions spread the electron cloud during drift. After a distance \(d\), its standard deviation along a direction \(\hat {u}\) is

Here, \(D_{\hat {u}}\) has units of square-root length, following the Garfield++ gas-table convention [72]. For uniform drift, it is related to the diffusion coefficient \(\mathcal {D}_{\hat {u}}\), expressed in length squared per time, by \(D_{\hat {u}}=\sqrt {2\mathcal {D}_{\hat {u}}/|\vec {v}_d|}\). The longitudinal and transverse spreads in Figure 2.5 describe the cloud along and perpendicular to the mean drift direction.

Transverse diffusion shares charge between neighboring strips, while longitudinal diffusion spreads its arrival times. The measured pulse width also includes electronic shaping and reconstruction, so it cannot be identified directly with the longitudinal cloud width. Recombination and attachment reduce the charge reaching the mesh; gas purity and the removal of oxygen and water therefore affect both amplitude and stability.

In the narrow amplification gap, a stronger field allows the electrons to ionize the gas and generate avalanches. Neglecting electron losses, the mean amplified electron population is

where \(G\) is the mean gas gain. For independent avalanches, let \(b=\sigma _G^2/G^2\) denote the relative single-electron gain variance. With independent additive electronic noise \(\sigma _{\mathrm {el}}\) referred to the amplified charge, the relative full width at half maximum (FWHM) of an approximately Gaussian peak is

This expression separates primary-ionization statistics, avalanche fluctuations, and electronic noise [73]. Charge losses and fluctuations shared across an event can broaden the measured peak further; calibration tests the combined detector response.

Avalanche ultraviolet photons can initiate further avalanches through photoionization or electron emission from surfaces. Isobutane suppresses this feedback through absorption and nonradiative molecular relaxation. It also changes drift and diffusion, so its concentration affects both stable amplification and the charge distribution reaching the readout.

2.1.5 Micropattern Gaseous Detectors: Micromegas

Micromegas (MICRO-MEsh GAseous Structure) detectors separate the drift volume from a narrow amplification gap with a thin metallic mesh [74]. The relatively weak drift field carries the primary electrons toward the mesh. With a suitable ratio between drift and amplification fields, the electrons pass through its openings and enter the high-field gap, where they multiply before reaching the anode strips. This separation allows charge transport and amplification to be controlled through different fields while retaining fast signals and fine spatial segmentation.

For axion helioscopes and other rare-event searches, microbulk Micromegas provide a thin readout with a small material budget. Photolithographic processing of copper-clad Kapton forms the mesh, insulating pillars, and readout pattern in a mechanically uniform structure [75]. The use of radiopure copper and Kapton reduces the activity close to the gas, while the orthogonal strips resolve the two-dimensional distribution of the collected charge. These properties combine efficient soft X-ray detection with the spatial information needed to reject many extended background events.

The IAXO-D1 readout has three distinct length scales. Its \(6\,\mathrm{cm}\) width contains 120 strips per coordinate, corresponding to a strip pitch of \(500\,\mathrm{\mu m}\). At each X–Y strip crossing, the IAXO-D1 mesh photograph resolves a \(3\times 3\) group of microscopic openings. Microbulk structures in this detector family have holes of order \(40\,\mathrm{\mu m}\) in diameter on an approximately \(100\,\mathrm{\mu m}\) triangular pitch, with an amplification gap of approximately \(50\,\mathrm{\mu m}\) defined by the etched polyimide [56, 76]. The strip pitch sets the readout granularity, whereas the smaller holes and gap determine electron transmission and avalanche formation. Figure 2.6 shows how the mesh and the two strip coordinates fit together.

The operating fields must transmit electrons through the mesh and provide enough gain to resolve a kiloelectronvolt signal above noise. At a fixed mesh voltage, scanning the drift field with an X-ray source identifies the transmission plateau, where the calibration peak position is approximately constant. Increasing the amplification field within this region then raises the gain until discharge behavior limits operation. The peak position, width, and discharge rate together define a suitable operating range for each gas, pressure, and electronics configuration [77]. These characterization scans establish the operating point; Table 2.2 lists the recorded conditions of the R02729 reference acquisition.

The combination of radiopurity, segmentation, low threshold, and operation in CAST underpins the use of microbulk Micromegas in the IAXO experiment [12, 16, 42]. The next section describes how these principles are implemented in the two prototype generations used in this thesis.

2.2 The BabyIAXO Micromegas Detector Prototypes

The BabyIAXO detector prototypes retain the compact TPC and segmented microbulk readout developed for CAST. The cylindrical gas volume has a diameter of 10 cm, a drift length of 3 cm, and a volume of approximately 236 cm³. A square readout of side length 6 cm collects the charge on 120 strips in each coordinate, giving 240 channels. The gas depth sets the conversion probability and maximum drift distance, while the strips measure the two projections of the ionization cloud.

Solar X-rays are concentrated near the center of the readout by the telescope, whereas background interactions can occur throughout the chamber. The background analysis therefore uses a fiducial region smaller than the full 6 cm × 6 cm readout. The adopted criterion requires the paired X–Y center of the calibrated maximum-energy reconstructed track to satisfy \(r<10\,\mathrm{mm}\), giving \(A_{\mathrm {fid}}=\pi ~\mathrm {cm}^{2}\). Earlier studies used a 15 mm-radius region, either to integrate readout energy or to select the hit centroid; their results retain that separate definition. The baseline selection and its rate normalization are described in Section 5.1.7.

IAXO-D0 and IAXO-D1 share the TPC dimensions, readout size, number of strips, and nominal lead-shielding thickness. Their differences concern how the chamber, pipe, readout connections, and electronics fit inside the shielding and how the detector can be accessed. Table 2.1 summarizes these differences and identifies the role of each prototype in this thesis.

The simulation geometries in Figure 2.7 show how these changes affect the material surrounding the gas and the openings through the shield. The D0 backplate extends laterally beyond the lead bricks, while the D1 chamber fits within a movable shield and connects to a thicker copper pipe. These structures must be represented separately when calculating radiation transport to the gas.

2.2.1 IAXO-D0

The IAXO-D0 chamber is cylindrical and closes with a large copper backplate that extends laterally from the shielding. Its copper pipe has a thinner central section, and the lead shield is built from bricks. Access to the chamber requires removing part of this shield, making detector interventions dependent on its disassembly. Four AGET chips read the strips through flat cables connected to a combined front-end card (FEC)–Feminos unit; the Feminos card supplies the back-end electronics [79].

The Zaragoza campaign used a Micromegas readout shortly after its decommissioning from CAST to study the detector response and test rejection of cosmic-ray-induced background with the prototype veto. Earlier campaigns used other readouts from the same prototype generation [80]. These campaigns established the detector-operation and veto-integration procedures used in this thesis.

2.2.2 IAXO-D1

The IAXO-D1 design provides access to the detector by moving the lead shield laterally on linear rails. The shield forms a box with a central square shaft around a chamber with a square footprint and a thicker copper pipe. A flexible Micromegas PCB carries the strip connections parallel to the pipe through the shielding aperture. This arrangement allows the readout and its services to fit within the shield while retaining access to the chamber. The identified D1 calibrations supply the measured reference for the quantitative detector-response comparisons in Chapter 3.

Figure 2.8 compares the chamber used in the simulation with the assembled detector. The copper walls provide the mechanical enclosure, and the inner polytetrafluoroethylene (PTFE) liner helps suppress copper fluorescence reaching the gas [78]. The field-shaping ring lies outside this liner and is intended to reduce distortions of the drift field near the chamber boundaries.

The exploded view in Figure 2.9 identifies the layers between the beam pipe and the readout. The thin entrance window seals the gas volume and acts as the cathode, while its supports withstand the pressure difference across the window. The readout and mesh close the opposite end of the drift region, where the arriving electrons are amplified and collected.

The PCB must bring all 240 strip signals outside the active area without interrupting the two-coordinate readout. Figure 2.10 shows the routing reconstructed from the Gerber layers. One strip direction is connected in the top copper layer and the other through the bottom layer, preserving the orthogonal pixel pattern introduced in Figure 2.6.

Figure 2.11 follows the readout from its flexible extension to its installation and then to the microscopic mesh pattern. The flexible section accommodates the chamber and shielding geometry; the perforated mesh and strip pattern determine how the avalanche charge is collected across neighboring channels.

The intended D1 electronics place four STAGE chips on FECs close to the readout and an ARC-compatible back-end outside the passive shield (Figure 2.11a and Figure 2.11b). Keeping the analog connection short reduces its capacitance and exposure to noise pickup. This placement also brings the FEC materials close to the gas, where radioactive contamination can contribute to the background. The March 2025 electronics report lists radiopure PCB substrates but does not classify the populated cards as fully radiopure; the mounted components and connectors must therefore remain in the material-background inventory [81]. The back-end contains more conventional components and is placed outside the shield, with flexible interconnects carrying data and control signals through the penetration. The same report describes produced boards whose FEC–back-end link still required testing, so this layout specifies the intended architecture rather than the electronics used in every D1 acquisition.

2.3 Detector Ancillary Systems

Stable gas composition, pressure, and electrode voltages are needed to maintain the detector response throughout a run. Gas lines and electrical cables pass through the shielding and must allow access to the chamber; the acquisition separately synchronizes the Micromegas and veto signals.

2.3.1 Gas System

The prototypes can operate with argon–isobutane or xenon–neon–isobutane mixtures. CAST operated mainly with argon and 2% isobutane at 1.4 bar [12]; its final campaigns used equal partial pressures of xenon and neon with \(2.3\%\) isobutane [42]. The xenon–neon mixture removes the argon escape structure near the signal region and the intrinsic \(\ce {^{39}Ar}\) contribution. Because xenon is costly, recovering the gas through purification and recirculation becomes an important operating requirement.

In a closed loop, contaminants introduced by the chamber, pipework, pump, buffer volume, valves, and filters can remain in the circulating gas. Leaks and outgassing affect electron transport, while radon emanation can introduce radioactive decays in or near the conversion volume. IAXO-D1 measurements found substantial changes in the low-gain alpha rate between open-loop and recirculating configurations, motivating checks of radon sources and purification methods [82]. Chemical purification and radiological control are therefore both needed when evaluating a recirculation system.

The mixture composition, pressure, temperature, drift field, flow stability, and gas purity determine the transport conditions during each measurement. These conditions must be matched when choosing the gas tables for simulation, since changes in drift velocity, diffusion, or electron attachment alter the recorded charge distribution. Section 3.4.1 describes the calculation of these properties with Garfield++ and Magboltz. Open-loop operation exhausts the used mixture; closed-loop operation recirculates it through purification. Evacuation assists gas changes, and pressure relief protects the entrance window.

2.3.2 High Voltage and Slow Control

Separate high-voltage channels bias the cathode and mesh to establish the drift and amplification fields. Voltage changes affect electron transport, mesh transparency, avalanche gain, and the reconstructed event shape. The veto photomultiplier tubes are biased independently, and their gain affects the threshold and timing of the coincident signals. Controlled voltage ramps, current monitoring, and filtering help maintain stable operation. If the current exceeds the protection threshold, the supply trips and switches off the high voltage to protect the detector during a discharge.

The slow-control system records the voltages together with the gas and environmental conditions so that changes in gain or noise can be compared with the operating history. It also allows remote intervention during long runs. We developed the reusable hvps control library to operate the high-voltage supplies; its implementation is described in Section 3.8.3.

2.3.3 Shielding and Veto Integration

Passive shielding attenuates external radiation before it reaches the gas, while the active veto records coincident activity around the detector. The pipe, gas lines, electrical feedthroughs, and calibration access create openings that must be included when assessing the complete detection line. Micromegas waveforms provide the X-ray candidate and its timing reference; the synchronized veto signals then identify activity associated with that event. Chapter 4 develops the passive-shielding studies, cosmic-ray-induced background simulations, and scintillator–cadmium veto design using this combined information.

2.4 Data Acquisition System

The data acquisition (DAQ) system records the strip waveforms and the surrounding veto activity associated with a trigger. The front-end card (FEC) amplifies and shapes the strip signals, the front-end module (FEM) controls their digitization and readout, and the DAQ computer stores the events. Their timing must be coordinated so that a TPC candidate can be compared with pulses in the veto panels. The acquisition software developed in this thesis, including the feminos-daq refactor and online viewer, is described in Section 3.8.2.

The prototype acquisition follows the AGET/Feminos approach used for the IAXO pathfinder at CAST. In the pathfinder, four AGET chips read the 240 Micromegas strips, and an otherwise unused channel recorded the external muon-veto signal [77]. The commissioned prototype chain expands this arrangement into separate TPC and veto branches, synchronized through a common Trigger Clock Module. Figure 2.13 shows how this connection preserves the information needed to associate the two detectors event by event.

Four AGET chips acquire the TPC strips, while Feminos supplies configuration, timing, readout control and Ethernet transfer [79, 83]. The IAXO-D1 calibration measurements used an AGET/Feminos TPC readout. The detector generation and electronics generation must therefore be identified separately when comparing measurements.

2.4.1 Run Conditions and Waveform Observables

The acquisition records identify the detector conditions and electronics settings used for each run. Gas composition and pressure determine electron transport, while the cathode and mesh voltages establish the drift and amplification fields. Electronic gain, shaping and sampling then determine how the collected charge appears in the waveform. Table 2.2 records the R02729 reference acquisition. Figure 2.14 summarizes the settings of the 40 calibration runs compared in Section 3.6.

The mesh voltage magnitude spans 320–335 V and the cathode magnitude spans 700–850 V, giving calculated drift fields of 123.3–175 V cm⁻¹. The two gain/shaping groups contain 23 and 17 runs. All 40 runs have a recorded pressure of 1.4 bar, nominal Ar–isobutane (99:1), and a sampling period of 40 ns in the reconstruction settings. These distributions show which conditions changed between calibrations; a stability measurement would also require their time dependence and the measured peak positions.

A pedestal acquisition measures the mean \(m_i\) and standard deviation \(\sigma _i\) of the quiet signal in each channel. Feminos subtracts the channel means and restores a common baseline, usually 250 analog-to-digital converter (ADC) counts. A channel can generate a trigger when its amplitude exceeds a threshold relative to this baseline; the prototype procedure described here uses three pedestal standard deviations. The readout can return all channels or only those passing its channel threshold. These choices affect both the measured charge and the number of strips available to reconstruct a low-energy event. Figure 2.15 illustrates the display of signals from active strips.

The signal in each active strip has an amplitude and arrival time, together with a width set by charge transport and the shaping electronics. Figure 2.16 illustrates how these quantities are measured relative to the restored baseline. Pulse height and integral provide charge estimators, while relative pulse times describe the extent of the event along the drift direction. The threshold-selected integral sums the baseline-subtracted signal in samples that pass the threshold. The reconstruction used in this thesis obtains energy from fitted pulse amplitudes, as detailed in Section 3.4.6. The rise and fall times also help identify pileup or signals that differ from the expected shaped response.

Shaping time controls the pulse width, and the sampling period fixes its time granularity. The trigger delay determines how much baseline precedes the pulse and how much of its tail is retained. A threshold that removes low-amplitude strips can reduce the reconstructed energy and narrow the apparent charge distribution. For this reason, data and simulation must use compatible acquisition settings before their reconstructed observables can be compared.

Figure 2.17 illustrates how spatial extent and relative pulse timing distinguish a compact charge cloud from an extended ionization track. Charge distributed along the drift direction reaches the mesh at different times, even when its transverse projection is small. A track nearly parallel to the drift direction can therefore resemble an X-ray in the strip plane while producing a wider arrival-time distribution. Some background interactions also produce localized deposits, so compactness alone cannot identify the incident particle.

Reconstruction combines the strip amplitudes and times with their positions to form hits and tracks. The resulting energy estimators measure the charge through pulse heights, integrals or reconstructed hits. Widths, hit counts, charge balance and asymmetry describe how that charge is distributed. These quantities connect the detector physics developed earlier to the event selection used in the following chapters.

2.5 Detector Calibration

Calibration relates the recorded charge to deposited energy and checks whether the response remains stable between runs. Changes in gas purity, pressure, voltage or electronics noise can shift a photopeak or alter its width. We therefore compare calibration spectra and detector conditions before transferring an energy scale to a background acquisition. At the CAST pathfinder, regular \(\ce {^{55}Fe}\) measurements supplied the nearby calibration used for each background or tracking period [77]. The same principle applies to the prototype measurements: the calibration must describe the conditions under which the physics data were recorded.

2.5.1 Standard X-ray Calibration

A source placed in front of the entrance window produces X-rays with known energies in the detector gas. The routine source is \(\ce {^{55}Fe}\), whose dominant manganese \(K_{\alpha }\) line at 5.9 keV lies within the signal region. Its photoelectric conversions provide localized charge clusters for measuring the energy scale and checking reconstructed shapes. Sources such as \(\ce {^{109}Cd}\) can add higher-energy points when testing the response over a wider interval.

The reconstructed position map first checks that the source illuminates the expected region and that no inactive area or large asymmetry has appeared. The photopeak position then measures the charge scale, while its width describes the combined fluctuations of ionization, collection, amplification and readout. Comparing these quantities between calibrations distinguishes a stable response from a change associated with detector operation. A numerical stability result requires a sequence of measured runs; the single-run spectrum below illustrates the calibration features.

In argon, the 5.9 keV photopeak and the escape structure around 2.9 keV provide two energy anchors [77]. They can determine both the scale and offset of a linear calibration. For xenon-based operation, the main line determines a one-point scale when a zero offset is assumed. Additional lines or calibrated charge injection are then needed to test that assumption and the linearity of the response. The accepted calibration is applied before event selection; it is not readjusted to increase the fraction of simulated events passing the analysis requirements.

Figure 2.18 shows the measured R02729 calibration used as the reference for the response comparisons in Chapter 3. The spectrum contains 9956 valid reconstructed events from a 10 000-entry sample, before the TPC baseline selection. Its energy estimator combines the fitted amplitudes of the maximum-energy tracks in the two strip views. The main manganese photopeak and argon escape feature illustrate full-energy absorption and fluorescence escape under the conditions in Table 2.2. The main peak is fitted with two Gaussian contributions for manganese \(K_{\alpha }\) and \(K_{\beta }\), with fixed relative energies and integrated intensities and widths proportional to the square root of energy. The fitted \(K_{\alpha }\) FWHM divided by its centroid is \(26.3\%\) for this sample and fit interval; the fit does not change the accepted energy scale. The response comparison in Section 3.6.3 uses a separate Gaussian core-width definition.

This measured spectrum establishes the experimental reference; the comparison with reconstructed simulations, event shapes, and selection acceptance follows in Section 3.6.

2.5.2 Spatial-Resolution Measurements at SOLEIL

The published SOLEIL measurements provide a direct test of the D1 position reconstruction [78]. The detector operated with argon and \(5\%\) isobutane at atmospheric pressure, an open gas flow of 5 L h⁻¹, and a mesh-voltage magnitude of 360 V. The measurements used AGET/Feminos electronics, with the field shaper disconnected because its connection introduced noise. For a \(90\,\mathrm{\mu m}\times90\,\mathrm{\mu m}\) X-ray beam at \(6\,\mathrm{keV}\) and a drift field of \(100\,\mathrm{V}\,\mathrm{cm}^{-1}\), Gaussian fits to the event-centroid distributions gave standard deviations slightly below \(100\,\mathrm{\mu m}\) in both views. Charge sharing across neighboring strips thus permits centroid reconstruction finer than the \(500\,\mathrm{\mu m}\) strip pitch. The measured widths include the finite beam size and depend on the event selection; they describe the distribution of reconstructed positions, rather than the size of each ionization cloud. Their variation with energy and field constrains the diffusion and reconstruction models, provided the beamline noise and operating conditions are retained in the comparison.

2.5.3 UV-Light Calibration R&D

During a three-month internship at CEA Saclay, we investigated whether pulsed ultraviolet (UV) light could provide localized primary electrons with a known creation time. Such a source would complement X-ray calibration by allowing charge transport and timing to be studied independently of the photon conversion depth. The concept follows the use of UV-induced photoelectrons in Micromegas-based photocathode detectors such as PICOSEC [84].

We used a pulsed deuterium gas-discharge lamp to illuminate an aluminum photocathode deposited on a UV-transparent \(\ce {MgF2}\) window. A single-channel Micromegas detector measured the amplified photoelectron charge, with the lamp trigger providing the timing reference. We designed and printed spacers with nominal heights of 3.0, 5.0, 7.5 and 10.0 mm and a height tolerance of 0.1 mm to vary the drift distance. Argon–isobutane mixtures flowed through the chamber at 10 L h⁻¹, and an oscilloscope recorded 5000 pulses per timing point [85].

The arrival time includes electron drift and delays from the lamp, amplification, and electronics. Comparing two distances at the same reduced drift field \(E/p\), while keeping the amplification voltage fixed, removes a common delay \(t_0\): \begin{equation} t(d,E/p)=t_0+\frac {d}{v_d(E/p)}, \qquad v_d(E/p)=\frac {d_2-d_1}{t(d_2,E/p)-t(d_1,E/p)}. \label {eq:uv-drift-velocity} \end{equation} We interpolated the measured arrival times as functions of field to compare configurations at matching \(E/p\). The velocity estimates below use the 3.0 mm and 7.5 mm spacers. This difference method also avoids using photoemission from the mesh as a second timing reference: that signal was visible at low quencher concentration but weakened as isobutane absorbed the UV light [85].

Figure 2.19 compares the historical estimates for nominal 1% and 5% isobutane with Magboltz calculations. The measured curves reproduce the scale and broad field dependence of the calculated velocity, including its maximum, but the maxima occur at different fields. The comparison therefore demonstrates sensitivity to gas transport without establishing agreement sufficient for an absolute drift calibration.

The gas analyzer readbacks differed from the nominal mixer settings: for example, the reported 1% and 5% settings gave 1.32% and 5.59% isobutane. Mixture equilibration and possible charge accumulation were also identified during the study as effects requiring further tests [85]. The lamp produced large pulse-amplitude fluctuations, limiting its use as a controlled charge source even when arrival times could be measured. These observations motivate a more stable UV source, a characterized photocathode, and controlled gas conditions before quantitative calibration of the BabyIAXO detector. X-ray sources remain the calibration method used for the detector and background analyses in this thesis.

Summary

The prototypes measure X-ray energy and topology through the charge collected on orthogonal strips and the relative timing of their pulses. Stable gas and electrical conditions, monitored with calibration data, determine the response used in the simulations and background analysis.

Chapter 3
Simulation and Analysis Framework

3.1 From incident particles to detector events

To understand the background measured by the detector, it is necessary to follow the particles from their source to the signals recorded by the electronics. The simulation therefore includes particle generation, transport through the shielding, detector response and event reconstruction (Figure 3.1). The reconstructed events can then be selected in the same way as experimental data. This chapter describes the tools used for this calculation and the developments made during this thesis. After following the event through signal formation and reconstruction, we define the observables and common time projection chamber (TPC) selection in Section 3.5. The comparison with calibration data then tests the reconstructed distributions and selection acceptance before these methods are applied to the veto and background studies.

The calculation combines REST-for-Physics [86], Geant4 [87–89], ROOT [90], CRY [91] and the geometry tools developed within the IAXO collaboration. The main contributions are summarized in Table 3.1. They include a more efficient cosmic-ray generator, extensions to particle transport, a detailed Micromegas response and tools for large simulation campaigns and detector operation.

The measured signals described in Chapter 2 provide the experimental reference for the two TPC responses compared here. The developed Garfield++ response is introduced in Section 3.4, including the preliminary neutron extension in Section 3.4.3. Section 3.6 compares reconstructed calibration events with this model and the conventional energy-deposit response used in existing background productions.

3.2 REST-for-Physics

The comparison between simulation and data is simpler when both can be processed with the same tools. REST-for-Physics [86] (Rare Event Searches Toolkit for Physics) provides this common framework. Developed for rare-event experiments, it includes libraries for particle transport, detector response and data analysis, written in C++ and based on ROOT. It has already been used for the IAXO pathfinder detector at CAST, as described in the thesis of Cristina Margalejo Blasco [77].

Three programs cover the main tasks in this thesis. restG4 runs the Geant4 simulation, restManager applies a sequence of processing steps, and restRoot allows interactive inspection of the results. The geometry, source and processing steps are specified in RML configuration files, so different detector conditions can be studied without modifying the programs.

3.2.1 Data storage and analysis

Simulation and experimental data are stored in ROOT files [90], together with the detector and processing settings needed to interpret them. The tree structure of these files allows selected observables to be read efficiently, which is useful when comparing large samples or testing different selection criteria. Most figures in this thesis were produced in Python with Matplotlib or Plotly. The data were accessed through PyROOT, which also gives access to the REST classes, or Uproot [92], which reads ROOT files directly in Python.

3.2.2 Events and reconstruction

An event contains the information associated with one particle history or one acquisition trigger. As it passes through the processing chain, its description changes: particle interactions become electronic signals, and signals become reconstructed hits and tracks (Figure 3.2). REST provides corresponding event classes, such as TRestGeant4Event, TRestRawSignalEvent and TRestTrackEvent, derived from the common TRestEvent class.

The results are stored in two complementary trees. The EventTree contains the event at the chosen processing stage, while the AnalysisTree contains quantities such as energy, position, width and multiplicity. These observables can be used to draw control plots or change a selection without repeating the reconstruction. Earlier stages, such as waveforms or transport hits, are saved separately when they are needed for later reprocessing.

In the TPC, the reconstructed shape helps distinguish compact X-ray events from background. In the veto, pulse amplitudes, times and panel multiplicities identify activity associated with a TPC event. For both detectors, simulated waveforms are processed with the same algorithms and settings as measured waveforms. The original particle history remains available to study the interactions responsible for an event.

The TPC baseline selection is defined in Section 3.5.3 and illustrated in Figure 3.15. Section 3.6 tests the resulting observables and acceptance with calibration data. Chapters 5 and 4 then apply the TPC and veto selections to the background studies.

3.2.3 Readout geometry and channel mapping

A recorded signal must be associated with a position in the detector. In the Micromegas readout, connected pads form strips; in the veto, each channel corresponds to a scintillator panel. The readout description relates these elements to their positions, orientations and electronics identifiers, and is shared by simulation and data (Figure 3.3).

We developed readout-generation tools for the IAXO-D0 and IAXO-D1 Micromegas detectors and their veto systems. For the TPC, the description includes the shapes of individual pads, including those at the edges. This is needed to assign arriving electrons to pads in the detailed response model and to reconstruct positions from strip signals. For the veto, the mapping includes the orientation and sensitive depth of each panel.

We checked the mapping by comparing the sensitive volumes, acquisition channels and reconstructed positions. These checks help identify geometry or channel-assignment errors.

3.3 Particle generation and radiation transport

3.3.1 Cosmic-ray source generators

Cosmic rays produce showers of secondary particles in the atmosphere. Their flux at the laboratory can be calculated with programs such as CRY [91] or CORSIKA [93]. The detector simulation then follows these particles through the shielding and active volumes. The source tools described here make this second calculation more efficient by reusing atmospheric distributions and directing particles toward the detector.

We developed a program to obtain cosmic-ray secondary distributions from CRY for the chosen site conditions [94]. For each species—muons, electrons, positrons, photons, protons and neutrons—it stores the joint kinetic-energy and zenith-angle distribution, \(H_i(E,\theta )\), in a ROOT histogram. These histograms are then sampled by restG4. The particles are generated independently. This is a reasonable approximation for a compact detector: atmospheric muons and neutrons can be spread over kilometer scales, and coincidence measurements with meter-scale detectors found no significant neutron–muon correlation [95]. Coincidences between separate atmospheric particles are therefore omitted, while secondaries created by the same incident particle in the shielding are still followed together by Geant4.

Calculating the atmospheric distributions once makes it possible to reuse them for different shield thicknesses and veto geometries. They can also be compared with EXPACS calculations [96, 97] or HENSA measurements [98] before running the detector simulation. The background studies use the Guan distribution [99] for muons, CRY for photons, protons, electrons and positrons, and the measured HENSA spectrum [100] for the nominal outdoor-neutron energy distribution. CRY provides an alternative source for muons and neutrons. The HENSA energy spectrum is combined with an assumed angular distribution proportional to \(\sin \theta \cos ^2\theta \). The conversion from plane to spherical generation also affects the sampled angles; the distributions produced by the complete generator are examined in Section 5.4.1.

3.3.2 Probability Distribution Projection cosmic-ray generator

In conventional cosmic-ray simulations, particles are generated over a large plane above the detector. Most trajectories miss the geometry, and their transport contributes little to the background calculation. For a compact detector such as IAXO-D0, this can account for a large fraction of the computing time.

The Probability Distribution Projection (PDP) method was developed and published during this thesis to reduce this cost [101]. It generates only trajectories that cross a sphere enclosing the geometry. For a given direction, their starting points lie within the ellipse obtained by projecting the sphere onto a horizontal plane (Figure 3.5). If \(f_{\mathrm {plane}}(\theta )\) is the distribution of horizontal-plane crossings per unit zenith angle, the distribution for the sphere is \begin{equation} f_{\mathrm {sphere}}(\theta ) \propto f_{\mathrm {plane}}(\theta )\sec \theta . \end{equation} The factor \(\sec \theta \) accounts for the different projected areas. To obtain the simulated exposure, the generation rate must be calculated using the same convention. For intensity \(I(E,\Omega )\) per unit energy, solid angle, time and area perpendicular to the direction of incidence, 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}

The integrals cover the chosen incident hemisphere and energy range; for azimuthal symmetry, \(\mathrm {d}\Omega =2\pi \sin \theta \,\mathrm {d}\theta \). An input already defined per unit area perpendicular to the ray does not require the plane-to-sphere correction again.

The sampled zenith angles and distances from the detector axis agree with conventional generation within statistical uncertainties when the generation plane is sufficiently large. The IAXO-D0 benchmark also shows why this convergence matters (Figure 3.6). Small conventional generation disks are fast, but underestimate the physical event rate. Relative to PDP, the deficits are about 6.4%, 1.0% and 0.5% as the disk radius increases. The analytical projection and the trajectory-distribution checks support using PDP as the reference; the zero in the difference panel follows from this choice. PDP gives about three times more saved events per unit computing time than the fastest of these configurations, and about 37 times more than conventional generation at comparable physical accuracy. This improvement made the large cosmic-ray samples used in the following chapters more practical.

3.3.3 Detector geometry

Comparing shielding and veto designs requires geometries that can be changed easily while keeping the detector dimensions and materials consistent. The IAXO-D0 and IAXO-D1 geometries were therefore built from parameterized descriptions and exported to the Geometry Description Markup Language (GDML) [102], which can be read by Geant4 and ROOT.

Some veto geometries contain more than 400 components. The collaboration’s Kotlin tool, gdml.kt, constructs these geometries from reusable elements rather than requiring each volume to be written by hand. During this thesis, we contributed to its development and testing, and integrated the generated geometries with particle transport, readout mapping and event visualization.

The geometry files are versioned, so the configuration used in each simulation can be recovered. The restG4 interface was also extended to resolve volume names changed during GDML assembly parsing and to accept logical-volume names. This allows transport settings to be applied consistently to repeated components. The same detector description is used for the channel map and event viewer: a panel with a simulated energy deposit can be highlighted and checked against its reconstructed signal (Figure 3.7).

3.3.4 Particle transport with restG4

Geant4 [87–89] calculates particle interactions and transport through matter. REST supplies the application, restG4, and the Geant4Lib library needed to configure the calculation and store the resulting histories. Several extensions were developed during this thesis to reduce computing and storage costs and to study delayed activity.

Particle histories and delayed activity

Each simulated event begins with one or more primary particles. Geant4 follows their trajectories in steps and also tracks the secondary particles produced by their interactions. The stored history contains the positions, momenta, times, energies and interaction processes needed to understand how energy reaches the active detector volumes.

Some secondaries produce signals long after the initial interaction. A stacking action was added to identify new tracks and separate long-lived activity into delayed subevents. Their times and parent identifiers are preserved, so prompt and delayed signals can be studied separately while remaining associated with the same primary history.

Multithreading and track pruning

Independent particle histories can be processed in parallel. Multithreading was added to restG4 to use several processor cores, together with synchronized output and clean interruption of a running simulation.

Track pruning reduces the amount of stored information. Only tracks related to the chosen sensitive volumes are kept, including the trajectories through passive material that led to those interactions. This reduced file sizes by factors of 1–10 in the tested configurations while preserving the checked TPC and veto observables. The retained information depends on the response to be calculated: scintillator quenching may need step lengths and recoil identities, while delayed coincidences need times and parent associations. These quantities must therefore be included when preparing a sample for such studies.

3.4 TPC detector response and event reconstruction

We developed a Garfield++ detector response that follows primary electrons through drift, amplification and individual collection before forming channel waveforms [72]. This is the response adopted for subsequent simulations; Section 3.4.3 describes the neutron conversion intended for the final response and marks its current development status. The REST detector response used in the existing background productions provides a comparison. Both responses enter the same reconstruction as measured waveforms (Figure 3.8); the physical processes underlying the signals are described in Chapter 2.

3.4.1 Gas-transport tables and response models

The gas mixture, pressure, temperature and electric field determine the transport coefficients used by both responses. We developed gas-cli to prepare Magboltz tables for these conditions [103]. Figure 3.9 compares the drift velocity and diffusion coefficients as the isobutane fraction changes.

Increasing the isobutane fraction generally reduces transverse diffusion in these scans, giving a narrower cloud after the same drift distance. Changes in drift velocity and longitudinal diffusion also affect pulse timing. The dotted lines identify reference fields, rather than an optimized operating range or the conditions of every calibration run. The \(2\%\) argon–isobutane curve illustrates the transport study; the conservative IAXO-D1 background reference in Chapter 5 uses \(1\%\) isobutane. The \(2.3\%\) xenon–neon–isobutane mixture belongs to the separate BabyIAXO response studies.

The Garfield response uses Heed to generate primary ionization and then calculates drift, multiplication and collection of individual electrons. In the REST response, Geant4 supplies gas energy deposits, which REST converts into primary charge with statistical fluctuations. Drift is described through transport coefficients and amplification through effective gain parameters before the charge is assigned to channels and converted into sampled pulses. Its effective response is calibrated against measured signals, making this calculation practical for large background samples.

3.4.2 Ionization and electron drift

Geant4 transports the incident particle through the chamber materials and entrance window. For photons and the charged particles supported by the present Heed interface, the position, direction, energy and time are recorded at first gas entry, and Geant4 transport is stopped before any gas interaction. Heed then calculates the interaction and ionization [104], avoiding a second calculation of the same gas interaction. Each ionization site supplies primary electrons with their positions and creation times. Neutrons and other particles outside this interface require the treatment described in Section 3.4.3.

Bulk drift samples diffusion and attachment through macroscopic transport coefficients, without following every electron collision. The microscopic mesh calculation starts from each electron’s drift endpoint and accumulated time. These calculations describe successive parts of the electron’s path.

3.4.3 Neutrons and primary-electron generation

The present Heed interface supplies primary electrons for photons, electrons, positrons and muons directly to Garfield [104]. Their number is not sampled again from the deposited energy. Neutrons and other particles outside this interface must remain in Geant4 inside the gas, so their collisions, recoils, captures and secondary particles are calculated there. An additional conversion from gas deposits to primary electrons connects these interactions to the same Garfield drift, amplification and waveform calculation (Figure 3.10).

TODO / PRELIMINARY. Complete and validate the neutron deposit-to-electron interface. The description below specifies the method intended for the final version of this thesis; the current response comparisons do not test this neutron extension.

The deposit-based interface applies the primary-charge yield and fluctuation relations in Equations 2.7 and 2.8 to the electron-equivalent energy \(E_{\mathrm {ee}}\). For a recoil stopped in the gas, \begin{equation} E_{\mathrm {ee}}=q_{\mathrm {ion}}(E_{\mathrm R})E_{\mathrm R}, \end{equation} where the ionization quenching factor \(q_{\mathrm {ion}}\) is defined in Section 2.1.3 and depends on recoil species, energy and gas composition [69]. The interface samples an integer electron number according to the charge-yield and fluctuation model and places the electrons along the recorded gas steps, retaining their creation times. As an existing example, the local REST conversion used in the timing study starts from a Poisson draw (the \(F=1\) approximation), replacing a zero count by one electron for a positive deposit. Other REST configurations specify Fano fluctuations; the sampling prescription must therefore be identified for each response. The mean pair-creation energy \(W\) determines the charge yield, rather than the initial kinetic energy assigned to each electron.

3.4.4 Focusing and amplification at the Micromegas

The local field describes the nominal \(3\times 3\) pattern of circular mesh holes above a diamond readout pad. Figure 3.11 shows the field around the holes and through the amplification gap. For the illustrated Ar/isobutane 99/1 mixture at 1.4 bar, the drift field is 155 V cm⁻¹, while the 50 µm amplification gap has a nominal field of 67 000 V cm⁻¹, over 400 times stronger.

The microscopic calculation follows multiplication and losses by attachment or to the conductors, retaining each electron’s position relative to the holes. The mean collected gain includes injections that produce no collected charge. Figure 3.12 follows one event from chamber-scale drift to microscopic amplification. The calculation uses an ideal periodic geometry; the complete chamber field and variations in manufactured dimensions remain to be studied.

3.4.5 Charge collection and channel waveforms

Each electron reaching the anode is assigned to the pad containing its landing position, and connected pads contribute to the same channel. This retains sharing between strips when an avalanche spans several pads, instead of assigning all its charge to the centroid. Electrons lost before collection or landing outside the active readout do not contribute to channel charge.

The Python waveform calculation adds pulses delayed by the collected electrons’ arrival times, samples the result and converts it into integer analog-to-digital converter (ADC) values. Measured acquisitions provide the shared pulse template, channel delays and residual noise; the development energy peak fixes the conversion from collected charge to ADC amplitude. The effective template may include gas and illumination time spread, while induced currents and the complete electronic circuit are not calculated separately. Figure 3.13 illustrates the resulting waveforms and reconstruction.

3.4.6 Common event reconstruction

For the measured calibration run used in the response comparison, REST removes slow baseline variation with a 75-sample moving average, limiting the influence of large excursions. It then estimates the common fluctuation at each time sample from the median of the channels and subtracts its variation about the baseline. TPC and veto channels are treated separately, and the median reduces the influence of pulses confined to a few channels.

The saved measured waveforms have already undergone these corrections. We generate simulated waveforms at the same stage, using the collected-electron response, empirical pulse and residual noise obtained from calibration data. Both samples enter the same REST reconstruction with the same readout mapping and settings, without repeating the common-mode correction. The remaining baseline and noise are estimated from samples 20–199, approximately 0.8–8.0 µs at the 40 ns sampling period, before detecting pulses above noise and fitting the accepted signals. The channel fixes each strip hit’s transverse position, the fitted peak time its drift coordinate and the amplitude its weight. Summed hit amplitudes supply track energies; the two main tracks provide the calibrated event energy used for selection (Section 3.5.3), rather than waveform integrals or deposited truth energy. Weak channels can be lost through thresholding or unsuccessful fits.

Hits are clustered independently in the XZ and YZ projections. All reconstructed tracks contribute to multiplicity, while the track with the largest summed amplitude in each view supplies the main-track observables: the weighted center and widths, energy, and charge and hit-count balance. These projections do not give a unique three-dimensional track. The longitudinal width reflects pulse times after shaping and fitting as well as gas diffusion.

Section 3.5 defines these observables and the fixed baseline, and Section 3.6 compares their distributions and selection acceptance with calibration data. No correction is applied to reconstructed observables after waveform reconstruction; the additional gain calibration in Section 3.6.3 acts on the signal before this stage.

The IAXO-shaped cathode aperture provides a simple check of the reconstructed transverse positions. Figure 3.14 compares measured \(\ce {^{55}Fe}\) calibration events with a REST detector response simulation using a similar source position. The IAXO lettering is clearly visible in both samples.

3.5 Event observables and multivariate selection

The reconstruction provides the quantities needed to identify X-ray candidates and compare measured events with simulations. Energy, position and track multiplicity define the initial candidate population; the reconstructed charge distribution then provides further discrimination. This section introduces these observables, fixes the common TPC baseline and describes how a multivariate selection combines the shape information. The following section tests whether the simulated response reproduces both the observables and the fraction of calibration events passing that baseline.

3.5.1 Energy, position and track multiplicity

The most energetic track in each strip view supplies a charge estimate and a position in that projection. The two charge estimates are combined and converted to energy using the accepted calibration for the run or simulated sample. Their amplitude-weighted positions give the transverse track center. These quantities determine whether the candidate lies in the energy window and central detector region used for the background comparison.

The number of reconstructed tracks describes whether the hits form one connected track or several in each view. A localized X-ray conversion usually forms one track per view, while extended interactions and separated secondary deposits can form additional tracks. Track multiplicity is therefore useful for selection, although it does not directly count the physical particles that interacted. Section 3.5.3 specifies the exact requirements on these reconstructed quantities.

3.5.2 TPC observables used by the BDT

The TPC boosted decision tree (BDT) uses fifteen quantities derived from the main track in each view, listed in Table 3.3. Pulse amplitudes weight the hit positions when calculating the track center and widths. The transverse widths describe the spread of charge over strips, while the longitudinal width is obtained from the fitted pulse times and drift velocity. It therefore includes the effects of signal formation and reconstruction as well as electron diffusion. Hit counts describe how many reconstructed strip hits contribute to a track, and the balances compare the charge and shape reconstructed in the two views. Skewness measures departures from a symmetric charge distribution.

Calibrated energy, radius and number of tracks enter the baseline selection rather than the BDT. Particle identity and simulated interaction information are also excluded, so the classifier can be applied to reconstructed data. The main-track energy fraction is retained in the existing classifier, although the one-track requirement makes it essentially unity at this stage.

3.5.3 Universal TPC baseline selection

Throughout this thesis, the TPC baseline denotes the conjunction \begin{equation} C_{\mathrm {baseline}}=C_V\cap C_E\cap C_M\cap C_F. \label {eq:tpc-universal-baseline} \end{equation} The four criteria in Table 3.4 apply to laboratory data and reconstructed simulations for every source, including \(\ce {^{55}Fe}\), muons and neutrons. They use measured or emulated detector observables rather than simulation truth. The criteria remain fixed when the gas, voltage, available readout channels or calibrated response change between runs. The term fiducial refers specifically to \(C_F\).

The maximum-energy XZ and YZ tracks supply \(E_X\), \(E_Y\) and their respective amplitude-weighted centers \(\bar x\), \(\bar y\). The energy scale is fixed before evaluating the selection. These quantities describe the main tracks, rather than all event hits or the true gas deposit.

Reconstruct first; select afterwards. All channels admitted by the documented readout and waveform processing are reconstructed before applying the baseline. The native direct hits-to-track chain clusters XZ and YZ hits separately: an edge joins two hits if their distance in that projection is strictly less than 3.5 mm, and connected components form tracks. Connectivity is transitive, so 3.5 mm is not a maximum track diameter. An isolated hit is a track; there is no exemption for a low-energy secondary track. No radial hit mask is applied before counting them. A second track outside the central circle therefore still fails \(C_M\). One track in each view does not establish that only one physical particle interacted.

The validity checks establish usable observables, not fit quality or particle identity. The spatial requirement concerns only the maximum-track center: some hits may lie outside the circle, and no additional selection on \(z\) is imposed. Widths, energy or hit-count balance, pulse shape, learned classifiers and veto activity are not baseline requirements. Undefined unused topology features do not remove an otherwise accepted event. Waveform thresholds, channel masks and drift conversion are reconstruction settings applied before this event selection and documented separately.

Selection sequence and scope of efficiencies. Report the stages in the order input, valid reconstruction, energy, multiplicity and fiducial, retaining the failures at each stage in the accounting. The arrows in Figure 3.15 follow this reporting order; an event must satisfy all four criteria. Every quoted acceptance states its numerator and denominator. An acceptance among saved or valid reconstructed events is not an absolute efficiency per generated photon; the latter also requires primaries with no saved or reconstructed event. Diagnostic plots may deliberately precede the baseline, provided their population is named. Additional veto or topology selections are separate stages and cannot be absorbed into the word “baseline.”

The TPC baseline selection at a glance

3.5.4 Calibration and background distributions

Figure 3.16 shows six of these observables for the simulated calibration and cosmic-background candidates used to check the conventional-response classifier. The calibration sample contains 11 499 \(\ce {^{55}Fe}\) events from the original test partition of one merged simulation file. This retrospective partition separates events by their identifiers; it is not an independent simulation production or a blinded validation sample. The background sample contains 172 candidates from 129 cosmic-production groups excluded from classifier development: 141 neutron, 30 proton and one electron candidate. Both populations pass the common baseline and have finite values for all 15 classifier inputs, before applying the BDT or veto selection. Each candidate is counted equally; these shapes do not represent source-normalized background rates. These samples illustrate the populations entering the conventional-response selector. The measured-data comparison in Section 3.6 checks how well the response models reproduce the reconstructed shapes.

The remaining cosmic candidates often occupy fewer strips and have smaller widths than the calibration events: the median minimum hit count is two, compared with nine for \(\ce {^{55}Fe}\). Their transverse widths are also less balanced between views. The energy balance overlaps substantially, showing why no single quantity fully separates the two populations. These are backgrounds that already passed the compact-event baseline; extended tracks rejected earlier do not appear in this comparison. The BDT combines the differences and their correlations into one selection.

3.5.5 Multivariate event selection

Combining reconstructed observables can improve the separation of signal and background compared with individual selection criteria. A multivariate classifier assigns a score \(s(\mathbf {x})\) to the reconstructed observables \(\mathbf {x}\), and events are selected by placing a threshold on this score. Two methods are used here: binned log-likelihood ratios and boosted decision trees. The TPC classifier uses the shape quantities introduced above, while the veto classifier uses its own pulse and panel observables.

Binned log-likelihood ratio (“log-odds”). Normalized histograms of the training samples estimate how each observable \(x_j\) is distributed in signal (\(S\)) and background (\(B\)). Their contributions are combined as \begin{equation} s_{\mathrm {LO}}(\mathbf {x})= \sum _j\ln \frac {\widehat p_j(x_j\mid S)}{\widehat p_j(x_j\mid B)}. \label {eq:software-log-likelihood-score} \end{equation} Values more common in signal contribute positively to the score. Small smoothing terms avoid infinite ratios in empty bins. The method is easy to interpret, although it neglects correlations between observables within each class, as in the naive-Bayes approximation [105].

Boosted decision trees (BDTs). A decision tree separates events through successive selection criteria on their observables. Boosting combines many trees. In gradient boosting, successive trees are fitted to improve the combined prediction [106]. This allows correlations and more complex boundaries to be used, but also makes overfitting possible. Applications include particle-identification studies for MiniBooNE [107], rejection of misreconstructed pulses in XENON1T [108], and selection of rare \(B_s^0\to \mu ^+\mu ^-\) decays in CMS and LHCb [109]. The classifiers used in this thesis are implemented in scikit-learn [105].

Selection and performance. Training, threshold choice and final evaluation use separate samples. Splitting by complete runs or simulated histories helps avoid using closely related events for both training and testing [105]. The partitions used for the TPC and veto studies, and the limitations of the archived calibration samples, are described in their respective chapters. For a threshold \(t\), events with \(s\geq t\) are accepted. The signal and background acceptances are \(\varepsilon _S=N_{S,\mathrm {pass}}/N_S\) and \(\varepsilon _B=N_{B,\mathrm {pass}}/N_B\), and the background rejection is \(1-\varepsilon _B\). A tighter threshold generally rejects more background but also loses signal. For example, a working point with \(\varepsilon _S=0.90\) and \(\varepsilon _B=0.01\) keeps 90% of the signal sample and rejects 99% of the background sample. These acceptances refer to the samples entering the classifier, rather than the full detector efficiency. Applying the result to measured data also requires an adequate description of the detector response.

Comparing classifiers. Scanning the threshold shows the background rejection achievable at each signal acceptance. This efficiency curve is called the receiver operating characteristic (ROC), a term also used in HEP tools such as TMVA [110]. Its standard form plots signal acceptance \(\varepsilon _S\) against background acceptance \(\varepsilon _B\); HEP plots often show the equivalent background rejection \(1-\varepsilon _B\) against signal acceptance instead. The latter directly answers a useful experimental question: how much background can be rejected while retaining a chosen fraction of signal?

The area under the ROC curve (AUC) summarizes the separation over all thresholds [110]. With \(\varepsilon _B\) on the horizontal axis and \(\varepsilon _S\) on the vertical axis, an uninformative score gives a diagonal curve with AUC \(0.5\), while perfect separation gives AUC \(1\). A larger AUC indicates better overall separation, but it does not determine the best operating point for the experiment. For rare-event searches, the background rejection at the required signal acceptance remains the more direct measure of selection performance.

Chapter 4 applies these methods to distinguish neutron-associated veto activity from calibration-triggered activity; the control acceptance measures the fraction not tagged by the veto. Chapter 5 sets the TPC working point and evaluates the background surviving it, using the observables described in Section 3.5.2.

3.6 Response calibration and comparison with data

The refined response was compared with IAXO-D1 \(\ce {^{55}Fe}\) acquisitions in Ar/isobutane 99/1 to test reconstructed event properties and baseline acceptance. We first calibrated the mean amplitude and compared the reconstructed distributions, then examined an additional gain correction at the reference condition. These comparisons test the calibrated response as a whole, including waveform inputs derived from measured data.

3.6.1 Calibration across operating conditions

The gas, geometry and fields determine electron transport for each operating condition. Two electronics groups use shared effective pulse shapes and channel delays learned from 28 whole development runs. Each acquisition provides its residual-noise sample, trigger placement and reconstruction settings. In this initial comparison, only the conversion from collected electrons to ADC amplitude is fitted within each run, using the energy-peak position in its development sample. Widths, multiplicity, spatial distributions and selection acceptance are not used in that fit. The per-run amplitude calibration therefore accompanies a shared empirical waveform response, as summarized in Table 3.5.

The comparison covers 40 acquisitions, including twelve whole checking runs excluded from the shared-pulse calibration. Measured and simulated checking blocks are separate from amplitude fitting; previously inspected acquisitions and shared simulation histories make this a consistency check. Before the additional R02729 gain variation discussed below, the median simulation/data width ratios in the twelve checking runs are 0.977 transversely and 0.943 longitudinally. Nevertheless, simulation has greater baseline acceptance in 38 of 40 acquisitions, with a median absolute difference of 16.1 percentage points in the twelve checking runs (Figure 3.18). Agreement of central widths therefore does not establish agreement of the selection efficiency.

The larger R02729 sample below examines the response distributions and their effect on selection in more detail.

3.6.2 A representative calibration run

To compare the response distributions with larger samples, we selected run R02729, recorded in nominal Ar/isobutane 99/1 at 1.4 bar. It contains over 62 000 saved events, with a calibration-peak variation of about 1% across twelve time blocks. We used 10 000 measured waveforms spread across its checking blocks and 15 000 fresh gas-entry histories for the individual-electron Garfield model. A new conventional REST production supplies 12 000 gas-interacting histories, of which 200 are reserved for the amplitude calibration and the remaining 11 800 for the comparison. The two simulations use the reference chamber geometry and source position, with the same nominal gas, pressure and 155 V cm⁻¹ drift field.

REST starts from gas energy deposits, while Garfield starts from particles entering the gas. The comparison is therefore conditional on these populations and does not measure the efficiency for an emitted photon to produce a recorded event.

The measured and simulated waveforms undergo the same REST reconstruction, with the same readout, energy conversion and settings. Both simulations use residual noise from the measured development sample. The conventional calculation retains its analytic pulse and additional charge smearing common to the whole event, while Garfield uses microscopic avalanches and the shared empirical pulse described above. The avalanches fluctuate, but no additional event-by-event gain variation is included in this Garfield comparison. The amplitude calibration and separation of development and checking events follow the procedure above; widths, positions and acceptance are not fitted. The previously inspected acquisition provides a consistency check of the complete calibrated chains.

Figure 3.19 compares the reconstructed energy, position, widths and balances between strip views before the baseline selection criteria. Energy and radius provide response checks alongside the shape variables used by the BDT.

Garfield better reproduces the longitudinal-width distribution and the charge balance between the two strip views. For example, the median \(\sigma _z\) is 0.91 mm in data, 0.71 mm with conventional REST and 0.88 mm with Garfield. The transverse-width distribution changes more modestly, and both models describe the hit-count balance reasonably well. The agreement is not uniform: the Garfield energy peak remains too narrow, conventional REST describes the energy distribution better, and both models place events somewhat closer to the detector center than the measurement. Table 3.6 tests how these differences affect acceptance when the common selection criteria are applied together.

Chapter 5 develops the BDT selection using the separate calibration and background productions.

3.6.3 Energy response and additional gain variations

The remaining difference in the energy spectrum motivates an additional gain calibration. Primary ionization and avalanche multiplication both contribute to the energy width [73]. Garfield calculates these processes for the reference gas and mesh, and the waveform calculation adds the measured residual noise. The REST detector response also applies a common gain fluctuation to all hits in an event. We introduced a similar additional term in the Garfield waveforms to describe the remaining energy spread. Unlike fluctuations of separate electron avalanches, this term changes the signal from the whole charge cloud together.

The conversion from collected electrons to signal amplitude is multiplied by one positive factor \(g\) for the whole event: \begin{equation} g=\exp \left (s_g Z-\frac {s_g^2}{2}\right ), \qquad Z\sim \mathcal {N}(0,1). \label {eq:software-additional-gain-variation} \end{equation} Here \(s_g\) sets the spread and the subtraction in the exponent gives \(\mathrm {E}[g]=1\). We therefore keep the mean amplitude calibration while adding a gain variation between events. The reconstructed peak need not remain at exactly the same position after digitization, pulse detection and fitting. The same factor applies to the signal in both strip views before ADC conversion and reconstruction; the noise is added separately. This term describes an effective variation of the measured response, rather than changing the simulated ionization, electron trajectories or avalanches. The spectrum alone does not identify whether the missing spread comes from gain variations, the electronics response or other unresolved effects.

We fitted \(s_g\) to the width of the main energy peak in separate measured and simulated development events, keeping the existing mean amplitude conversion, pulse and noise fixed. The measured sample contains 9961 valid reconstructions from 10 000 events. The simulation uses 2000 fresh development histories from the reference source production, separate from the 15 000 checking histories. We fit a Gaussian in the same 4.4–7.5 keV window in the two samples, before applying the baseline or classifier selection, and compare its width in keV. The peak position is checked separately. The fitted spread corresponds to an additional gain RMS of about 9%. Separate checking events test the resulting spectrum after the parameter is fixed. This is a refinement motivated by the observed discrepancy, rather than a blind validation of the original response.

Figure 3.20 compares the measured and REST spectra with Garfield before and after the additional gain calibration. The two Garfield samples use the same checking histories. The measured, REST and Garfield checking samples contain, respectively, 9956, 11 792 and 12 574 valid events; the Garfield count is unchanged after the gain correction.

Before the additional gain variation, the Garfield response already reproduces the main calibration and escape-peak structures, alongside the improvements in drift width and charge balance shown in Figure 3.19. Its main energy peak is nevertheless too narrow. In the separate checking sample, the additional gain spread changes the fitted Gaussian width from 0.533 keV to 0.771 keV, close to the measured 0.751 keV. The fitted center and the high-energy tail still differ: 0.76% of corrected Garfield events lie above 8 keV, compared with 9.91% of measured events. With normalization to all valid events, the smaller simulated tail also contributes to the larger fraction in the main peak. The microscopic calculation therefore provides a useful description of the charge cloud response, while the additional empirical term improves the central energy spread. Section 3.6.4 evaluates the baseline acceptance after this correction, including the effect of the remaining spectral differences.

3.6.4 Impact of the detector response on event selection

The response distributions determine how many reconstructed events survive the baseline selection. A broader energy peak can move events across the energy limits, while secondary tracks and positions near the edge of the fiducial region affect the multiplicity and spatial selection criteria. We therefore apply the unchanged requirements of Section 3.5.3 to the same R02729 checking samples used above. Table 3.6 compares the selected fractions of valid reconstructed events; no response parameter or selection criterion is adjusted using these checking results.

The REST and original Garfield acceptances exceed the measured value by 6.7 and 10.4 percentage points, respectively. The additional gain variation reduces the Garfield discrepancy to 7.2 percentage points, but does not remove it. The improved energy width therefore accompanies a remaining difference in the selected fraction, for which the energy tails, positions and track multiplicities also matter. These selected fractions must be checked before transferring the response to the background studies in Chapter 5.

3.6.5 Limitations and further checks

Separate tests of electron assignment and noiseless waveform reconstruction check charge accounting, timing and pulse addition. These establish that the calculation is implemented consistently, while its physical accuracy requires comparison with measurements. The empirical pulse can include gas or illumination time spread, and the amplitude calibration can absorb both avalanche gain and electronics conversion. Consequently, the agreement above does not independently determine transport coefficients or absolute gain. A change in the field grid altered the collected charge per injected primary by about 5.8%, so gain convergence also requires further study.

Further checks must address the discrepancy in selection acceptance as well as the gain convergence.

3.6.6 Computational cost

The Garfield detector response follows individual electrons through drift and avalanche multiplication, while the REST detector response uses parameters for diffusion and effective gain. We compared the calculation times for calibration photons, muons crossing the gas, and a muon background sample transported through the shielding and veto geometry. The comparison quantifies the cost of the additional detail used in the response validation above. Both calculations use Ar/isobutane 99/1 at 1.4 bar and the same central 60 mm × 60 mm region, with fixed response parameters. The Garfield calculation omits ionization before entry into this region and gas-to-surroundings transport feedback; equal admitted areas do not ensure identical microscopic paths. They save channel waveforms after pulse formation, noise and ADC conversion; common event reconstruction is excluded. Each calculation uses a long continuous batch, spreading the initialization cost over many events.

Table 3.7 gives the generated particle counts and total wall time, including initialization and output. Figure 3.21 shows the fractions of CPU time spent in each stage and the CPU time per generated particle. Particles producing no gas signal remain included, so the background comparison also accounts for the transport of muons that do not produce a TPC event.

The microscopic gas calculation accounts for about 99% of CPU time for calibration photons and 96% for gas-crossing muons. The REST calibration calculation instead spends most of its time forming and saving waveforms. For the muon background, only 151 of the 150 000 incident particles have a primary or secondary reaching the gas; 44 events produce waveforms with REST and 46 with Garfield. Transport outside the gas takes 57% of the complete CPU time with REST and 48% with Garfield. Including the remaining Geant4 event processing, these fractions rise to 95% and 80%, respectively. In this background sample, the complete Garfield calculation takes 18% more wall time than REST, although its individual gas responses are much more expensive. The cost of the microscopic response therefore depends strongly on how often the simulated background produces a gas signal.

A single worker runs on the same processor core in both cases. The neutron guard rejects unsupported gas interactions; its success in these muon samples does not implement a general neutron charge response. The timing comparison is conditional on these source populations and response boundaries.

3.7 Simulation production

The background studies require large samples for several particle sources, shielding configurations and veto designs. These samples are generated in independent jobs following the chain in Figure 3.1. The simulation settings are maintained in the collaboration’s repository [111]. To obtain background rates, the exposure is calculated from the source distribution and the number of generated primary particles, including those that leave no recorded detector event.

3.7.1 Batch production

HTCondor [112] distributes the jobs across the DESY NAF-IAXO computing environment, with files stored in dCache [113]. The restG4ToCondor.py tool developed in this thesis prepares and submits the jobs and collects their logs and outputs. The workflow is shown in Figure 3.22.

An initial validation campaign comprised approximately 600 jobs and 40 000 saved cosmic-neutron and cosmic-muon events. Larger campaigns followed, as described in Chapter 5. Before combining the results, the files, simulation settings and exposure are checked (Table 3.8).

3.7.2 Reprocessing and saved information

Saving intermediate stages allows part of the calculation to be repeated when a model or analysis setting changes (Table 3.9). The starting point depends on the change: the Garfield response requires particle information at gas entry, while saved charge arrivals allow new waveforms to be generated. Each change also requires the following stages to be repeated.

Repeated responses and delayed subevents remain linked to their original particle for statistical analysis. Cosmic-production grouping also applies to classifier training and testing, so that related events do not appear in both samples. The retrospective partition of the archived calibration sample is described in Section 3.5.2. Threshold calibration and final evaluation are recorded separately.

Software versions, input files, geometry, seeds and analysis settings are saved to make the calculation reproducible. Automated software tests were migrated to GitHub Actions during this work. Physical validation relies on the comparisons with detector data and the source-normalization studies presented in the following chapters.

3.8 Supporting software and detector operation

We developed several tools to inspect simulated events, acquire waveforms and monitor the detector during operation. Figure 3.23 summarizes their roles.

3.8.1 Browser-based event inspection

We developed a browser-based viewer to display simulated particle tracks in the IAXO geometry. It uses three.js to render event information exported from REST, allowing events to be inspected without a ROOT installation. The design was inspired by the Phoenix event-display project [114].

The display helps identify the interactions responsible for a detector event and check the geometry and readout mapping. Time playback makes it possible to follow prompt cascades and delayed neutron captures. The viewer was also used to prepare the event illustrations in Chapter 5.

3.8.2 Acquisition and online waveform inspection

We developed feminos-daq from the legacy mclient software for the AGET/Feminos electronics [115]. It adds ROOT output, monitoring and a waveform viewer, with a CMake build. Incoming UDP frames are buffered while events are decoded and written, reducing the effect of short processing delays (Figure 3.25).

Event information and waveform samples are stored without custom ROOT dictionaries, allowing them to be read with ROOT or Uproot and converted to REST events.

The Python application feminos-viewer displays waveforms, channel activity and readout positions from local or remote files, including files still being written. During detector operation it was used to identify malformed events, inactive or noisy channels and incorrect readout mappings.

3.8.3 High-voltage control and operating conditions

We developed the hvps library [116] to provide a common Python interface to CAEN and iseg serial high-voltage supplies. It allows voltages, currents and channel status to be read, channels to be switched and voltage ramps to be configured. Command-line tools, Node.js bindings and a Node-RED node support scripts and slow-control dashboards. We also developed a graphical prototype for the CAEN N1471H supply.

These quantities help monitor the detector and identify periods affected by trips or unstable conditions (Table 3.10). Modeling gas transport also requires the electrode geometry and gas conditions. The library was distributed through PyPI and npm.

3.8.4 Uproot and fsspec integration

During a three-month IRIS-HEP fellowship, we contributed to the integration of fsspec into Uproot, the Python library for reading ROOT files. Previously, local files and remote protocols such as HTTP and XRootD required separate implementations in Uproot. The integration, released in Uproot v5.2.0, provides a common file-access interface and adds support for protocols handled by fsspec, such as SSH, cloud object stores and WebDAV.

This development allowed feminos-viewer to open remote DAQ files over SSH during acquisition and the background-analysis scripts to read simulation files directly from NAF-IAXO dCache storage. The experience with the ROOT format also informed the design of the DAQ output.

3.8.5 Python prototyping with Geant4

We developed geant4-python-application for small transport studies in notebooks and scripts. The package runs Geant4 in separate worker processes and was demonstrated with a photon-transmission calculation. The main simulation campaigns used restG4.

3.9 Summary

The framework described in this chapter follows particles from their generation to the reconstructed detector event. We extended restG4 and Geant4Lib with multithreading, track pruning, delayed-subevent handling and geometry-name resolution. The PDP method improved cosmic-particle injection, and the HTCondor tools allowed large simulation samples to be produced.

The Garfield response follows gas ionization, electron drift, amplification and individual charge collection before the common REST reconstruction. Measured pulses and residual noise complete the waveform response. The planned deposit-to-electron conversion extends this calculation to neutron gas interactions; its implementation and validation are marked preliminary in this draft. The reconstructed energy, position and multiplicity define the common TPC baseline. Widths, hit counts, charge balance and track asymmetry provide the inputs to the TPC BDT. Calibration and background distributions illustrate their role in event selection. After an empirical waveform calibration, typical reconstructed event widths are close to measurements, but the simulation overestimates baseline selection acceptance (Section 3.6). Chapter 5 fixes the additional BDT working point and evaluates signal acceptance, background rejection and source-normalized rates. Event viewers and readout mapping tools supported the simulation studies, while acquisition and high-voltage software supported detector operation. The Uproot/fsspec contribution and Python interfaces made local and remote data accessible for analysis and prototyping.

The following chapters apply these tools to the shielding and veto studies (Chapter 4) and the background model (Chapter 5).

Chapter 4
Shielding and Veto System

Introduction

Surface operation exposes the BabyIAXO detectors to cosmic-ray particles and their secondaries as well as to environmental radioactivity. Lead shielding attenuates environmental photons, but energetic neutrons can interact in the lead and produce additional neutrons, photons, and charged fragments. The active veto must detect activity associated with a low-energy Micromegas event, including showers whose primary particle never crosses the gas. This requires both prompt muon tagging and sensitivity to the later scintillator signals produced after neutron moderation and capture.

We studied a three-layer veto of plastic scintillator and cadmium surrounding the lead shield and compared its reconstructed response with measurements from the IAXO-D0 surface prototype. The chapter develops the shielding and geometry choices, explains the adopted prompt-plus-neutron selection, and assesses its experimental controls. We also compare passive-shielding alternatives for a future detector iteration, using the calibrated 2–7 keV background \(B^E\) as the main comparison and the TPC baseline as a separate check. The classifier studies test whether timing and segmentation add useful rejection and whether the gain remains stable across calibration runs.

Veto rejection is evaluated for a specified event population and compared at a specified calibration-control acceptance. For the background prediction, the veto is applied to the same X-ray-like time projection chamber (TPC) candidates selected in Section 3.5.3; the published prototype comparison retains its original selection. Chapter 5 relates the surviving counts to source activities or incident fluxes and treats radioactive decays outside the coincidence window separately. The simulation and reconstruction methods use REST-for-Physics and restG4, described in Chapter 3 [86–89].

4.1 Surface backgrounds and detector requirements

4.1.1 Detector configurations and requirements

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.

The design studies, prototype measurements, and BabyIAXO projection refer to distinct detector configurations, summarized in Table 4.1. The transport geometry, the prototype readout, and the operating channels have different panel inventories. The illustrated three-layer IAXO-D1 design contains 59 scintillator panels, while a separate geometry snapshot captured in September 2026 contains 60. The readout extracted from the original IAXO-D0 data defines 59 panel positions, of which 57 provided operational signals. Matching the number of positions does not establish equal panel dimensions or channel states, and neither geometry revision is assigned retrospectively to every historical simulation campaign. A background prediction for BabyIAXO at DESY requires finalized detector, source, and response specifications; the Zaragoza prototype result cannot simply be rescaled to obtain it.

4.1.2 Surface source inputs

The selected design studies use source-specific inputs rather than one generic “cosmic” sample. We simulated cosmic muons with the correlated sea-level parameterization of Guan et al., implemented in the CosmicMuons generator [99]. The neutron layer scans use the archived HENSA outdoor-spectrum input in the 1 MeV–10 GeV interval [117]. In the layer and inclination scans, the sampled zenith-angle distribution was proportional to \(\sin \theta \cos \theta \), instead of the intended \(\sin \theta \cos ^2\theta \). Transferring these results to the intended distribution requires angle-dependent event weights or new simulations. The source normalization and angular-distribution audit are documented in Chapter 5. The layer and inclination scans used the same HENSA input and sampled angular distribution. Earlier passive-shielding scans and cross-checks used CRY, while EXPACS provides an independent spectral comparison [91, 96, 97]. The fixed-volume alternatives in Section 4.2.5 instead use the full outdoor HENSA spectrum, extended down to 1 meV, with the corrected downward \(\cos ^2\theta \) angular distribution.

The HENSA input describes the outdoor neutron field, including atmospheric neutrons and neutrons produced or modified by the surroundings. The shielding comparisons use this field over the stated generation range. The background model instead approximates cosmic neutrons as predominantly downward and environmental neutrons as approximately isotropic, with some unquantified overlap (Section 5.3.2). The generators are described in Section 3.3.1.

4.2 Limits of passive shielding

4.2.1 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 sheets between the scintillator stages capture neutrons after they have slowed, producing 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 Micromegas gas 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.

Section 4.3.5 tests the transport models supporting this mechanism.

4.2.2 Comparison observables for shielding studies

Shielding optimization requires comparing many combinations of material, thickness, and position. The complete TPC baseline of Section 3.5.3 gives the event population used for the background prediction, but only a small fraction of generated particles produces an accepted event. At the available simulated exposure, the resulting statistical uncertainty can obscure differences between configurations. We therefore use earlier selection stages to compare broad shielding trends and evaluate promising arrangements with the complete baseline.

The closed-layer neutron scan of Section 4.2.4.0 illustrates this limitation. The Pb-only reference contains 8653 valid reconstructed events, of which 26 pass the complete TPC baseline. The configuration with the lowest observed valid-event yield contains 2169 valid events and six baseline events. For independent rare-event counts, the approximate relative statistical uncertainty scales as \(1/\sqrt {n}\). The baseline counts therefore have counting uncertainties of about \(20\%\) and \(41\%\), whereas the valid-event counts have uncertainties of approximately \(1\%\) and \(2\%\). Distributing the available computing resources among many configurations makes a precise baseline comparison substantially more demanding.

The first comparison observable is the yield of valid reconstructed TPC events, before the energy, track-multiplicity, and fiducial requirements. For configuration \(i\), its yield relative to a reference configuration is \begin{equation} R_i^{\mathrm {Valid}} = \frac {V_i/N_i}{V_{\mathrm {ref}}/N_{\mathrm {ref}}}, \label {eq:closed-shielding-valid-proxy} \end{equation} where \(V_i\) counts valid events and \(N_i\) includes all generated particles, including those producing no saved detector event. For the same physical source and generation normalization, the common source rate cancels. This ratio measures how the shielding changes the production of reconstructable TPC activity. It does not itself select the X-ray energy region.

The relationship to the baseline background depends on the remaining selection. Let \(\epsilon _i=N_i^{\mathrm {baseline}}/V_i\) be the fraction of valid events satisfying the energy, track-multiplicity, and fiducial requirements. For the same baseline area and energy interval in every configuration, \begin{equation} \frac {B_i^{\mathrm {baseline}}}{B_{\mathrm {ref}}^{\mathrm {baseline}}} = R_i^{\mathrm {Valid}}\, \frac {\epsilon _i}{\epsilon _{\mathrm {ref}}}. \label {eq:shielding-proxy-baseline-relation} \end{equation} The valid-event ratio approximates the baseline-background ratio when the remaining-selection efficiencies are sufficiently similar. A reduction in valid-event yield then implies a comparable reduction in baseline background. If the efficiencies change appreciably, the two ratios can differ.

The second observable retains an energy requirement while omitting the more restrictive track-multiplicity and fiducial requirements. The corresponding mean differential background-level approximation is \begin{equation} B_i^{E}=\frac {N_i^{E}}{T_i\,\Delta E\,A_E}, \label {eq:shielding-energy-selected-background} \end{equation} where \(N_i^{E}\) is the accepted count, \(T_i\) is the equivalent simulated exposure including all generated particles, \(\Delta E\) is the energy-window width, and \(A_E\) is the area over which these events are counted. Its units are counts keV⁻¹ cm⁻² s⁻¹. Restricting the energy interval makes this comparison more closely related to the analysis region and retains sensitivity to spectral changes that the unrestricted valid-event yield would conceal. It also retains fewer events. The energy-selected observable is therefore preferable when its statistical precision is sufficient for the comparison.

Each study must specify the energy definition and counting area. The lead-thickness and closed-layer comparisons below select calibrated maximum-track energies in 2–7 keV after detector response and valid reconstruction. Earlier comparisons used sensitive-gas deposits in 0.1–10 keV, without detector-response broadening. An estimate averaged over the full readout area also cannot be assigned to the smaller fiducial region without an additional assumption about the spatial distribution. The normalization in Equation 4.3 preserves these distinctions; it does not supply the missing selection efficiency.

These approximations are physically motivated when the shielding mainly changes the number of particles producing TPC activity while leaving the relevant energy, track-multiplicity, and position distributions approximately unchanged. Keeping the chamber, gas, and detector response fixed makes this plausible, but does not establish it. Moderator placement can alter the neutron spectrum, capture-photon contribution, and relative importance of electromagnetic deposits and nuclear recoils, changing the remaining-selection efficiency. The available spectra and selection efficiencies provide checks of this assumption; complete-baseline calculations for representative configurations are needed to test the inferred background reduction. Compatibility within broad statistical intervals cannot establish equal efficiencies. The earlier-stage observables guide the choice of configurations for further study, while final background predictions require the complete selection. Neither observable includes additional TPC classification or active-veto rejection unless those stages are evaluated explicitly.

4.2.3 Lead thickness and penetrations

We repeated the lead-thickness scan with complete detector response and the energy-selected observable \(B^E\) defined in Equation 4.3. The lead thickness ranges from zero to 250 mm, around an 18 cm cubic cavity. Both configurations retain the copper chamber and detector internals, without veto assemblies. The capped-pipe configuration also includes the copper X-ray pipe and its 5 mm end cap. Photon energies follow the tabulated atmospheric CRY spectrum [91], sampled over its full stored range. Neutrons use the full outdoor HENSA spectrum and source convention of Section 4.2.5; its distinction from the environmental model follows Section 4.1.2.

The comparison selects valid reconstructed events with calibrated maximum-track energy in 2–7 keV, before track-multiplicity, fiducial, classification, or active-veto requirements. We normalize each count to the 5 keV window, the full 36 cm² readout area, and the equivalent exposure obtained from all completed generated primaries and the geometry-specific source rate. Completed blocks with no accepted event contribute to the exposure; failed blocks and incomplete transfers are excluded. These rates describe energy-selected TPC activity and do not predict the background after the complete baseline selection.

The photon-induced response falls strongly with increasing lead thickness, while the capped-pipe configuration retains a larger contribution at large thicknesses. This difference demonstrates the importance of penetrations, although the scan does not separate transmission through the pipe from scattering around it. The thickest closed-shield photon configurations have few accepted events, so their upper limits remain relevant to the comparison.

The neutron-induced response rises at intermediate thicknesses and then decreases, with much weaker suppression than for photons. This behavior is consistent with competing attenuation and secondary production in lead; the scan alone does not identify the dominant interaction channels. It supports combining passive photon shielding with an active neutron-sensitive veto, without establishing 200 mm as an optimum. The statistical intervals exclude source and detector systematic uncertainties, and the snapshot can favor faster-finishing jobs while production continues.

4.2.4 Passive neutron moderation

We studied whether borated polyethylene (BPE) could reduce neutron-induced TPC activity while retaining the full 20 cm of lead required for photon attenuation. Hydrogen slows neutrons, while boron captures part of the moderated population; capture photons can also contribute to the detector response. The material ordering therefore matters as well as the total moderator thickness.

The closed-geometry study in Figures 4.2 and 4.3 compares BPE thickness, position, and layer count under this constraint. It concerns a future shielding iteration; the adopted detector design retains the full lead shield.

Moderator position and multiple layers

We compared closed cubic arrangements to study moderator placement with a fixed 20 cm total lead thickness on every face. The additional borated polyethylene (BPE) thickness, \(M\), takes values of 2.5 cm, 5 cm, 7.5 cm and 10 cm. The modeled BPE contains \(5\%\) natural boron by mass, with density 1.04 g cm⁻³. The detector occupies the same 18 cm cubic cavity in each arrangement. These idealized geometries omit the beam-pipe opening, electronics, and scintillator veto assemblies; they therefore test passive material ordering rather than the response of the complete detector installation.

We varied the lead thickness between the cavity and the first BPE layer, \(p\), from 0 cm to 20 cm in 5 cm steps. The BPE is divided into \(n=1\), 2, or 3 equal layers, each followed by a lead layer. For \(p<20\,\mathrm{cm}\), the remaining lead thickness is divided equally among these \(n\) layers. At \(p=20\,\mathrm{cm}\), a single BPE layer lies outside the full lead thickness. The comparison contains 52 BPE arrangements, 52 air controls with the same lead positions and outer dimensions, and a closed Pb-only shield.

Figure 4.2 illustrates the three-layer arrangement with \(M=10\,\mathrm{cm}\) and \(p=5\,\mathrm{cm}\).

Energy-selected background

We compare the energy-selected background \(B^E\), defined in Equation 4.3, relative to the Pb-only configuration. The selection retains valid events with calibrated maximum-track energies in 2–7 keV over the full 36 cm² readout, before the track-multiplicity and fiducial requirements.

The simulations use the full outdoor HENSA spectrum from 1 meV to 10 GeV and a downward \(\cos ^2\theta \) neutron field [100], with the same source surface and detector-response settings for all configurations. The cosmic trajectories are generated with the Probability Distribution Projection method described in Section 3.3.1. The combined sample contains approximately 3.55 × 10⁹ generated neutrons, 45 502 energy-selected events, and 524 events passing the complete TPC baseline. The two productions use independent random seeds, and no neutron contributes more than one energy-selected event in the accepted blocks. The exposure includes all generated neutrons in completed blocks, including those without a saved TPC event. Neither the TPC BDT nor active-veto rejection is applied.

The common source rate, energy interval, and counting area cancel in \(B^E/B^E_{\mathrm {Pb}}\), while the normalization accounts for the different generated exposures. Central 68.27% Clopper–Pearson intervals and one-sided 90% binomial limits are divided by the observed Pb acceptance; the reference uncertainty is shown separately. These pointwise intervals exclude model uncertainty and simultaneous coverage for the lowest observed result across the scan. The Pb-only control is therefore at 1.0 in Figure 4.3.

The lowest observed central yield occurs for \(M=10\,\mathrm{cm}\), \(p=5\,\mathrm{cm}\), and \(n=1\): approximately 963 energy-selected events per \(10^8\) generated neutrons, compared with 1384 for Pb only. This places a single 10 cm BPE layer between 5 cm of inner lead and 15 cm of outer lead. The ratio \(B^E/B^E_{\mathrm {Pb}}=0.696\) corresponds to a \(30.4\%\) reduction after energy selection. Placing all BPE outside the lead, \(p=20\,\mathrm{cm}\), gives little reduction at the largest moderator thickness. Dividing the BPE into several layers does not consistently lower the energy-selected background; the preferred ordering depends on the total thickness. At \(M=10\,\mathrm{cm}\) and \(p=5\,\mathrm{cm}\), two and three BPE layers give ratios of 0.771 and 0.778, respectively.

Replacing the BPE in the lowest-yield arrangement with air gives approximately 1221 energy-selected events per \(10^8\) neutrons, or 0.882 relative to Pb. The matched-air control has a higher central yield than BPE, with broader statistical intervals because of its smaller sample.

The remaining-selection efficiencies are compatible within the limited baseline statistics, which cannot establish their independence from shielding geometry. The \(B^E\) comparison therefore identifies promising arrangements without predicting a background level after the complete selection.

Lithium-containing capture layers

Capture on \(\ce {^{6}Li}\) produces an alpha particle and a triton [118], motivating an absorbing layer beside the moderator. We tested four BPE arrangements: \(M=10\,\mathrm{cm}\) with \(n=1\), 2, or 3, and \(M=7.5\,\mathrm{cm}\) with \(n=1\). Each retains 20 cm total Pb, \(p=5\,\mathrm{cm}\) inner Pb, and the original cavity and outer dimensions.

The composite contains equal LiF and poly(methyl methacrylate) (PMMA) mass fractions, \(95\%\) \(\ce {^{6}Li}\) abundance in the lithium, and density 1.62 g cm⁻³, as in Section 4.2.5. This assumed composition is not a characterization of a procured component. Only its passive effect on transported particles is included.

Composite layers of thickness 1 mm, 2 mm and 5 mm replace BPE on the detector-facing surface of either the innermost BPE layer or every BPE layer. Here \(M\) denotes the initial BPE thickness, and the thickness \(t\) applies to each treated interface. Treating \(m\) interfaces leaves \(M-mt\) of BPE, with \(m=1\) or \(m=n\). The placements coincide for \(n=1\), giving 18 distinct composite arrangements, four BPE controls, and a Pb-only control.

Preserving the envelope does not preserve the material mass or the amount of BPE. Outer interfaces cover larger surfaces: for \(n=3\) and \(t=5\,\mathrm{mm}\), treating every interface requires about 20.0 L of composite, compared with 2.44 L for the innermost interface alone. The corresponding composite masses are approximately 32.5 kg and 4.0 kg. The two placements therefore compare different quantities and distributions of absorbing material while displacing different amounts of BPE.

We used the same neutron source and TPC response as in the preceding scan. The current comparison contains 1 468 800 000 generated neutrons, with 15 705 events passing energy selection and 199 passing the full TPC baseline. Figure 4.4 compares \(B^E\), defined in Equation 4.3, relative to the Pb control from the same sample. Each configuration contains between 63 600 000 and 64 000 000 generated neutrons; the normalization accounts for these different exposures.

The lowest central value occurs for the BPE-only arrangement with \(M=10\,\mathrm{cm}\) and \(n=1\): \(B^E/B^E_{\mathrm {Pb}}=0.767\). Replacing 1 mm of its BPE with composite gives 0.779. Across the composite arrangements, central values relative to the corresponding BPE controls range from about 0.88 to 1.07, without a monotonic improvement with thickness. The comparison does not establish an advantage from lithium over the lowest-background BPE arrangement. After selecting energy, the remaining TPC criteria may reject different fractions of events in the BPE and LiF/PMMA configurations. Too few events survive the complete selection to determine whether the small differences in \(B^E\) persist.

Implications for a future shielding iteration

These closed-geometry results concern a future shielding iteration. The adopted design retains the full lead shield, and any proposed moderator arrangement requires further study with the beam opening, services, and veto materials restored. The treatment of thermal scattering in hydrogen bound in polyethylene also remains to be validated. The separate study below replaces part of the lead while preserving the outer dimensions, and therefore also requires a comparison of photon attenuation.

4.2.5 Fixed-volume shielding alternatives

The moderator scan described above retained the full 200 mm of lead and required additional space. For a future detector iteration, we also investigated whether part of the lead could be replaced by neutron-moderating and absorbing materials while preserving the outer dimensions of the shield. This comparison addresses a different design constraint: the material substitution reduces the lead thickness, so an improvement in the neutron response must eventually be assessed together with the change in photon attenuation. The adopted detector design retains the full lead shield.

We compared three configurations with the same 600 mm by 600 mm by 550 mm outer envelope. The Pb-only control contains 200 mm of lead. The Pb + BPE configuration replaces the innermost 50 mm with borated polyethylene (BPE), leaving 150 mm of lead on the exterior. The Pb + BPE + LiF/PMMA configuration uses 49 mm of BPE followed by a 1 mm lithium-fluoride/poly(methyl methacrylate) composite (LiF/PMMA) on the detector side. Both replacement configurations retain 150 mm of effective lead at the front collar; the existing 200 mm by 200 mm aperture in the lead remains an exception to the nominal lead thickness. Figure 4.5 shows three orthogonal sections of the Pb + BPE + LiF/PMMA configuration and an enlarged view of the thin capture layer beside the copper. The drawing omits chamber internals, electronics, the beam pipe, and veto assemblies.

The BPE model contains \(5\%\) natural boron by mass and \(95\%\) polyethylene, with density 1.04 g cm⁻³. The LiF/PMMA model contains equal LiF and PMMA mass fractions, a \(\ce {^{6}Li}\) isotopic abundance of \(95\%\) in the lithium, and density 1.621 94 g cm⁻³. These assumed compositions define the simulated materials; they are not measured properties of procured shielding components. The copper shield, beam pipe, and plastic-scintillator veto panels with their cadmium layers are unchanged. The veto material therefore participates in neutron transport and moderation even when its signals are not used to reject events.

Common source and TPC selection

We used the full outdoor HENSA neutron spectrum from 1 meV to 10 GeV, with an assumed downward \(\cos ^2\theta \) angular distribution [100]. This energy range extends below the 1 MeV threshold used for the archived HENSA layer and inclination comparisons. The source is treated as one outdoor neutron field; it is not added to a separate HENSA-derived environmental-neutron contribution. Each generated primary is one physical neutron, and all configurations use the same source normalization and detector-response settings.

The comparison applies the TPC baseline defined in Section 3.5.3 in the 2–7 keV region: valid reconstruction, one reconstructed track in each projection, and the 10 mm radial fiducial requirement. Neither the TPC boosted decision tree nor active-veto rejection is applied. The neutron-induced background after this selection is denoted \(B^{\mathrm {TPC}}\).

We converted the fraction of accepted events into a rate using the nominal neutron-generation rate of 1336.87 s⁻¹. Dividing this rate by the 5 keV energy-window width and the fiducial area of \(\pi \,\mathrm {cm}^{2}\) gives the mean differential background level. The simulated exposure includes every neutron in the completed, reconstructed simulation blocks, including those that produce no saved detector event.

We also calculate \(B^E\) using Equation 4.3, retaining valid events with calibrated maximum-track energies in 2–7 keV before the track-multiplicity and fiducial requirements. This estimate averages over the full 36 cm² readout rather than the baseline fiducial area. Both selections use the same generated sample and equivalent exposure.

The figure shows the background estimate with a central \(68.27\%\) statistical interval and a separate one-sided \(90\%\) upper limit. The interval summarizes the statistical precision of the estimate; the upper limit provides a one-sided bound under the adopted statistical model. Both quantify simulation statistics with the nominal source flux, geometry, material composition, and detector response held fixed. For \(k\) selected events among \(N\) generated neutrons, we scale the central 68.27% Garwood interval and the one-sided 90% Poisson count limit by the same factor \(\lambda /(N A\Delta E)\), with source rate \(\lambda \) and the area of the stated selection. This conditional Poisson model excludes uncertainty from source and response assumptions and does not establish coverage under the computing-time stopping rule or exclusion of failed blocks.

Preliminary comparison

Figure 4.5(e,f) compares the three shielding configurations at both selection stages. The Pb-only control gives the highest estimated neutron background. Replacing its inner lead with BPE lowers the central estimate, and adding the detector-facing LiF/PMMA layer gives the lowest estimate in this sample. The intervals show the statistical precision of these preliminary predictions; the individual upper limits do not establish the significance of the differences between configurations. The energy-selected estimates also decrease with the substitutions, but their relative changes are smaller than those after the complete baseline.

Implications for a future design

The lower central estimates motivate further simulation of both replacement layers. The present comparison does not establish an additional benefit from LiF/PMMA over BPE alone. As the samples increase, the incident-neutron energies and capture locations can help explain the differences between the configurations. The treatment of thermal scattering in hydrogen bound in polyethylene remains to be validated; increasing the sample size cannot resolve that model uncertainty.

Reducing the lead thickness can change the photon contribution and material-induced backgrounds even if the neutron response improves. A design recommendation therefore requires the corresponding photon and muon calculations, material radiopurity information, and a comparison after the final TPC and veto selections. These neutron-only results describe a possible future shielding iteration and are not inserted into the adopted full-lead background budget.

4.3 Neutron-sensitive active veto concept

The limits of passive shielding motivate a veto sensitive to the secondary shower surrounding a TPC event. We first identify the incident neutron energies that produce reconstructable activity and examine the neutrons generated in the lead. We then follow moderation and capture through scintillator deposits to reconstructed veto peaks, establishing the physical basis for the multilayer comparison in Section 4.4.

4.3.1 From surface primaries to taggable secondaries

The integral surface-neutron field does not directly describe the neutrons that produce reconstructable TPC activity. Figure 4.6 compares the CRY and HENSA outdoor primary spectra with the populations surviving the TPC validity requirement \(C_V\) of Section 3.5.3. This comparison precedes the energy, track-multiplicity, fiducial, classifier, and veto selections. The HENSA diagnostic uses the full input spectrum, including incident energies below 1 MeV, unlike the historical layer scans described in Section 4.1.2. The rates use the respective incident fluences and all generated primaries; bands show 68% statistical intervals.

The abundant low-energy source population is strongly suppressed after shielding and valid reconstruction. For CRY, the narrowest logarithmic interval containing 95% of valid events extends from approximately 20.7 MeV to 16.9 GeV. This interval is determined from the full-spectrum sample and identifies the primary energies that dominate reconstructable activity, rather than the energies of the resulting gas deposits.

The energy dependence also guides the allocation of simulation time. Figure 4.7 compares the valid-event yield per launched neutron and per transport CPU-hour. The CRY and HENSA samples are combined within each half-decade energy bin, so the result describes their sampled energy and angular mixture. Independent timing samples measure neutron generation and transport, including event recording; detector reconstruction, process startup, and finalization are excluded. The yield per primary rises with energy, whereas the yield per CPU-hour has a broad maximum around a few GeV because higher-energy showers cost more to simulate.

Additional CRY simulations restricted to energy intervals above 10 GeV extend this conditional-yield study to the input-spectrum endpoint, 8.17 × 10⁶ MeV. They do not enter the full-spectrum normalization or its 95% population interval. The sparse highest-energy results remain preliminary: failed simulations are excluded and may bias the completed sample. The CPU-yield axis starts at one event per CPU-hour; uncertainty intervals may extend below the frame.

4.3.2 Neutron multiplication in lead

Inelastic neutron collisions in lead leave excited residual nuclei that can emit additional neutrons through statistical evaporation [119]. Their characteristic energies reflect a nuclear temperature of order MeV, producing a broad low-energy component alongside faster cascade particles [120, 121]. The MeV component in Figure 4.8 is consistent with this mechanism, although the inclusive spectrum does not isolate evaporation. Its apparent peak shifts upward in logarithmic bins, which weight \(dN/dE\) by an additional factor \(E\).

We follow monoenergetic neutrons to their first nuclear interaction in natural lead, without a TPC selection. The prompt outgoing multiplicity, \(\nu _{\mathrm {out}}\), includes any surviving incident neutron, and its mean includes zero-neutron outcomes; the local change is \(\Delta n=\nu _{\mathrm {out}}-1\). At 1 GeV, the mean is approximately 7.9 outgoing neutrons per interaction. GeV-scale structure overlaps transitions between the hadronic models and requires model comparisons before assigning a physical origin. The following spectra and maps describe subsequent transport through the complete shield.

Secondary-neutron energies provide a complementary description of the cascade within the shield. The recorded birth spectrum in Figure 4.9 is concentrated around the MeV scale, where moderation in hydrogen-rich scintillator and subsequent capture become effective. The three-layer simulation uses HENSA outdoor primaries from 1 MeV to 10 GeV; first lead exits include neutrons from all birth volumes. The birth and exit spectra describe different populations, so their ratio does not give an escape probability. The next recorded volume after the first lead exit defines the copper-box and world fractions, which do not measure TPC acceptance. This diagnostic precedes the reconstructed TPC selection and describes recorded activity rather than complete secondary-neutron production.

Figure 4.10 locates the recorded lead-born neutrons in two central slices. The maps and their projections describe the spatial distribution of this activity, without correcting for the local lead volume. Births extend through the lead around the cavity, so neutron production cannot be represented by a single interaction point next to the TPC. This distributed origin motivates surrounding the shield with active material; the maps alone do not determine its optimum placement or thickness.

4.3.3 Tagging the secondary shower

The distributed cascade provides two complementary signatures: prompt charged-particle scintillation and gamma emission after moderated neutrons capture in cadmium near an active panel. Figure 4.11 connects their origin to their timing relative to the TPC trigger. Neutron line width qualitatively indicates kinetic energy; the local material section and signal times are schematic.

Figure 4.12 compares the physical origin of HENSA outdoor neutron events after TPC validity, the additional 2–7 keV energy requirement, and the complete TPC selection with the fixed BDT of Section 5.1.7.0. Each event is classified by following the ancestry of its largest depositing track within the gas back to the incoming energy carrier. Photons, electrons, and positrons form the electromagnetic class, while the neutron class includes local recoil energy and explicitly transported descendants. Protons and nuclei entering from surrounding material are separated from recoils produced by neutrons inside the gas. Other contains the remaining carriers, such as charged mesons and muons, and any histories that cannot be assigned uniquely. The valid and energy-selected populations contain 847 and 172 events, respectively. The BDT comparison uses a wider independently checked archived sample with only 13 survivors. The plotted fractions describe the composition of each selected population; they do not give category-by-category selection efficiencies between these different samples. Statistical intervals resample complete neutron histories; independent BDT events use Wilson intervals.

Electromagnetic carriers account for approximately two-thirds of both the valid and energy-selected events. An incident neutron can therefore produce low-energy TPC activity through photons and electrons generated elsewhere in its shower. Tagging the surrounding activity remains necessary even when the gas signal resembles an electromagnetic event. The class fractions after the complete TPC selection remain preliminary because of the small surviving sample.

We used simplified slab comparisons to examine how the position of lead changes the scintillator response (Figure 4.13). The BC408 slab is 10 cm thick; the three lead-coupled arrangements each contain 20 cm of lead, placed before, after, or on both sides of the active material. A bare slab provides the control. The configured source samples neutron energies uniformly in \(\ln E\) from 1 MeV to 100 GeV. Each point gives the fraction of saved scan entries whose total scintillator-energy proxy exceeds the stated threshold, without a TPC selection, acquisition gate, or reconstructed-peak requirement.

Electron-equivalent energy, denoted \(\mathrm {keV}_{\mathrm {ee}}\) or \(\mathrm {MeV}_{\mathrm {ee}}\), expresses scintillation response on the electron calibration scale. The scan uses a nominal \(500~\mathrm {keV}_{\mathrm {ee}}\) threshold to compare arrangements before light collection and waveform reconstruction; it is not the reconstructed veto operating point. Section 4.6.1 explains the detector light-response model and its sensitivity checks.

The effect of lead depends on the incident neutron energy and the layer order. For 1–10 MeV primaries, the fraction above threshold is 36.4% in the bare slab and 11.9% with upstream lead. For 0.1–1 GeV primaries, the corresponding fractions are 12.8% and 64.0%. The increased response at higher energy is consistent with detecting the secondary cascade produced in lead. These controls support coupling active material to the passive shield, while the complete geometry and reconstructed response are needed to assess veto coverage and background rejection.

4.3.4 Moderation and capture in the veto

The capture signature develops as neutrons from the shielding shower lose energy and move through the surrounding materials. Repeated elastic collisions with hydrogen in the plastic scintillator can transfer a large fraction of their kinetic energy to recoil protons. These protons produce quenched scintillation, while the slower neutrons continue to scatter, escape, or be absorbed. Moderation and capture are therefore separate processes: slowing a neutron does not guarantee its absorption in cadmium, and captures can also occur in the scintillator, shielding, and detector materials.

Natural cadmium has a large, energy-dependent absorption cross section for slow neutrons. At thermal energies, \(\ce {^{113}Cd}\) provides the dominant contribution. Consequently, a 1 mm sheet can absorb thermal neutrons efficiently even though it provides little shielding against fast neutrons. The radiative reaction forms an excited compound nucleus, illustrated schematically by \begin{equation} \ce {^{113}Cd} + n \longrightarrow \ce {^{114}Cd}^{*} \longrightarrow \ce {^{114}Cd} + \sum _i \gamma _i . \label {eq:veto-cadmium-capture-reaction} \end{equation} Slow-neutron capture releases approximately 9 MeV of nuclear binding energy, distinct from the initiating surface neutron’s kinetic energy. The nucleus generally emits several photons while returning to lower excitation states [122]. The cascade is prompt relative to the capture; moderation and transport determine when that capture occurs relative to the TPC trigger.

The cadmium sheets place this radiation close to active scintillator. Capture photons can Compton scatter, be absorbed, or produce electron–positron pairs in the surrounding materials, and their charged secondaries generate scintillation. Photons may escape or deposit energy in several panels, so the emitted cascade energy differs from the energy deposited in any panel or in all active material. Quenching then determines visible energy, and light collection and electronics determine reconstructed amplitude. Finite thresholds and the recorded time interval can leave a physical capture without a reconstructed peak. The effective 46.9 µs capture-tail timescale discussed in Section 4.3.9 consequently describes the selected geometry and gas-deposit trigger proxy, rather than the lifetime of the nuclear de-excitation.

4.3.5 Neutron transport and capture modeling

We calculate neutron collisions and the correlated secondary particles with Geant4, then convert scintillator deposits into reconstructed veto signals. The transport configuration of the optical-response study combines Livermore electromagnetic physics, the QGSP_BIC_HP hadronic component, high-precision (HP) neutron elastic scattering, and radioactive decay, with PhotonEvaporation enabled for capture de-excitation. Below approximately 20 MeV, HP models use evaluated neutron cross sections and scattering final states; higher-energy hadronic models supply the energetic shower [123]. An accurate absorption cross section alone does not determine how the excitation energy is partitioned among capture photons. Table 4.2 separates these stages from the detector response.

The supporting neutron-data validation used Geant4 11.0.3 with G4NDL4.6 [124]. At thermal energies, hydrogen is bound in the plastic, and its scattering law \(S(\alpha ,\beta )\) describes energy and momentum transfer to bound atoms. Agreement of constituent-weighted cross sections does not validate this treatment, which is not established by the archived high-precision settings and material mapping. The moderation-time distribution therefore remains incompletely validated. Section 4.6 distinguishes the historical scintillator response from the explicit optical and waveform study.

We checked two transport steps independently. A thin-target benchmark of outgoing neutrons from natural lead at 14.1 MeV was compared with EXFOR data in the measured energy and angular acceptance. The four tested high-precision reference lists lie \(8\)–\(9\%\) below the experimental integral and differ from one another by less than 1%. This comparison supports the secondary-shower interpretation but does not validate the full GeV-scale neutron response.

For capture de-excitation, the earlier default and strict-isotope ParticleHP treatments and PhotonEvaporation were replayed through the same detector-response and peak-finding chain. The evaluated capture final state samples available photon distributions, whereas PhotonEvaporation generates the compound nucleus’s de-excitation through nuclear transitions, including internal conversion. Different partitions of the cascade energy among photons change threshold-dependent response even when total emitted energies are similar. The probability of reconstructing any veto peak remains between 0.719 and 0.742, whereas the fraction of the processed response sample above the 10 MeV-equivalent operating point changes from 0.314 to 0.383. The any-peak response is therefore more stable than rejection at a fixed reconstructed-energy threshold. For PhotonEvaporation, selected gamma-line yields differ from evaluated values by up to approximately a factor of five, limiting the accuracy of individual spectral lines. This model spread is not a confidence interval on the true response; its incomplete propagation to the adopted classifier is discussed in Section 4.8. Capture histories provide the physical interpretation of timing; the adopted classifier receives reconstructed veto observables rather than capture-truth labels.

4.3.6 Capture multiplicity and initiating energy

A source neutron can initiate a shower containing several secondary neutrons, each of which may capture. We count captures in 3864 saved histories of the 60-panel, three-layer optical-response study described in Section 4.6, retaining 26 histories without captures. This population is conditional on the simulation saving the event; final TPC and veto selections are not applied.

The 101 091 captures give a mean of 26.2 per history and a median of 14; the mean in cadmium is 20.6. Figure 4.14 shows the mean increasing from 1.0 capture at 1–10 MeV to 58.1 at 1–10 GeV. The initiating energy is distinct from the neutron energy at capture and the binding energy released. The increase reflects multiple capture opportunities within the shower; these captures remain correlated descendants of one incident neutron. We resample complete histories to retain correlations among captures from the same shower.

4.3.7 Capture materials, faces, and layers

Capture locations determine which scintillator panels can intercept the emitted radiation. Figure 4.15 groups the volumes where captures occur, distinguishing cadmium sheets, active plastic, shielding, and other detector components. Cadmium sheets account for 78.8% of the 101 091 capture endpoints, and active plastic for 13.7%. The saved volume names assign cadmium captures to detector faces and native layer indices, ordered from the shielding outward. Layers 1, 2, and 3 contain 62.7%, 29.3%, and 8.0% of cadmium captures, respectively; captures reach all three in 55.0% of stored histories. These are successive layers within a single design. Most captures occur in the inner stage, but the response extends across the surrounding layers, motivating a comparison of their additional reconstructed tagging contribution.

Each capture contributes to the material and position distributions, so a history with many captures carries more weight than one with a single capture. Source direction, geometry, and stored-event selection influence these fractions, which lack face-area or incident-exposure normalization. They describe the absorbed-neutron population, rather than capture efficiency for an incident neutron. Section 4.3.8 tests how capture location translates into scintillator deposits.

4.3.8 Capture photons and scintillator deposits

We sum the direct photon energies, \(E_{\mathrm {emitted}}^{(\gamma )}\), for each cadmium capture and trace their electromagnetic descendants into the plastic. Direct conversion electrons and subsequent nuclear or radioactive-decay branches are excluded. The attributed plastic energy, \(E_{\mathrm {vis,plastic}}^{(\gamma )}\), already includes the saved quenching. We compare these energies through \begin{equation} R_\gamma = \frac {E_{\mathrm {vis,plastic}}^{(\gamma )}} {E_{\mathrm {emitted}}^{(\gamma )}} . \label {eq:veto-capture-visible-fraction} \end{equation}

The median \(R_\gamma \) over 79 645 captures is 18.1%; the ratio of total visible to total emitted energy is 25.2%. A capture reaches a median of four panels (Figure 4.16); 2.68% give no attributed plastic deposit. For nonzero responses, the largest panel carries a median 64.5% of the attributed plastic visible energy. These deposit counts use all saved times, without an acquisition gate or DAQ threshold. The complement \(1-R_\gamma \) includes photon energy deposited outside plastic, quenching, escape, and omitted descendant branches; it does not measure escape alone. The partial and shared deposits explain why a large capture probability does not translate directly into a large signal in one panel. Panel thresholds and the combination of signals across channels therefore enter the reconstructed response studied next.

4.3.9 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. To test how physical captures translate into observed signals, we use the separate 2706-entry processed three-layer sample in Figure 4.17. No additional TPC selection is applied. Here a late peak has reconstructed time \(t\geq 10\,\mathrm{\mu s}\); peaks before this boundary include the 5–10 µs interval as well as prompt and near-trigger activity. These peak times use the reconstruction alignment and are distinct from the truth-level gas-deposit time used below.

In this response sample, 98.3% of analysis entries contain a cadmium-sheet capture. At event level, however, 23.8% contain a cadmium capture but no reconstructed veto peak. Another 24.6% contain a cadmium capture and peaks only before 10 µs, while 49.9% contain a cadmium capture and 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 three-layer neutron 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 over 10–300 µs gives \(\tau =46.9\,\mathrm{\mu s}\). The cumulative retention uses captures with positive gas-relative delays below 2000 µs; it counts captures, not independently weighted events. Of these captures, 79.7% occur by 70 µs and 88.8% by 100 µs. 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. The prototype record spans approximately \([-30,+70]~\mu \mathrm {s}\) relative to its hardware trigger; relating that trigger to the first-gas-deposit proxy requires a separate response mapping.

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. Section 4.6.6 examines this timing information with reconstructed observables. 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 5.2.2. 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.

Together, these studies connect neutron multiplication in lead to spatially distributed prompt and post-trigger activity in the veto. Only part of the capture radiation appears as visible scintillator energy, and thresholds and timing determine which signals are retained. Section 4.4 therefore compares the reconstructed response of multilayer designs. Chapter 5 evaluates absolute background levels using the corresponding source normalization and TPC selection.

4.4 Multilayer design comparison

We compared the reconstructed tagging gained by adding active panel stages around the lead shield. The scan includes one-, two-, three-, and four-layer cadmium configurations, together with three-layer gadolinium and stainless-steel variants. It uses the historical HENSA outdoor input from 1 MeV to 10 GeV, with the common angular setting described in Section 4.1.2. The detector-response chain includes quenching, light attenuation, waveform formation, and veto-peak reconstruction.

Figure 4.19 illustrates the repeated-stage concept using the panel construction in the preserved September 2026 reference geometry. A layer denotes an active panel stage; the reference construction has cadmium on both broad faces of the scintillator, so the stage count differs from the number of capture foils. Repeating the stages adds moderator and active volume in which recoil and capture-induced energy deposits can be detected. The schematic omits detector-wide panel segmentation and services and does not specify the full historical scan layouts. Section 4.5 describes the prototype geometry and readout separately.

The scan exporter retains every entry in each processed AnalysisTree; it applies no additional one-track, 2–7 keV, fiducial, or X-ray-topology selection. The neutron-tagging fractions below are conditional on that processed response population. The nominal reconstructed-energy proxy is the sum of the exported veto-peak energies over an entry; its threshold is applied to that sum, rather than separately to each panel. It is distinct from the simulated scintillator-energy proxy used in the slab comparison of Figure 4.13.

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 stages, respectively. At a nominal \(10~\mathrm {MeV}_{\mathrm {ee}}\) threshold, the corresponding conditional rejection fractions 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, at the cost of another active layer and its associated readout channels. The gadolinium variant gives results similar to cadmium for these aggregate observables, whereas stainless steel provides substantially weaker tagging. The statistical intervals resample complete simulation files, treating files as independent and retaining correlations among entries within each file; they exclude source and detector-response systematic uncertainties.

Table 4.3 places these conditional tagging measures alongside the historical classifier rejection and the absolute background levels evaluated in Chapter 5, with their respective populations and treatments.

Normalizing the processed analysis-entry count to the number of generated primaries gives a probability of approximately \(2.2\times 10^{-5}\) for each of the one- through four-layer cadmium samples. The processed-entry probability is similar across these samples, so the principal gain shown here is in conditional tagging.

Each additional layer also adds channels that can contribute accidental activity. An illustrative overlay model samples the measured calibration-triggered veto activity. At relative accidental level \(\alpha \), an \(n\)-stage configuration receives an average of \(\alpha n/3\) independent calibration-template entries. Thus \(\alpha =1\) assigns one complete template entry to the three-layer reference, with fewer or more accidental opportunities for the other layer counts. The scalar addition assumes a common nominal energy scale for simulation and the calibration-derived template; this model does not validate that correspondence or the acquisition-window response.

To display the gain after accidental veto losses, we use the relative sensitivity proxy \begin{equation} Q(\alpha )=\frac {\epsilon _{\mathrm {noise}}(\alpha )} {\sqrt {1-r_{\mathrm {n+noise}}(\alpha )}} , \label {eq:veto-layer-sensitivity-proxy} \end{equation} where \(\epsilon _{\mathrm {noise}}\) is the acceptance against accidental vetoes alone and \(r_{\mathrm {n+noise}}\) is the rejected fraction of the overlaid neutron-response sample at the nominal \(10~\mathrm {MeV}_{\mathrm {ee}}\) threshold. We use \(\epsilon _{\mathrm {noise}}\) as a signal-retention proxy, assuming that signal events produce no correlated veto activity. The reference is the same conditional population without a veto, for which both signal and background retention are unity.

Over the scanned accidental range, the four-layer configuration retains the largest sensitivity proxy. At \(\alpha =1\), \(Q\) is \(1.274\) for four layers and \(1.232\) for three layers, while the corresponding noise-only acceptances are \(0.860\) and \(0.897\). These curves show a frozen realization of the scalar-overlay model, without a full uncertainty band for the detector response or accidental population. Three layers are an engineering and channel-count compromise made after most of the conditional tagging gain has been obtained; this model does not establish a statistical optimum. 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 \(S/\sqrt {B}\). The following section describes the three-layer prototype and its synchronized readout.

4.5 Prototype geometry and synchronized readout

4.5.1 Geometry and prototype construction

The three-stage veto surrounds the lead shield with Top, Bottom, Left, Right, Front, and Back panel groups. Layer 1 is closest to the shield, and layer 3 is outermost. The front group accommodates the X-ray beam pipe.

The prototype reused NE-110 plastic scintillator bars from a former time-of-flight spectrometer [125]. The bars were cut to 150 cm and 65 cm, with a \(20\times 5~\mathrm {cm}^2\) cross-section, and coupled to photomultiplier tubes (PMTs) through light guides. Cadmium sheets of 1 mm thickness were placed between neighboring panels to capture moderated neutrons close to active material [17]. The preserved transport references use BC408 scintillator and 80 cm short bars; their paired cadmium foils and wrapping are illustrated in Figure 4.19.

Atmospheric muons provided the gain-equalization reference. For muons crossing 5 cm of plastic, the most probable energy loss is approximately 10 MeV [17]. Measurements on the long bars showed that the collected light at the far end can be reduced by approximately a factor of two [17]. The reconstructed panel energy therefore depends on attenuation and calibration. This single-panel reference is distinct from the sum of reconstructed veto-peak energies used as the nominal threshold proxy in Section 4.4.

Figure 4.21 shows the spatial arrangement and group–layer–panel naming convention of the selected 59-panel IAXO-D1 design. The dimensions and spacings in the expanded drawing are schematic.

The archived prototype readout defines 59 panel positions, including two inactive channels, while the publication reports 57 installed panels [17]. Table 4.4 summarizes the resulting 57 operational channels. The readout map alone does not establish an installed-bar inventory; the transport and prototype configurations remain distinct (Table 4.1).

4.5.2 Electronics and timing

The Micromegas and veto branches each use four AGET application-specific integrated circuits, with 64 channels per chip and a 512-sample circular buffer [17, 83]. Separate field-programmable gate arrays (FPGAs) permit different readout settings for the two branches, while a common module supplies the trigger and clock reference. The Micromegas electronics trigger readout of all veto channels. The TPC record was set between 10 µs and 30 µs to contain the drifting charge, while the nominal veto record lasts 100 µs with the trigger 30 µs after its start [17].

Figure 4.23 relates the acquisition branches to the veto time coordinate. The veto record spans approximately \([-30,+70]~\mu \mathrm {s}\) relative to the Micromegas hardware trigger. Activity near zero supplies the prompt tag, while later capture-related peaks contribute to the post-trigger tag if they arrive before the waveform ends. This hardware trigger differs from the first simulated gas deposit used as the time origin in Figure 4.18.

The long veto record makes prompt muon and shower activity and a substantial part of the capture-related tail available for analysis. A wider accepted coincidence interval also increases the probability of accidental vetoes; its effect on acquisition live time depends on the trigger and readout settings. The following section describes how the recorded signals are reconstructed into the observables used for event selection.

4.6 Veto response and event selection

The recorded veto signals described in Section 4.5.2 depend on the light produced by each deposit, its collection along the bar, and the waveform reconstruction. We follow these stages to construct veto observables, test prompt tagging with experimental TPC tracks, and define the selection used for the background model. The nominal response uses an effective attenuation law; a separate optical-photon study tests response assumptions with measured activity added before waveform reconstruction. The adopted prompt-plus-residual-BDT selection is presented before the historical classifier comparisons that explain its choice.

4.6.1 Scintillation quenching for neutron-induced deposits

Neutrons produce scintillator light through the charged particles created in their interactions, including recoil protons and heavier nuclei such as carbon. These particles can deposit energy densely along short paths, reducing the light produced per unit deposited energy. The reduction depends on the particle and its energy, so neutron-induced deposits cannot be assigned one constant quenching factor. Capture photons produce light mainly through secondary electrons and positrons, whose response differs from that of nuclear recoils.

For an explicit charged-particle step, the first-order Birks approximation relates deposited and visible energy through \begin{equation} E_{\mathrm {vis}}\simeq \frac {E_{\mathrm {dep}}}{1+k_{\mathrm {B}}E_{\mathrm {dep}}/\Delta x}, \label {eq:veto-scintillator-birks} \end{equation} where \(\Delta x\) is the charged-particle path associated with the deposit [126, 127]. We use the nominal coefficient \(k_{\mathrm {B}}=0.126\,\mathrm{mm}\,\mathrm{MeV}^{-1}\). With no dedicated recoil-light measurement for these bars, this is an adopted response parameter. The visible energy is a light-yield proxy before optical collection and electronics, rather than the energy ultimately reconstructed in a channel.

This treatment follows established simulation practice. Ros et al. used the same coefficient in Geant4 simulations of electron and proton response in polystyrene scintillator [128]. For thermal-neutron detection in boron-loaded plastic, Porosev and Savinov adopted Birks parameters from published work and examined the response dependence on step limits and secondary-production thresholds [129]. Their capture products and material differ from ours, so this comparison supports the modeling approach rather than a numerical transfer of light yield. Measurements by Pöschl et al. further show that quenching depends on the plastic composition [130].

The archived response introduces an additional approximation: local energy-loss density is estimated using distances between neighboring stored hits instead of the true charged-particle step. For energy deposited locally on a neutron track, that distance need not represent the stopping path of the unresolved recoil. This limits the physical accuracy of the light estimate, especially for short recoil tracks. The saved scintillator energies already include this historical Birks treatment and enter the optical response once; applying another quenching factor would suppress the same energy twice.

The neutron-veto predictions therefore remain conditional on the adopted light-response model. The separate optical-response study below tests the consequences of this approximation while keeping the muon gains fixed.

4.6.2 Veto readout geometry and light attenuation

The position of an energy deposit in a scintillator determines which veto channel receives its signal and how far the light travels before collection. These two operations must describe the same bar: an incorrect orientation can assign a deposit to the wrong channel or reverse its attenuation along the bar. We therefore extended the spatial readout description in REST-for-Physics and developed tools to construct the veto channel map from the simulated geometry [86].

In TRestDetectorReadout, each scintillator is represented by an independent readout plane, with one module and one channel covering its cross-section. The plane lies at the light-guide end of the bar, and its normal points along the bar toward the opposite end. Its sensitive depth is therefore the bar length, rather than its thickness. The generator obtains the bar center and light-guide position in global coordinates, derives the longitudinal direction from their separation, and places the plane at the corresponding bar end. Local transverse axes describe each panel’s cross-section in its own orientation.

For a deposit at position \(\mathbf {r}\), the projection onto the local transverse axes determines whether it lies within the channel cross-section. The longitudinal coordinate is \begin{equation} d_j=(\mathbf {r}-\mathbf {r}_{0,j})\cdot \hat {\mathbf {n}}_j, \qquad 0\leq d_j\leq D_j, \label {eq:veto-readout-distance} \end{equation} where \(\hat {\mathbf {n}}_j\) is the unit normal of panel \(j\). With a numerical guard \(\delta =1\,\mathrm{mm}\), the readout origin \(\mathbf {r}_{0,j}\) lies \(\delta \) before the physical bar end and its sensitive depth is \(D_j=L_j+2\delta \), where \(L_j\) is the bar length. The transverse acceptance is also slightly enlarged to retain deposits on numerical boundaries. Panel spacing must keep these readout regions unambiguous. The panel alias records its face, layer, and position; a separate map supplies the acquisition-channel identifier.

The same longitudinal coordinate sets the effective light attenuation applied before waveform formation: \begin{equation} E_{\mathrm {att},i}=E_{\mathrm {vis},i} \exp \!\left [-\frac {d_j(\mathbf {r}_i)}{\lambda _{\mathrm {att}}}\right ]. \label {eq:veto-readout-attenuation} \end{equation} Here \(E_{\mathrm {vis},i}\) is the visible-energy proxy for deposit \(i\) after the scintillator quenching described in Section 4.6.1, and \(j\) is its assigned panel. The attenuated deposits are then summed in their channel at the sampled arrival times, retaining the position dependence of each contribution. The nominal response configuration uses \(\lambda _{\mathrm {att}}=215\,\mathrm{cm}\), giving a factor \(0.50\) over 150 cm, consistent with the approximate decrease measured along the long prototype bars [17]. This effective length describes the collected response, including optical losses and coupling; it is not the manufacturer’s bulk-material attenuation length. The attenuation process also adds a configurable propagation delay. Subsequent signal conversion and acquisition timing must be included when defining the final peak time.

The generation checks recover the expected channel identifiers at panel centers and require unique identifiers in the combined Micromegas–veto readout. During attenuation, a veto deposit must match exactly one veto plane; missing or multiple assignments stop processing. Figure 4.24 illustrates the geometry and distance calculation. It uses the preserved 60-panel IAXO-D1 transport reference. The archived IAXO-D0 prototype readout instead defines 59 positions and 57 operational channels, with different short-bar dimensions. Geometry and acquisition maps must consequently be selected together for each comparison. For each geometry, the readout links deposits to panel labels and acquisition channels; response calibration remains a separate requirement.

4.6.3 Detector response and reconstructed observables

The nominal detector-response simulation converts the quenched and attenuated deposits into channel signals, shapes and digitizes them, and applies the REST-for-Physics peak finder (Fig. 4.25). Simulated and measured signals then have the same definitions of peak time, amplitude, multiplicity, and channel quality. This common reconstruction permits direct comparisons of observables, while agreement of the physical response must be tested separately.

A separate optical-response study follows 3864 saved neutron histories, with separate development and checking files. Explicit photon transport replaces the effective attenuation law, and a muon-calibrated bipolar pulse model is combined with one joint measured waveform record before reconstruction. Only 37 common channels contribute rejection; their optical properties and geometry transfer remain assumptions. The checking population contains 170 valid reconstructed 2–7 keV events, without the final TPC multiplicity or fiducial requirements. At a selection fixed with a 1% development-sideband activity budget, net additional tagging is 32.4% (95% whole-file bootstrap interval 26.3–38.3%). The same selection retains 468/473 and 1546/1560 actual-trigger \(\ce {^{55}Fe}\)-enriched controls in two acquisitions, or 98.94% and 99.10%; these fractions are not pure signal efficiencies or measured dead time. Varying \(k_{\mathrm {B}}\) by \(\pm 50\%\) with muon gains fixed changes net tagging to 28.2–35.3%, a model sensitivity rather than a confidence interval. These saved histories supply no generated-primary exposure, so this conditional check does not replace the adopted hybrid-veto background evaluation.

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

4.6.4 Prompt tagging and the adopted hybrid veto

We selected extended, approximately straight TPC tracks from measured background runs to test prompt tagging independently of the veto response. The selection requires sufficient strip multiplicity and spatial extent, compatible charge-weighted line fits in XZ and YZ, and no flagged TPC saturation. It yields 351 candidates in four background runs. These events are muon-like, but the selection does not establish particle purity or represent muons that miss the TPC and produce low-energy secondaries. The subsequent veto comparisons informed the choice of the hybrid selection, so they are development controls rather than an independent test of the adopted rule.

The fixed prompt-amplitude reference tags 339/351 candidates, or 96.6% with an exact 90% statistical interval of 94.5–98.0%, while retaining 87.8% of the calibration controls from run 1347. The historical neutron level-1 boosted decision tree (BDT) tags 57.5%, and the revised neutron level-2 amplitude and counts/timing models tag 25.4% and 37.6%, respectively. The muon-trained amplitude model tags 77.8%. These conditional experimental fractions demonstrate that the high simulated muon rejection cannot be transferred directly to measured tracks. A broader response comparison applies matching TPC requirements on strip multiplicity, spatial extent, and valid charge, without the straight-track refinement, and includes all experimental TPC saturation states. The data have larger median peak amplitudes and a substantially stronger high-multiplicity veto tail than simulation; full signal-distribution agreement is not established.

The nominal 88% calibration-retention target defines the adopted level-2 amplitude-aware hybrid for the background evaluation. It retains the fixed prompt-amplitude tag and applies a residual neutron BDT to prompt survivors, with its threshold set exclusively on calibration run 1345. Table 4.5 compares the hybrid with the fixed 500-ADC prompt reference and a 455-ADC prompt threshold set to the same nominal retention target.

Relative to the fixed 500-ADC reference, the hybrid adds 280 simulated neutron tags while preserving all 339 prompt-tagged experimental tracks. The gain is 6.94 percentage points, with a central 90% paired-bootstrap interval of 6.29–7.61 percentage points. At comparable calibration retention, the net gain over the 455-ADC reference is 215 neutron tags, or 5.33 percentage points, with a 90% interval of 4.73–5.92 percentage points; the hybrid tags one fewer experimental track. These paired intervals hold the models, thresholds, and activity donors fixed and exclude detector-response and run uncertainties. These results support the hybrid in this control comparison; they do not establish experimental neutron efficiency or agreement of the full detector response. At the lower 85% retention target, the hybrid tags 340/351 tracks, rejects 77.3% of simulated neutrons, and retains 84.7% of calibration controls. Mixed-particle BDTs, including a monotonic model and a development-derived timing correction, do not reproduce prompt-level experimental tagging.

The rejection rule is \begin{equation} V = \left [\sum _{190\leq b_i\leq 210} A_i \geq 500\right ] \lor \left [s_{\mathrm {res}}\geq s_{\mathrm {thr}}\right ], \label {eq:veto-adopted-hybrid} \end{equation} where \(A_i\) is the nonnegative reconstructed peak amplitude in ADC counts, \(b_i\) is its stored or aligned sample index, and \(s_{\mathrm {res}}\) is the residual neutron-BDT score. The fixed threshold is \(s_{\mathrm {thr}}\simeq 0.9382\); the archived model preserves the full precision, feature order and separate simulated and measured channel maps. Figure 4.28 shows the two rejection paths.

The residual BDT must distinguish neutron-induced scintillator activity from unrelated activity that survives the prompt veto. Its 163 inputs describe peak amplitudes, timing, and their distribution among panels. Table 4.6 groups these inputs using the same partition as the permutation analysis. TPC observables and the inconsistent total-energy scalar used in the earlier hierarchy are excluded.

Reading a ROC curve and its area. A classifier assigns a score to each event; a threshold determines which events the veto tags. For simulated neutrons and calibration controls, the tagged fractions are \begin{equation} \mathrm {TPR}=\frac {N_{\mathrm {n,tag}}}{N_{\mathrm {n}}}, \qquad \mathrm {FPR}=\frac {N_{\mathrm {cal,tag}}}{N_{\mathrm {cal}}}, \label {eq:veto-roc-fractions} \end{equation} where TPR and FPR denote the true-positive and false-positive rates of this two-class comparison. Calibration retention is \(1-\mathrm {FPR}\), used as the horizontal coordinate in the subsequent comparison plots. Lowering the score threshold generally increases both fractions. The receiver operating characteristic (ROC) traces this tradeoff over all thresholds, as illustrated in Fig. 4.29. Its area under the curve (AUC) measures score ordering: an AUC of 0.5 corresponds to random ordering and 1 to perfect separation. Equivalently, AUC is the probability that a randomly selected neutron entry receives a higher score than a calibration entry, with tied scores contributing one half. Rejection at a chosen threshold is read from one point on the curve; AUC summarizes the complete ordering.

To identify the information used by the frozen model, we shuffled individual inputs or complete families across events and measured the resulting decrease in ROC AUC. Figure 4.30 compares the two tests. The model and thresholds remain fixed, and this diagnostic reuses the existing held-out data, including calibration controls from run 1347.

Maximum peak amplitude is the most important individual input in this AUC diagnostic: its permutation decreases AUC by approximately 0.048, compared with 0.014 for prompt amplitude in the inner layer. Jointly shuffling the amplitude-derived family gives a decrease of approximately 0.294. This family includes amplitudes resolved by time window, face, and layer, their fractions and entropies, and amplitude-weighted timing. Its dominance therefore does not separate amplitude information from timing or spatial patterns. This reliance makes the unresolved amplitude and saturation differences between measured and simulated tracks relevant to transferring the adopted veto response.

Correlated inputs can substitute for one another, so individual and grouped losses are not additive contributions. These dimensionless AUC decreases measure model reliance in the stated sample, not experimental neutron efficiency or importance for rejection at the frozen nominal 88% retention operating point. At the frozen threshold, joint permutation of the amplitude-derived family lowers neutron rejection by 6.44 percentage points and control retention by 0.95 points on average. This comparison keeps the prompt decisions fixed; shuffle variability and activity-donor sampling have different uncertainties.

Timing and spatial information in the residual classifier

The small timing and spatial losses in Fig. 4.30 require interpretation because moderation, capture, and the multilayer geometry motivate precisely these correlations. The permutation groups classify input formulas, rather than independent physical mechanisms. Of the 68 amplitude-derived inputs, only one is the maximum amplitude; 50 are sums resolved by window, face, or layer, 15 are fractions or entropies, and two are amplitude-weighted times. Consequently, this group retains information about when and where activity occurs. The separate spatial inputs describe coarse occupancies and spread, rather than a reconstructed neutron trajectory. Moreover, the prompt rule already rejects 2462 of 4035 neutron entries, leaving the harder residual comparison.

We first compared the existing full model with an archived 95-input model trained without amplitude-derived quantities. Both models use the same amplitude-based prompt selection. Figure 4.31 shows that permuting timing, spatial, and spatiotemporal summaries has a larger effect in the latter model. Its AUC is 0.690 on the complete post-prompt population, compared with 0.772 for the full model. These results establish predictive information in unweighted timing and occupancy summaries, while their usefulness to a fitted classifier depends on its other inputs.

To test additional information directly, we trained four models with the same records, run partitions, and fitting settings. Table 4.7 defines the three input blocks and the four model combinations. Both \(N\) and \(A\) retain timing and position information; \(A\) also describes how the measured amplitude is distributed.

The full refit reproduces the adopted scores and threshold to numerical precision. Each threshold uses run 1345 alone at nominal 88% total control retention; achieved run-1347 retention spans 87.51%–87.67%. The prompt rule alone retains 87.80% in that run, bounding every residual selection.

Adding \(N\) to \(G\) gains 92 neutron tags, or 2.28 percentage points in total rejection (central 90% paired resampling range: 1.76–2.79 points). Adding \(N\) after \(A\) changes the net count by \(-2\), or \(-0.05\) points (\(-0.24\) to \(+0.15\)), consistent with no resolved additional rejection at this operating point. Block \(A\) contains both additional amplitude-scale information and timing and spatial structure; this comparison does not isolate those physical effects. The results support overlapping information as an explanation of the small separate permutation losses. Their ranges exclude training, threshold, run, and detector-response uncertainties. The physical motivation for timing and segmentation remains, while their incremental classification gain depends on prompt selection, representation, and the measured waveform response.

Time conventions and acquisition response. The fixed prompt interval is defined in stored or aligned sample indices. Table 4.8 distinguishes this interval from the published hardware window and the empirical coordinate used in the historical capture-delay diagnostic.

The archived application requires a response-specific timing check. An audit completed on 2 October 2026 found that the legacy veto conversion expected acquisition bin 262, while both independent-electron files and the processing logs covering all 29 independent neutron TPC-BDT survivors used bin 234. The difference is 28 samples, or 5.6 µs, and can change whether physical scintillator activity enters the prompt interval. A separate reference-window replay of the two electron baseline events preserved their TPC decisions and generated exposure but changed the diagnostic selection sequence from \(2\to 1\to 1\to 1\) to \(2\to 1\to 0\to 0\). The corresponding neutron replay was incomplete at that audit. Waveform-edge and peak-finding effects require reconstruction of the veto response; shifting exported peak times alone is insufficient. This response diagnostic qualifies the archived application without replacing the reported source yields or establishing experimental neutron efficiency.

The threshold is fixed; the 85% and 80% settings remain comparison points. Background predictions use the actual joint TPC-plus-veto event decisions wherever the necessary response and exposure are available, rather than multiplying by the control-sample rejection fraction. Section 4.6.5 explains the separation of development and evaluation samples and the interpretation of the joint acceptance.

4.6.5 From veto development to a background prediction

The background model requires the count surviving the complete TPC and veto selection. The TPC selects low-energy, X-ray-like candidates, which differ from the general neutron and muon populations used to develop the veto. We therefore follow each simulated candidate through the common TPC baseline, the TPC topology BDT, the prompt veto, and the residual neutron BDT. Reporting the two veto stages separately shows the additional rejection after prompt tagging. The surviving count is obtained from these event decisions rather than from a control-sample efficiency factor.

Separate learning, threshold setting, and evaluation. Training samples determine the BDT response; the adopted veto threshold is set only on calibration run 1345 at a nominal 88% retention target. The cosmic evaluation uses separate primary histories after the TPC and veto models and their thresholds have been fixed, with all descendants of a primary kept together. Calibration run 1347 is separate from the veto-model training runs 1335, 1339, and 1342 and from threshold setting, but its controls informed the hybrid development comparisons and its records are reused for the activity overlay. The cosmic yield therefore tests independent particle histories using this previously studied activity population.

The earlier independent neutron evaluation, with 141 baseline candidates, is preserved in the technical companion; its larger development inventory is excluded from that exposure. The updated source estimates in Section 5.4.2 use separately qualified samples and retain each sample’s generated-primary exposure.

More statistics without changing the selection. Additional independent primary histories can increase the evaluation statistics without changing the adopted response or selection. Compatible productions combine selected physical-parent contributions and generated-primary exposures, including primaries that produce no stored detector event. Production blocks are defined before their results are inspected; missing reconstruction is recorded as incomplete processing, not as rejection.

Grouped cross-validation can instead assess the selection procedure using models trained without the group being tested. Because it evaluates several fitted models, it remains distinct from an independent test of the single adopted model.

Signal retention and accidental veto activity. The 80% TPC-BDT target and the 88% veto target refer to different reference populations. Their product is not a measured acceptance of the joint selection. That acceptance requires following calibration events through the complete chain and measuring veto retention among the TPC-selected survivors. Each simulated parent receives one complete measured veto record from run 1347, retaining the donor’s channel, timing, and amplitude correlations. Repeating this overlay tests sensitivity to the activity realization without adding independent neutron exposure. For a later radioactive-decay acquisition, scintillator activity from the original production interaction is not credited as a veto tag.

Acquisition timing. The acquisition-response audit accompanying Table 4.8 limits the archived evaluation preserved in the technical companion. The updated calculation in Section 5.4.2 uses the native TPC acquisition and grants veto rejection only when physical coincidence is established. Both veto stages act on the same independent TPC candidates; unresolved timing receives no rejection credit.

4.6.6 Classifier-development comparisons

Capture timing and detector segmentation can distinguish neutron activity from isolated veto pulses, but added model complexity is useful only if it also preserves control-sample stability. We tested this information in a historical hierarchy, from aggregate observables to a panel–time neural model. These comparisons use the original aligned response at nominal 90% calibration-control acceptance. The historical level-1 benchmark and the level-3 neural hybrid are distinct from the adopted prompt-plus-residual-BDT rule, whose residual threshold is fixed at the nominal 88% target.

The hierarchy uses 20 274 aligned simulated neutron events and 139 454 experimental calibration events. Each neutron peak train receives one independently sampled calibration train, preserving correlations within the measured activity but omitting pulse merging, saturation, and baseline shifts before peak finding. Separate calibration runs define training, threshold setting, and held-out evaluation; overlaid neutrons follow their activity donor’s partition, preventing reuse of its measured activity across partitions. The control class is calibration-triggered activity, so the scores are ordering statistics rather than neutron probabilities.

Level 1 uses six aggregates: total reconstructed veto-energy proxy, peak count, unique panel count, active face count, active layer count, and maximum peak amplitude. Level 2 adds waveform-window summaries and detector segmentation; level 3 combines a panel–time tensor with the six aggregates. No level uses Micromegas energy or topology. The total-energy scalar differs between experimental and simulated flattened inputs and is not a common calorimetric measurement; the adopted residual BDT excludes it. The historical input also retains simulated activity at two prototype-inactive panel positions.

Full level 2 gains 0.47 percentage points over level 1 in held-out rejection (central 90% paired-bootstrap interval: 0.07–0.82 percentage points), with an AUC difference consistent with zero. Across five calibration runs, acceptance spans 88.2%–90.9% for level 1 and 84.4%–90.5% for the full model: additional features increase one run’s acceptance shift for a small rejection gain. Total energy dominates the historical classification; its removal retains 79.1% rejection, but the remaining amplitude and multiplicity inputs prevent this comparison from isolating timing or position. The acquisition time range and energy calibration remain unresolved, so these conditional results do not establish an absolute neutron-veto efficiency. These historical results retain endpoint clipping of out-of-record peaks; the adopted hybrid instead discards them.

Capture-delay signature

The cadmium-capture timescale in Figure 4.18 motivates a prompt–delayed sequence, rather than a tag based on any late peak. Those truth times are measured from the first simulated gas deposit and never enter a classifier. The reconstructed capture diagnostic instead uses the empirical aligned coordinate \begin{equation} t_{\mathrm {rel}} = 0.2\,(i-231)~\mu \mathrm {s}, \label {eq:veto-capture-delay-coordinate} \end{equation} where \(i\) is the waveform bin and offset 231 aligns prompt populations without independently calibrating the hardware trigger. Bins 0–511 span \([-46.2,+56.0]~\mu \mathrm {s}\), but physical simulated peaks in the inspected flat neutron input end at 41.6 µs; calibration overlay can populate the remaining bins. The diagnostic prompt and capture-like intervals are −10–5 µs and 10–50 µs. Their 5–10 µs gap does not bound pulse tails or peak-finding leakage. These intervals differ from the broad hierarchy’s stored-bin windows: its legacy “capture” bins 240–280 map to 1.8–9.8 µs, rather than 10–50 µs. Neither historical scheme calibrates the relation to the hardware window or replaces the adopted stored-bin prompt rule.

The seven timing features describe delayed-peak times, their spread, and the presence of prompt and delayed activity. The full 18-variable signature adds multiplicities, amplitudes, detector occupancies, delayed fractions, and panels active only after the prompt interval.

Figure 4.33 illustrates the sequence and segmentation in a representative prompt-plus-delayed event.

We tested the sequence with 879 neutron events and 250 time-scrambled realizations. Circularly shifting complete neutron peak trains preserves their amplitudes, multiplicities, and spatial correlations while removing their alignment with the Micromegas trigger. This constructed control tests trigger-correlated timing; it does not measure the experimental accidental rate. A late peak alone accepts 52.4% of neutron events and 56.3% of the mixed control on average, whereas requiring prompt followed by late activity gives 46.4% and 14.3%, respectively. Figure 4.34 shows the additional segmentation and delayed-energy requirements.

The seven timing features reject 49.8% of held-out neutrons, and the full capture signature rejects 74.1%. Adding the signature to the six level-1 aggregates raises rejection from 83.69% to 84.19%: 20 additional neutrons among 4035, or 0.50 percentage points (central 90% paired-bootstrap interval: 0.20–0.82), with an AUC difference compatible with zero. The net gain comprises 40 newly rejected events and 20 lost level-1 tags. Minimum control acceptance across five runs falls from 88.20% to 86.33%. The sequence supplies a small additional rejection gain with poorer run stability; some captures produce no reconstructed veto peak, and calibration data also contain late activity.

Level-3 spatiotemporal neural model

The level-3 study tests whether a \(59\times 512\times 2\) panel–time tensor can recover useful structure without engineered summaries. Tensor-only temporal and tensor-plus-graph models reject 71.2% and 72.6% of held-out neutrons, respectively; adding the six aggregates gives a neural hybrid with 84.1% rejection. Its gain over historical level 1 is 0.42 percentage points (central 90% paired-bootstrap interval: 0.10–0.74), with an AUC difference compatible with zero. Control acceptance falls to 83.4% in run 1339, below the full level-2 and level-1 minima of 84.4% and 88.2%, failing the predeclared run-stability criterion.

These studies establish useful timing signatures without demonstrating a more stable replacement for the aggregate benchmark in the historical response. For background evaluation, we use the adopted prompt tag plus residual BDT at the nominal 88% target, excluding the inconsistent total-energy scalar. Section 4.7 tests the experimental basis of this approach: whether the prototype selection reproduces the measured background rejection and whether the broader late-window population is described by the simulated neutron signatures.

4.7 Experimental validation with IAXO-D0

The prototype data test two different aspects of the veto response. The published X-ray selection measures background rejection in a defined exposure; applying our residual BDT to the same candidates tests its transfer to that population. A separate, broader sample tests whether simulated neutron signatures describe late activity in the measured waveforms. We keep these populations separate because their gas mixtures, event selections, and response conditions differ.

4.7.1 Published surface selection sequence

The commissioned prototype was operated with IAXO-D0 at surface level in Zaragoza for an effective exposure of 52.1 d, with 57 operational veto channels [17]. Its readout has 59 positions and 57 operating channels (Table 4.4). The gas mixture was Xe–Ne–isobutane (48.85%–48.85%–2.3%) at 1050 mbar, rather than the argon-based reference used for the background model. The published selection uses a 2–7 keV region of interest and a 9 mm-radius focal region. This differs from the 10 mm fiducial radius in the final common TPC baseline of Section 3.5.3. We recovered the archived Micromegas-selected candidates and repeated both veto stages using the original gain-calibrated panel maxima and fixed thresholds. The resulting sequence, \(257\rightarrow 56\rightarrow 49\), reproduces the published veto decisions on the same historical events; it is a reconstruction of the reported result rather than a second measurement. This common candidate population permits the BDT comparison below.

The prompt selection removes \(201/257=78.2\%\) of the Micromegas-selected events and provides the largest reduction in the surface-background sample. 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 publication reports approximately 97% calibration retention for the advanced selection; cumulative efficiency is 79.4%, compared with 81.9% after the Micromegas selection. Together, the two veto stages remove \(208/257=80.9\%\) of the X-ray-like background candidates, a reduction by a factor of 5.24. The final background level is the published \(8.56\times 10^{-7}\,\mathrm {counts\,keV^{-1}\,cm^{-2}\,s^{-1}}\). Table 4.10 uses 90% confidence intervals, while Ref. [17] quotes a statistical uncertainty of \(1.22\times 10^{-7}\) at one standard deviation.

The prompt veto rejects a candidate when a panel signal exceeds 5 MeV in a 16 µs interval around the Micromegas trigger. The advanced selection requires fewer than 13 panel signals over the full record, a summed energy below 7034 keV in the record interval 23–53 µs, and fewer than 12 signals in 35–68 µs. The trigger is at 30 µs, so the latter intervals extend from −7 µs to 23 µs and from 5 µs to 38 µs relative to it. The published multiplicity counts at most one reconstructed signal per panel; it differs from a count of all peaks in a waveform. Figure 4.35 shows the resulting selection sequence.

Prompt activity provides the largest background reduction; the long record adds rejection through multiplicity and activity extending beyond the trigger. The seven additional removals demonstrate background discrimination in the post-prompt X-ray sample. Without identifying those events as neutrons, their number cannot determine neutron efficiency or the neutron fraction of the residual background.

4.7.2 BDT comparison on the published candidates

To compare the BDT with the published additional rejection, we applied the frozen residual classifier to the same 56 candidates surviving the original prompt veto. We recovered multi-peak records for 19 events from the archived reconstruction and reconstructed the remaining 37 from their original acquisition files. The classifier retains its 163 veto features, channel map, and fitted weights; the original Micromegas selection and prompt-veto decisions define the common candidate population.

At the adopted score threshold, \(s\geq 0.9382\), the residual BDT rejects three candidates, all among the seven removed by the published advanced veto. The additional prompt-amplitude requirement of 500 ADC counts removes four candidates, two of which also exceed the BDT threshold. Their union removes five events; after that additional prompt requirement, the BDT adds only one rejection among 52 survivors. The adopted BDT gives less additional rejection and retains 99.90% of the first-period evaluation controls from runs 1696 and 1698 after the original Micromegas, energy-region, and prompt selections. This retention excludes the additional 500-ADC criterion and exceeds the approximately 97% reported for the published advanced selection.

To test the dependence on the operating point, we fixed a second threshold using only the original post-Micromegas, post-prompt calibration population in runs 1663 and 1666, with a nominal 97% retention target. The threshold \(s\geq 0.7545\) retains \(7524/7756=97.01\%\) of these controls and \(8175/8344=97.97\%\) in the independent runs 1696 and 1698. It rejects \(7/56=12.5\%\) of the background candidates without using their scores or published advanced-veto labels to choose the threshold. Four rejected events coincide with the published selection and three differ; the rejected fraction is reproduced, while the event classification changes. Figure 4.36 compares the additional rejection and calibration retention at the two fixed thresholds.

Calibration retention varies between runs, including within the first period: the adjusted threshold retains 99.02% in run 1696 and 96.92% in run 1698. It retains 94.8% in run 1748 and 95.4% in run 1830. Separate 97% thresholds derived within the second and third periods retain only 94.0% and 93.8% in their reserved evaluation runs. The BDT therefore provides additional discrimination on the published candidates, but matching the seven removals does not establish the same event selection or a uniform calibration cost. These background candidates are not individually identified neutrons, so the comparison does not measure neutron efficiency. The adopted threshold and independent simulated-background yields remain those of Section 4.6.5.

4.7.3 Late-window control population

We developed an exploratory score to test whether archived prototype activity resembles the simulated neutron template more closely than calibration and muon controls. The campaign documentation identifies these measurements as an argon–isobutane acquisition at 1.4 bar, separate from the published 52.1 d Xe–Ne exposure. The flat background input contains 777 752 events without the published 2–7 keV, focal-region, or X-ray-topology selection; its gain and operating conditions are not matched to the simulation. Its selected fraction therefore cannot be compared directly with the published \(7/56\) additional rejection or converted to a background level using that exposure.

We removed events with at least two prompt peaks above 200 ADC counts in bins 190–210, and burst-like events with at least 100 peaks or 50 distinct recorded channels. The original score, \(S_6\), combines Micromegas energy with five veto amplitude and multiplicity observables. Table 4.11 compares it with \(S_5\), which omits the Micromegas-energy factor from each class likelihood while retaining the other five histograms and the same input events. Each threshold selects the upper 1% of its clean calibration distribution. Because pooled calibration events supply both the fitted histograms and the threshold, these tails are imposed rather than independently measured. The score is a log-likelihood ratio of the neutron-plus-activity template to the equal mixture of calibration and muon-plus-activity templates, using products of one-dimensional histograms. The veto inputs are peak-amplitude sums and counts in bins 240–280 and 211–511, plus unique-channel count; overlapping windows and correlations are ignored, so the result is an ordering statistic rather than a neutron probability.

The original score selects 3877 measured events, or 0.50% of the full input and 5.88% of the clean subset. Removing the Micromegas-energy factor reduces the selected clean-background fraction to 4.78% and the neutron-template fraction from 17.76% to 10.74%. The population therefore depends appreciably on that factor, but the veto-only variant does not resolve the response mismatch: its selected data and neutron template have median all-peak counts of 85 and 10, or 12 and 6 for peaks above 200 ADC counts. These \(S_5\) populations differ from the original \(S_6\) selection examined below. Additional channel correlations, event rasters, and Micromegas projections are preserved in the independent veto-validation document.

4.7.4 Template agreement and control stability

For the original \(S_6\) selection, Fig. 4.37 compares 3877 measured events with 1722 neutron-plus-noise events. Their median all-peak counts are 47 and 9, falling to 10 and 5 above 200 ADC counts. At that threshold, the median numbers of distinct channels are 4 and 5, while late-window peak counts are 7 and 4; multiple peaks can occur in one channel. Late-window amplitude-sum medians decrease from 6822 and 2707 ADC counts for all peaks to 2772 and 2241.5 ADC counts above threshold. Weak peaks account for much of the discrepancy, but the samples still differ in gain, noise, Micromegas energy, hit multiplicity, and topology. The amplitude sums are not calibrated deposited energies, and these unmatched population medians do not measure veto rejection in the published X-ray selection.

The calibration controls also depend on acquisition run (Fig. 4.38). Over the full input, run 1339 has a median of 19 peaks, compared with 4–5 in the other four runs, while all runs have a median of one peak above 200 ADC counts. After prompt and burst removal, \(S_6\) selects 2.35% of run 1339 and 0.62%–0.74% of the others, despite the pooled 1% target. Removing Micromegas energy does not eliminate this dependence. When each run is omitted from the \(S_5\) calibration histogram and threshold calculation, the selected fraction in the omitted run is 2.66% for run 1339 and 0.57%–0.70% for the others. The simulated templates retain their pooled calibration-activity overlays, which may include donors from the omitted run, so this checks calibration-reference sensitivity rather than independently validating the full response.

The historical cosmic-neutron template predates the HENSA layer scan and lacks tagged-neutron calibration in the commissioned configuration. Its geometry and response differ from the prototype’s 59-position readout and 57 operational channels in panel dimensions, channel states, gaps, gains, and thresholds. Other showers, accidental activity, or correlated electronics signals can populate the late window; long-lived activation is a separate background channel from an in-waveform capture response. The neutron origin of the selected events therefore remains undetermined.

A quantitative comparison requires a common Micromegas selection, run-matched gains and channel states, and off-time or time-shifted controls, with test runs excluded from fitting, activity donors, and threshold setting. Together with competing particle templates and independent neutron-response constraints, these checks would support a neutron-fraction or rate inference. The present results instead establish the response and control-stability limits discussed next.

4.8 Response uncertainties and limitations

The inspected electron files and neutron-survivor processing used acquisition bin 234, whereas the veto conversion expected bin 262 (Table 4.8). This 5.6 µs difference can change prompt rejection, so the affected archived yields remain conditional on the timing response. Testing its effect requires waveform reconstruction with the original TPC observables and generated exposure preserved; shifting exported peaks cannot recover waveform-edge or peak-finding effects.

Independent simulated histories do not imply independent measured activity: run 1347 informed hybrid development and supplies the nominal overlays. Peak-list overlays omit pulse overlap before reconstruction; the separate 37-channel optical-waveform study tests this response without supplying generated-primary exposure. Joint TPC-plus-veto retention must be measured on independent calibration events followed through both selections. Neither offline control acceptance nor the fixed-window cosmic-activity estimate in Section 5.4.3 establishes online live time.

The archived \(-25^\circ \) to \(+25^\circ \) inclination scan shows no resolved monotonic trend in processed entries per generated primary, but retains the historical neutron angular input. Its angular-measure discrepancy limits transfer to the final tracking exposure. Absolute background levels also require the source rate, complete generated exposure, and the selection’s energy interval and counting area; unresolved source rates permit only yields per generated primary.

4.9 Summary and outlook

Lead attenuates environmental photons but can generate secondary showers when energetic neutrons interact in it. Plastic scintillator and cadmium complement this shielding by detecting charged-particle activity and capture photons around the TPC. The simulations connect these processes to spatially distributed prompt and post-trigger signals, while showing that a physical capture need not produce a reconstructed veto peak.

The passive studies identify promising moderator arrangements for a future detector iteration. With 20 cm of lead retained, the lowest observed energy-selected background is obtained with 10 cm of BPE between 5 cm of inner Pb and 15 cm of outer Pb: \(B^E/B^E_{\mathrm {Pb}}=0.696\), a central reduction of 30.4%. This minimum was selected across the scan; its pointwise statistical intervals do not establish an optimal arrangement or the same reduction after the complete TPC selection. Within fixed outer dimensions, replacing the inner 5 cm of lead with BPE gives a smaller central reduction in \(B^E\), of approximately 9%; the additional LiF/PMMA layer has no established advantage over BPE alone. These neutron-only comparisons still require validation of thermal scattering and a joint assessment of photon attenuation and material backgrounds. The adopted geometry retains the full lead shield.

Adding active stages increases the probability of observing the surrounding neutron-induced shower. In the exported response population, three and four active stages with cadmium give any-tag fractions of 74.1% and 77.1%, respectively, without an additional X-ray-like TPC selection. The illustrative accidental-overlay model gives the larger sensitivity proxy to four layers, while three layers reduce the channel count and accidental opportunities after most of the conditional tagging gain has been obtained. Three layers are therefore an engineering compromise rather than a statistical optimum established by these simulations.

Measured TPC-track controls led us to preserve the fixed prompt-amplitude tag and add a residual neutron BDT, with its threshold set at a nominal 88% calibration-retention target. At comparable control retention, the hybrid gains 5.33 percentage points in simulated neutron tagging over the 455-ADC prompt reference (conditional 90% interval: 4.73–5.92), while tagging 339 rather than 340 of the 351 measured tracks. These development comparisons support the adopted rule without establishing experimental neutron efficiency or full agreement of the measured and simulated response. The documented 5.6 µs acquisition-setting discrepancy can change veto decisions, so the affected archived background application remains conditional on its timing response.

The published IAXO-D0 surface measurement provides the experimental demonstration of background suppression: the selection reduces 257 Micromegas-selected candidates to 56 after the prompt veto and 49 after the advanced veto, for 52.1 d of exposure. The publication reports approximately 97% calibration retention for the advanced stage. On the same 56 candidates, the adopted residual BDT rejects three events; a comparison threshold set only on separate calibration data rejects seven, with different event membership and run-dependent calibration retention. This comparison establishes additional background discrimination, not neutron identification. The broader late-window study likewise finds activity distinct from calibration controls, but response differences and run dependence prevent an inference of neutron fraction or rate.

Further validation should reconstruct the affected veto response with the recorded acquisition settings and measure joint TPC-plus-veto retention on independent calibration data. Compact modules with wavelength-shifting fibers and silicon-photomultiplier (SiPM) readout offer a future design option [131], but comparison with the PMT prototype requires the response of the assembled system in a common mechanical envelope. Transfer to BabyIAXO also requires finalized geometry, channel states, and site-specific source inputs. Chapter 5 follows the adopted event decisions with generated-primary exposure accounting, reporting background levels where source normalization is validated and conditional yields otherwise, with radioactive decays outside the coincidence window treated separately.

Chapter 5
Background Model

Introduction

In this chapter, we calculate how radioactive contamination and incident radiation produce low-energy background events in the IAXO-D1 Micromegas detector. We combine radiation transport, detector response, and event selection to obtain source-specific yields, which are converted into background levels where source activities or incident fluxes are established. The nominal calibration reference uses Ar–isobutane (1%) at 1.4 bar; source studies retaining different gas or response settings state those differences explicitly. These studies provide a basis for assessing background mechanisms and reduction measures; a BabyIAXO prediction additionally requires its xenon–neon response, optics, final veto configuration, and DESY source terms.

This study builds on the low-background Micromegas detector development for CAST [12]. Using the simulation and reconstruction methods of Chapter 3 and the veto selection of Chapter 4, we evaluate gas and surface contamination, radioactivity in detector and shielding materials, environmental radiation, and cosmic rays. Neutron-induced activities enter the radioactive-source model. The completed calculations provide a normalized radioactive-inventory subtotal and source-specific selection results. Together, these identify reduction priorities and the missing inputs needed to complete the model.

5.1 Simulation and analysis methodology

The background calculation follows each source from its activity or incident particle field to the events surviving the detector selection. We use REST-for-Physics [86] for radiation transport, detector response, and reconstruction, with the methods described in Chapter 3. Here, we specify how the source samples are compared and normalized.

5.1.1 Reference detector and normalization conventions

The nominal calibration reference is IAXO-D1 with Ar–isobutane (1%) at 1.4 bar. The source samples retain their recorded transport and response settings: several use 2% isobutane, and the conventional response can interpret pressure in atmospheres rather than bar. These differences are stated with the affected results; a common selection does not establish equal detector responses. Table 5.1 summarizes the reporting conventions.

Reading background estimates and upper limits

A background estimate gives the predicted contribution in the simulated sample; its Monte Carlo standard error describes sampling precision. A one-sided 90% upper limit bounds that contribution under a specified statistical model, including when no event survives. The superscript \(\dagger \) marks a conditional counting construction: Poisson for rare, effectively independent accepted events or a parent-correlated uncertainty calculation for populated decay chains.

The independent trial is a generated particle or complete decay history. One parent can produce several separated detector events, whose correlations are retained when estimating uncertainty. A bound on the probability of any accepted event is consequently not generally a bound on the mean accepted-event count. The generation stopping rule also enters the calculation: fixed-parent and target-saved-event samples have different sampling properties. A missing limit indicates an unresolved statistical construction; missing reconstruction or source normalization is identified separately.

For \(N\) generated histories, let \(K_j\) count the selected descendants of parent \(j\), including \(K_j=0\), and define \(S=\sum _jK_j\) and \(Q=\sum _jK_j^2\). At fixed activity \(A_s\), the estimate and its parent-correlated MC error are \begin{equation} \widehat B=c\frac {S}{N},\qquad \sigma _{\mathrm {MC}}=c\sqrt {\frac {Q-S^2/N}{N(N-1)}},\qquad c=\frac {A_s}{\Delta E A_{\mathrm {fid}}}. \label {eq:background-parent-estimator} \end{equation} For incident radiation, the generated-primary rate replaces \(A_s\) and any sampling weights remain grouped by physical parent. In the Poisson working model, an observed count \(n\) has one-sided mean limit \begin{equation} \mu _{1-\alpha }(n)=\tfrac 12 F^{-1}_{\chi ^2_{2(n+1)}}(1-\alpha ), \qquad \mu _{90}(0)=-\ln 0.1=2.3026. \label {eq:background-poisson-mean-limit} \end{equation} The same source normalization converts this mean limit into a rate [52, 132]. Sparse material chains use the moment-matched count \(n_{\mathrm {eff}}=S^2/Q\) and scale \(Q/S\); populated chains use a parent-correlated normal approximation [133]. Empty samples retain a positive rare-single-event limit; these working models do not constrain arbitrary unseen multiplicity tails. For joint radioactive-inventory bounds, source tail probabilities satisfy \(\sum _i\alpha _i=0.1\) before the normalized bounds are added; individual 90% limits are not simply summed.

For environmental photons, we report an approximate one-sided 90% upper limit, marked \(*\), from the estimated rate \(\widehat B\) and its physical-parent MC standard error \(\sigma _{\mathrm {MC}}\): \begin{equation} B_{90}^{\mathrm {approx.}}=\widehat B+1.28155\,\sigma _{\mathrm {MC}}. \label {eq:environmental-photon-count-limit} \end{equation} For the approximate shielding-plus-Pb sum, the independent MC errors are combined in quadrature before applying this expression. This Gaussian approximation describes the observed MC uncertainty; its 90% coverage has not been calibrated for finite weighted samples or unseen high-weight tails. It excludes source and model uncertainties and the unquantified bias from response-fit selection or data retention.

Common uncertainty convention. Unless stated otherwise, intervals and limits hold the source activity or flux, geometry, nuclear data, detector response, and selection fixed. They exclude uncertainty in energy calibration, diffusion, noise, and transfer between gas or field conditions. More simulated events improve counting precision but do not resolve these response differences. This convention applies throughout the chapter; source-specific qualifications remain beside the affected results.

5.1.2 Workflow overview

Figure 5.1 connects source generation to the selected background. The restG4 transport supplies gas and scintillator deposits; restManager forms their respective charge and light signals and reconstructs the event observables. Measured waveforms enter at reconstruction. Separating these stages allows response settings to be tested without repeating transport when the required deposits and particle information have been saved.

Each source is followed through stored events, reconstruction, the TPC baseline, and any evaluated BDT and veto stages. Additional rejection is measured among survivors of the preceding stages, retaining their correlations. The final count is normalized with the generated exposure and the corresponding activity or incident-primary rate. Section 5.1.7 defines the adopted selection and its calibration checks. Delayed activation receives no veto credit from the earlier production pulse.

5.1.3 Source-specific simulations

Radioactive sources sample the specified material volume or contaminated surface. A mass-specific activity \(a_m\) gives \(A_s=a_mM\); a surface-specific activity \(a_S\) gives \(A_s=a_SS\). The simulated chain segment and any equilibrium assumption determine which decays that activity represents. Assumed gas and surface activities remain explicit scenarios.

External sources instead require energy and angular distributions and the rate of primaries crossing the generation surface. Environmental spectra come from measurements or auxiliary material-emission calculations. Cosmic inputs use particle-specific parameterizations or CRY spectra [91, 96]. The geometry-aware injection method developed in this work reduces transport of trajectories missing the apparatus [101]; its normalization is discussed with each field.

The gas is the sensitive target, with additional scintillator information where veto response is evaluated. Full-detector source calculations retain the shielding and veto; calibration-response studies can use a reduced chamber geometry, and the telescope study adds its entrance pipe. The source sections identify electromagnetic, radioactive-decay, and hadronic transport settings and their relevant limitations.

5.1.4 Background-model component inventory

Table 5.2 groups the sources by their physical normalization. Separate samples allow an activity, flux, or response assumption to be revised without changing unrelated components. Only non-overlapping, compatible contributions enter a subtotal.

5.1.5 Event types and detector-response chain

The selection uses reconstructed energy, tracks, and veto peaks, rather than ideal deposited energy or particle ancestry. Chapter 3 describes the conversion from deposits to waveforms and reconstructed observables. Truth information is used afterward to explain physical mechanisms and surviving candidates; it is excluded from the classifier inputs.

Figure 5.2 illustrates measured and simulated signals for two different muon events. The plotting procedure applies separate TPC and veto time offsets to each sample. Their displayed alignment therefore does not independently validate the hardware-trigger mapping or the quantitative timing response.

5.1.6 Analysis processes and observables

The conventional REST response includes gas diffusion and empirical broadening, scintillator quenching, effective light attenuation, and subsystem-specific electronics settings. The gas-recoil treatment is described in Section 2.1.3; Birks saturation affects highly ionizing scintillator deposits [126, 127]. The archived neutron diagnostic changes energy-weighted gas and scintillator signals by approximately 0.22% and 25.7%, respectively, under its recorded quenching settings. These averages do not determine selection efficiency.

The Micromegas energy scale uses the reconstructed 5.9 keV \(\ce {^{55}Fe}\) peak; veto gains use through-going muons. Waveform reconstruction supplies energy, multiplicity, position, shape, and veto timing observables. The Garfield detector response is a separate comparison, not an additional selection stage.

5.1.7 X-ray selection and background-rejection strategy

The reference calculation selects compact, low-energy TPC candidates, applies the additional topology BDT, and evaluates the veto where a compatible response is available. Each source is followed through these stages before its surviving count is normalized. The resulting rates predict the response of the simulated detector; their transfer to laboratory data requires separate validation.

TPC baseline and adopted BDT

The baseline of Section 3.5.3 is common to data and simulation: \begin{equation} C_{\mathrm {ref}}=C_{\mathrm {baseline}} =C_V\cap C_E\cap C_M\cap C_F. \label {eq:background-xray-cut-definition} \end{equation} The full admitted readout is reconstructed before selection. An event must have usable native maximum-track observables, calibrated maximum-track energy in 2–7 keV, including both endpoints, exactly one track in each projection, and a maximum-track center at \(r<10\,\mathrm{mm}\). No width, classifier, or veto requirement is included in the baseline. A surviving event is an X-ray candidate; its compact charge deposit does not identify the incident particle.

The additional selection is \[ C_{\mathrm {selected}}=C_VC_EC_MC_F\,C_{\mathrm {BDT}}, \qquad C_{\mathrm {BDT}}=\mathbf {1}[s_{\mathrm {BDT}}\geq t_{80}]. \] The BDT combines the fifteen reconstructed shape variables in Table 3.3. Total energy, radius, track count, source identity, and transport truth are excluded. The archived model is retained, with \(t_{80}\simeq 0.694\) set using simulated \(\ce {^{55}Fe}\) candidates after the baseline; its full precision is preserved with the analysis configuration. Background counts do not determine this threshold.

For the conventional REST response, the calibration partition retains \(\num {12402}/\num {15502}=80.00\%\); the separate original test partition retains \(\num {9224}/\num {11499}=80.22\%\), with a 90% binomial interval of 79.59–80.83%. These are retrospective checks of historical samples. Missing or non-finite BDT inputs are rejected and remain in the baseline denominator; none occurs in these calibration or gas/cathode evaluations.

This 80% target is conditional on the calibration population. Figure 5.3 shows the fraction of baseline-selected test events that also pass the BDT in each reconstructed-energy bin, with the same threshold throughout. Acceptance is approximately 45–52% at reconstructed energies of 2–3.5 keV, compared with 81–83% at 5–7 keV. Energy is excluded as a direct BDT input, but the reconstructed shape variables can still depend on energy. The calibration-spectrum average therefore supplies neither an energy-independent signal efficiency nor a background survival factor. Every source supplies its actual post-BDT count, without division by 0.8. Gas and field differences retain their source-specific response-transfer qualifications. Cosmic evaluation excludes the production groups used to develop the classifier.

Veto selection and joint acceptance

The adopted veto is the fixed prompt-plus-neutron-BDT hybrid of Section 4.6.4, with a nominal 88% calibration-retention target. It follows the TPC BDT on the same candidates, as evaluated in Section 5.4.2. Source results without a compatible joint evaluation remain explicitly pre-veto.

The veto can reject correlated activity accompanying a prompt background, while unrelated particles or noise can also remove an X-ray. A later activation decay receives no coincidence credit from its production shower. The response, acquisition window, and activity controls must match the evaluated sample. The cosmic evaluation requires native acquisition coincidence and retains candidates whose physical timing cannot be established (Section 5.4.2).

The 80% TPC and 88% veto targets refer to different populations and are not multiplied. Joint signal retention must instead be measured among calibration events passing the preceding stages. Likewise, source-background survival is evaluated event by event, retaining TPC–veto correlations and the generated exposure.

Incident-photon signal efficiency

\(\ce {^{55}Fe}\) calibrations test the response near 5.9 keV; uniform-energy photon simulations over 0–12 keV provide a wider acceptance check. For the baseline, incident efficiency is \begin{equation} \varepsilon _{\mathrm {ref}}(E_{\mathrm {true}}) =\frac {N_{\mathrm {accepted}}(E_{\mathrm {true}}\mid C_{\mathrm {ref}})} {N_{\mathrm {generated}}(E_{\mathrm {true}}\mid \text {specified illumination})}. \label {eq:background-xray-efficiency} \end{equation} Non-interacting photons and reconstruction failures remain in the denominator. Acceptance among valid reconstructed events, such as Table 3.6, excludes these losses.

The historical uniform-photon selection, with its recorded response and calibration-like illumination, retains 24.49% over the 2–7 keV true-energy interval. This historical efficiency awaits recomputation with the final baseline. It is neither a Garfield detector-response result nor a final axion efficiency, which also requires the appropriate gas, spectrum, optical illumination, and exposure and veto losses.

Response transfer and validation limits

Chapter 3 compares measured calibration with the REST and Garfield detector responses. Their remaining baseline-acceptance differences prevent treating improved spectral agreement as a validated background-rejection factor. The IAXO-D0 surface-veto measurements provide separate checks of the scintillator response and operating backgrounds [17], as discussed in Chapter 4. The background calculations retain their documented response versions. In the historical BDT transfer test, the simulation threshold retained only 13.85% of measured R02756 calibration events, against 80.22% in simulation. A measured-data or Garfield prediction therefore needs a matching calibration check and working point.

Separate width-based calibration illustrations and gas-matched response pilots remain auxiliary studies; their small or empty background populations do not establish a rejection factor.

Selection used in the source inventory

A further rejection claim requires fixing the response, model, and calibration thresholds before testing separate calibration and background events at their achieved signal acceptance. Previously inspected samples cannot become independent validation by being renamed. Muon-rich data constrain response but do not alone validate neutron rejection. The source tables therefore distinguish the adopted simulation prediction from laboratory validation and from results awaiting a compatible calculation.

5.2 Radioactive background

The radioactive-source inputs combine gas and surface inventories, material screening and neutron-induced activities. Screening measurements are collaboration inputs from the Zaragoza radiopurity teams and the Canfranc Underground Laboratory (LSC), mainly obtained with high-purity germanium detectors [16, 81, 134, 135]. Most supplied activities are upper-limit scenarios; the gas-isotope, inner-lead \(\ce {^{210}Pb}\) and readout \(\ce {^{40}K}\) assumptions are stated with their source results.

5.2.1 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 [136]. 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 [137]. \(\ce {^{39}Ar}\) beta decays generally produce extended ionization tracks rather than compact few-keV X-ray-like clusters. This motivates an additional topology selection, but its rejection must be evaluated on the reconstructed candidates rather than inferred from the true beta track.

\(\ce {^{85}Kr}\) 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. GERDA measured \((0.36\pm 0.03)~\mathrm {mBq}\,\mathrm {kg}^{-1}\) at the start of Phase II, whereas WARP reported an atmospheric-argon contamination corresponding to \((120\pm 90)~\mathrm {mBq}\,\mathrm {kg}^{-1}\) [136, 138]. These are measurements of particular liquid-argon inventories, not interchangeable estimates of the activity in our gas. Distillation and subsequent handling can change the residual krypton content substantially; WARP also observed a commercial batch with three times its quoted contamination [136]. Without an assay of the actual batch, the background model adopts \(300~\mathrm {mBq}\,\mathrm {kg}^{-1}\) of argon as a conservative working scenario, obtained from the WARP central value plus twice its quoted uncertainty. This choice is not a confidence limit on an unknown gas batch, nor a guaranteed upper bound on commercial argon. For the simulated argon inventory it gives a post-BDT background of \((3.47\pm 0.59)\times 10^{-9}\) counts keV\(^{-1}\) cm\(^{-2}\) s\(^{-1}\), with the uncertainty here due to simulation statistics. The contribution is subdominant in the adopted background inventory, but it is not intrinsically negligible: its prediction scales linearly with the unknown activity. In particular, the reduction of \(\ce {^{39}Ar}\) in underground argon is not applied to \(\ce {^{85}Kr}\).

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 radon components are separated because they have different normalizations. \(\ce {^{218}Po}\), 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. This motivates a cathode-collection scenario: NEXT has measured radon-induced backgrounds from \(\ce {^{214}Bi}\) daughters deposited on the cathode of its gaseous TPC [139]. It does not establish complete collection in IAXO-D1, whose gas, field and geometry differ. Neutralization, gas motion and deposition on other surfaces can leave a different spatial distribution; the cathode-only case is therefore not assumed to be a conservative bound. 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. Its inventory can retain the history of radon exposure during fabrication, storage and assembly, including periods without an operating electric field. Radon-progeny deposition studies explicitly address this persistent surface contamination [140]. Thus Pb-210 on copper now hidden behind a PTFE liner can represent exposure before assembly; longevity does not itself redistribute the isotope over every surface. The model therefore treats gas \(\ce {^{222}Rn}\), cathode \(\ce {^{218}Po}\), cathode \(\ce {^{210}Pb}\), and vessel or surface \(\ce {^{210}Pb}\) as separate source hypotheses. Ion drift and plate-out are not dynamically simulated: their effect is represented by these distinct source locations and activity assumptions. The gas source contains the initial \(\ce {^{222}Rn}\) decay; the short-lived \(\ce {^{218}Po}\) samples follow the subsequent chain up to \(\ce {^{210}Pb}\), whose decays and descendants are simulated separately. This division permits different gas and surface activities without counting the same chain segment twice. The same concern about persistent surface contamination motivates dedicated \(\ce {^{210}Pb}\) screening with Micromegas detectors [141]. The source taxonomy is summarized in Table 5.4; Figure 5.4 shows exactly which decay-chain segments and source locations are simulated separately.

Testing the short-lived daughter location. The cathode reference is supplemented by a matched three-location comparison: \(\ce {^{218}Po}\) starts either uniformly in the active gas, in the original cathode-window aluminum volume, or on the gas-facing cylindrical PTFE wall. The same short-chain stopping rule, transport physics, detector response and selection are used in all three cases. These are source-location scenarios, not three additional full radon activities. The wall case does not cover every endcap or electrode, and no field-driven ion migration between decays is implied.

Let \(Y_j\) be the accepted-event yield per generated short-chain parent for \(j\in \{\mathrm {gas},\mathrm {cathode},\mathrm {wall}\}\). A mixture with one specified short-chain activity \(A_{\mathrm {short}}\) is \[ B_{\mathrm {short}}=\frac {A_{\mathrm {short}}}{\Delta E\,A_{\mathrm {fid}}} \sum _j f_jY_j,\qquad f_j\geq 0,\qquad \sum _j f_j=1. \] The pure cases and their mixtures test sensitivity to the unknown location fractions without fitting them to the sparse background data. The largest pure-case yield bounds these mixtures only within this restricted model, not all possible daughter-migration histories. In a stationary model supplied solely by radon decaying in the active gas, \(A_{\mathrm {short}}\) would be tied to that radon activity through retention and removal, rather than assigned a second independent inventory. The existing cathode surface benchmark is kept separate from this connected interpretation. Long-lived Pb-210 remains a distinct exposure-history hypothesis.

The completed comparison uses 4000 generated parents per location. After the final baseline, 64 cathode events, one gas event and no wall events remain; the unchanged BDT retains 12, zero and zero, respectively. The cathode post-BDT response is \((1.91\pm 0.55)\times 10^{-4}~\mathrm {counts\,keV^{-1}\,cm^{-2}\,s^{-1}\,Bq^{-1}}\), where the error is the parent-cluster Monte Carlo standard error. This finite comparison supports the cathode as the more consequential of the three tested starting locations; the empty gas and wall selections do not establish zero response or exclude all other plate-out distributions. The boundary-recoil and gas-response limitations stated above remain. These matched alternatives are not added to the reference inventory below.

Application of the common analysis chain. The gas and cathode samples have complete file coverage and use the final TPC baseline and frozen simulation BDT, without veto rejection. Transport uses argon–2% isobutane at 1.4 bar, while the calibration-tuned response uses 1% isobutane and nominal pressure 1.4 atm. The results remain conditional on this transfer between gas conditions. Equation 5.1 converts the selected counts to a response per becquerel using all generated parents and their correlated descendants. Table 5.5 gives the complete selection sequence, and Table 5.6 converts the selected counts into a response per unit source activity.

After the BDT, cathode \(\ce {^{218}Po}\) has 160 selected events from 159 parents and cathode \(\ce {^{210}Pb}\) has 1169 from 1168, requiring parent-correlated errors and limits. The 26 argon and 35 krypton events all have distinct parents; their limits use the Poisson working model. The radon single-event limit additionally accounts for its generation stopping rule; all samples retain daughter decays and secondary transport.

Absolute rates multiply these responses by the independently specified activities. The geometry and Ar2 mixture imply an argon mass of 0.519 g. Table 5.7 gives an absolute background prediction for every activity scenario in Table 5.8. The cathode scenarios refer to one projected 15 mm-radius source disk, not the TPC fiducial area used to normalize the output rate. The atmospheric \(\ce {^{39}Ar}\) prediction includes the literature activity uncertainty [136]; the underground-argon alternative adopts a fixed reduction factor of 1400. The krypton reference and the radon and surface benchmarks are held fixed for their conditional statistical limits. These benchmark activities are not detector assays; the argon alternatives are not added together.

Cylindrical-wall contamination. Wall activity is treated separately from the cathode source. Figure 5.5 distinguishes contamination on the gas-facing PTFE surface from contamination on the copper behind the 1 mm PTFE liner. Both models retain the full decay chain and secondary transport and use the same response, TPC baseline and additional simulation BDT as the other source components. They differ only in the specified source surface; neither includes endcaps or assumes a measured implantation-depth distribution. The completed fixed-parent production contains 500 000 parent decays per location. After the final baseline and BDT, 11 PTFE-surface events and one copper-surface event remain. For an explicitly illustrative surface activity of 1 mBq m\(^{-2}\), the corresponding background estimates are \((1.32\pm 0.40)\times 10^{-11}\) and \((1.22\pm 1.22)\times 10^{-12}\) counts keV\(^{-1}\) cm\(^{-2}\) s\(^{-1}\). These are alternative location benchmarks, not measured wall activities, and remain outside the known-inventory subtotals in Section 5.5.

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. Changes in gas recirculation and radon suppression during IAXO-D1 operation at LSC affected the alpha and low-energy backgrounds [82, 142, 143].

5.2.2 Neutron-induced cobalt in copper

Neutron reactions in the copper components produce radioactive cobalt whose later decays can contribute to the detector background. We focus on \(\ce {^{58}Co}\) and \(\ce {^{60}Co}\): these two ground states account for every event passing the baseline and BDT in the reference calculation. The accepted background depends on both activity and the decay radiation reaching the gas.

The reference assumes continuous irradiation by the Zaragoza outdoor HENSA field above 1 MeV, with scalar fluence rate 6.920 × 10⁻³ cm⁻² s⁻¹. This is a proxy for sea-level DESY operation rather than a site measurement. Moderation and capture inside the geometry are included, but lower-energy incident neutrons are absent. The activity estimate assumes zero initial induced inventory, complete retention and fixed target composition, and follows radioactive daughter feeding. Table 5.9 gives the cobalt activities after five years and at formal equilibrium, including daughter feeding. Formal equilibrium assumes unlimited irradiation; the finite-time activities describe the buildup during operation. For a retained isotope produced at constant rate \(P\), without daughter feeding, \(A(t)=P(1-e^{-\lambda t})\) with \(\lambda =\ln 2/T_{1/2}\); the numerical activities include the feeding delays along each decay chain.

Surface activation has been observed in copper later assayed underground: the TREX-DM sample measured at Canfranc shared the vessel’s prior surface-exposure history [144]. For comparison with formal equilibrium, two independent controlled-exposure studies give central sea-level saturation activities of 0.60–0.80 mBq kg⁻¹ for \(\ce {^{58}Co}\) and 0.34–0.46 mBq kg⁻¹ for \(\ce {^{60}Co}\), after altitude and decay corrections [145, 146]. Our equilibrium activities averaged over approximately 69.6 kg of copper in the reference geometry are 1.07 mBq kg⁻¹ and 0.873 mBq kg⁻¹, respectively. These comparisons establish the activity scale; the different incident fields and shielding prevent treating them as a validation of the production model.

The cobalt activities enter the same decay calculation used for screened contamination. For each cobalt state \(i\) and copper source volume \(v\), the activity \(A_{i,v}(t)\) in Bq multiplies the selected response per Bq, \(R_{i,v}\): \begin{equation} B_{\rm act}(t)=\sum _{i,v}A_{i,v}(t)\,R_{i,v}, \qquad R_{i,v}=\frac {\epsilon _{i,v}}{\Delta E\,A_{\rm fid}}, \label {eq:activation-selected-yield} \end{equation} where \(\epsilon _{i,v}\) is the mean selected count per generated decay, \(\Delta E=5\,\mathrm{keV}\) and \(A_{\rm fid}=\pi ~\mathrm {cm^2}\). The decay response uses the common baseline and fixed TPC BDT; the source state, physical placement, geometry and detector response must match before a response is reused. Activity already included in screening inputs, particularly \(\ce {^{60}Co}\), must be reconciled before adding an induced contribution.

The modeled equilibrium contribution from cobalt in copper is \(2.31\times 10^{-10}\) counts keV\(^{-1}\) cm\(^{-2}\) s\(^{-1}\), adopted in the final summary. The later decays lose the production interaction’s scintillator coincidence, so no veto rejection is assigned. This remains a partial activation estimate: incomplete response coverage prevents establishing that the other radionuclides are negligible, and production and source-model uncertainties are unquantified. An independent response study also selects \(\ce {^{62}Cu}\) and \(\ce {^{64}Cu}\), which dominate its restricted complete-cell diagnostic, \((2.57\pm 1.81)\times 10^{-9}\) in the same units at equilibrium. Other cells fail response qualification, so that diagnostic is neither a full rate nor a lower bound and does not establish an increase relative to the reference. Its nominal MC error excludes fit-selection bias and source/model uncertainties; the reference estimate remains adopted, without a main-budget upper limit.

5.2.3 Detector materials

Radioactive contaminants in nearby materials can produce low-energy deposits in the gas through their emitted particles and secondary radiation. We evaluate ten detector components, with decays distributed throughout each source volume. Their masses follow the transported geometry, including only the PET film of the aluminized entrance window; no separate aluminum-coating activity is supplied. Table 5.10 gives the adopted specific activities from the collaboration inventory [82]. Most are screening-limit scenarios, while readout \(\ce {^{40}K}\) uses reference values; unspecified assay uncertainties and confidence levels prevent treating this inventory as a set of measured central activities. Gas activity, surface plate-out, telescope contamination, electronics, and lead shielding are evaluated separately.

Neutron-induced activities from Section 5.2.2 enter the same decay-response calculation as screened activities. Each activity is assigned to its physical source volume; reusing a response requires matching the isotope state, geometry and decay-chain treatment. The screened-material subtotal and the partial activation result are reported separately because existing \(\ce {^{60}Co}\) screening inputs can overlap the induced inventory and the response geometries differ.

The additional \(\ce {^{235}U}\) inputs are 0.093 Bq kg⁻¹ for copper readout, 0.046 Bq kg⁻¹ for Kapton and 0.0029 Bq kg⁻¹ for PET. PET also uses 0.0059 Bq kg⁻¹ of \(\ce {^{226}Ra}\), 0.0036 Bq kg⁻¹ of \(\ce {^{228}Th}\) and 0.002 Bq kg⁻¹ of \(\ce {^{137}Cs}\); the first two are alternative full-chain hypotheses. Table 5.11 combines the supplied, non-overlapping activities with their simulated responses. For the adopted activities, the selected subtotal is \((2.33\pm 0.11)\times 10^{-8}\), with a conditional one-sided 90% upper limit of \(8.16\times 10^{-8}\)\(^{\dagger }\), in counts keV\(^{-1}\) cm\(^{-2}\) s\(^{-1}\). The uncertainty on the estimate is the parent-correlated MC standard error. The copper readout, Kapton readout, and PET film supply 80.6%, 14.2%, and 4.7% of the central estimate, respectively; the BDT reduces the baseline subtotal by a factor of 4.68. These rankings apply to the supplied activity scenarios. The upper limits show the limited sensitivity of sparsely populated samples: zero selected events do not imply zero background.

The subtotal includes 35 non-overlapping sources from the 54 simulated component–isotope hypotheses. Full-chain \(\ce {^{226}Ra}\) and \(\ce {^{228}Th}\) hypotheses overlap with their \(\ce {^{238}U}\) and \(\ce {^{232}Th}\) parent chains and remain alternatives; missing activities are excluded, not set to zero. The assumed chain activities and daughter retention do not establish equilibrium in the installed detector. All generated parents enter the exposure, with their decay subevents grouped for uncertainty calculations. The common baseline and fixed BDT are applied to each reconstructed event with no veto rejection. The REST response and calibration threshold are transferred to the transported argon–2% isobutane mixture; their nominal calibration acceptance is not independently validated for these gas and field conditions. The subtotal and its statistical limit are conditional on those activity and response assumptions and do not bound unassayed contaminants or the complete detector background.

5.2.4 Telescope and X-ray optics contamination

Radioactive decays near the X-ray optics can emit photons along the bore and into the detector through its magnet-facing aperture. We evaluate this separate source using a thin emission disc at the far end of the telescope pipe (Figure 5.6).

The telescope study uses the BabyIAXO mechanical geometry, which includes the telescope-side pipe. The source disc has radius 275 mm, thickness 0.1 mm, and its center is at \(z=5512.15\,\mathrm{mm}\) relative to the chamber origin. It represents the emission positions in vacuum, without modeling the optics material or self-absorption. For uniform projected activity, \(A_i=m_{\mathrm {optics}}a_i\), where \(a_i\) is the isotope-specific activity per unit mass.

The chamber, detector pipe, electronics box and passive shielding match the IAXO-D1 material definitions and placements; the veto arrangement differs. The BabyIAXO name here selects the mechanical layout: the active gas remains argon–isobutane 2 % at 1.4 bar. These shared detector components do not establish equal telescope-background rates, because scattering and angular acceptance depend on the surrounding geometry.

Photons from \(\ce {^{238}U}\), \(\ce {^{232}Th}\) and \(\ce {^{40}K}\) are sampled within a \(15^{\circ }\) cone towards the detector to improve sampling efficiency. Table 5.12 includes the isotropic-cone factor \[ f_{\Omega } = \frac {1-\cos (15^{\circ })}{2} = 1.70\times 10^{-2}, \] and therefore reports only that cone’s contribution per becquerel of isotropic activity. Photons emitted outside the cone can scatter towards the detector; this complementary contribution remains unconstrained. The \(\ce {^{40}K}\) sample uses a 1460.822 keV photon with a yield of 0.1067 photons per decay. The selected photon spectra for \(\ce {^{232}Th}\) and \(\ce {^{238}U}\) have yields of 2.69742 and 3.59079 photons per parent-chain decay, respectively, under the adopted chain-equilibrium convention.

The common TPC baseline and BDT use the fixed calibration response, transferred to these Ar2 conditions; the Ar1 calibration acceptance is not independently established for this mixture. The transport pressure of 1.4 bar and response pressure of 1.4 atm retain the same transfer limitation. No veto rejection is applied because the IAXO-D1 readout map does not cover every BabyIAXO veto placement; the full veto geometry remains in transport.

The selected \(\ce {^{40}K}\) sample contains nine independent photon histories, so its upper limit uses the sparse-count working model rather than the populated approximation used for uranium and thorium. Controls with source offsets of \(-100\), \(0\) and \(+100\) mm, including IAXO-D1 with the same telescope added, retain only one baseline event from nine gas interactions. They cannot establish equivalent background rates or negligible incidence outside the cone. The telescope therefore remains outside the absolute budget: it requires optics masses and activities, compatible response validation and the angular complement.

5.2.5 Front-end electronics

The front-end electronics must be placed close to the Micromegas readout to preserve signal quality, but they contain materials that are harder to radiopurify than bulk copper, Kapton, or PTFE. Their background contribution was therefore treated separately from copper and readout-plane contamination. The analysis follows Section 5.1.2; the card-induced rate is evaluated after the final TPC baseline and then the BDT, retaining the baseline comparison and applying no veto rejection. 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 [81, 147].

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 5.13. The optional contribution from the 10 Ω 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. Table 5.14 follows the six isotopes across the four cards through the cumulative baseline selection. Of the 121 baseline events, 37 pass the BDT; generated decays with no stored detector event remain in the normalization.

The response preserves the original argon–2% isobutane composition, but transfers the calibrated diffusion, shaping and energy-response parameters without fitting the background events. The transport pressure is 1.4 bar, while the retained response convention uses 1.4 atm; the \(1.3\%\) difference is also part of this conditional transfer. The baseline definition is unchanged, whereas the absolute detector response and transfer of the Ar1-calibrated BDT threshold remain explicit modeling assumptions. The latter is not a demonstration of 80% calibration acceptance under the Ar2 conditions.

Applying the per-card activities to their verified generated-decay exposures gives the conditional baseline estimate \[ B_{\mathrm {cards,baseline}}=(2.71\pm 0.65)\times 10^{-9}~ \mathrm {counts\,keV^{-1}\,cm^{-2}\,s^{-1}}, \] using the 2–7 keV window and the \(\pi ~\mathrm {cm^2}\) fiducial area. The uncertainty is the Monte Carlo standard error, with decay subevents grouped by their generated parent; it does not include activity or response-transfer uncertainties. The large \(\ce {^{238}U}\) activity makes that chain the dominant contribution in this source scenario.

The actual BDT survivors give the conditional selected-background prediction \[ B_{\mathrm {cards,BDT}}=(5.85\pm 1.21)\times 10^{-10}~ \mathrm {counts\,keV^{-1}\,cm^{-2}\,s^{-1}}. \] Table 5.15 gives the isotope contributions using the same per-card activities and generated-parent exposures. The quoted error is a parent-correlated MC standard error, not a 90% interval. The sparse-count treatment of Section 5.1.1.0 gives the card-only one-sided 90% working-model upper limit \[ B_{\mathrm {cards,BDT}}\leq 6.37\times 10^{-9}\,{}^{\dagger }~ \mathrm {counts\,keV^{-1}\,cm^{-2}\,s^{-1}}. \] The four cards have different simulated exposures, so their events are weighted separately before combining the predictions. The limit also includes card–isotope combinations with no selected event: a zero count does not establish a zero contribution. For the six-isotope subtotal, the statistical error budget is shared among all 24 card–isotope combinations, rather than adding six individual 90% limits and calling the sum a 90% limit. This deliberately conservative combination explains why the upper limit is much larger than the central estimate. All 37 selected events come from distinct generated parents; the \(\dagger \) still marks an assumed rare-event counting model, not evidence that multiple accepted descendants are impossible. This prediction is not corrected by dividing by the X-ray acceptance.

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 result now uses the final selection, but the conditional response transfer and incomplete service-material geometry still prevent it from establishing that all front-end electronics are subdominant in the full background inventory. Within the adopted activity scenario, \(\ce {^{238}U}\) supplies about 60% of the selected central estimate, followed by \(\ce {^{232}Th}\) at about 39%. The practical priority is therefore to constrain these activities and their locations in the cards, rather than treating the small unweighted event counts as evidence that the electronics can be neglected.

5.2.6 Shielding

The lead shield is the most massive passive component around the detector. Its radioactivity is therefore a background source as well as a means of suppressing external radiation. For photons and electrons, self-absorption makes the detector-facing lead particularly important. The calculation below applies the final TPC baseline and simulation BDT of Section 5.1.2; it does not credit any veto rejection.

The reference source is \(\ce {^{210}Pb}\), distributed uniformly through the innermost 10 mm of lead. The adopted activity is \[ A_{\ce {^{210}Pb}}= 38.8624\,\mathrm{kg}\times 80\,\mathrm{Bq}\,\mathrm{kg}^{-1} =3.1090\times10^{3}\,\mathrm{Bq}. \] This is a lead-activity scenario, not a measurement of the installed shield. The copper liner and all transported decay products are retained. Because lead activity varies with material history, lower-activity inner lead scales this source term directly at fixed geometry.

The preserved \(\ce {^{210}Pb}\) transport uses the final, unmasked TPC reconstruction, baseline and BDT. Only reconciled exposure enters the normalization, including decays with no stored detector event. As for the other material sources, the Ar/2% isobutane response and BDT threshold use the explicitly conditional calibration transfer described in Section 5.1.7.0; the result is not an independent validation of this gas response.

The result is a prediction for the inner shell. Escape-particle diagnostics support a surface-dominated electromagnetic contribution, but do not establish convergence of the selected rate as deeper lead is included. A full-shield prediction therefore requires additional depth shells.

Copper liner and low-activity inner lead. The lead and copper have complementary roles. Lead attenuates external radiation, but its own radioactive decays produce electrons and photons. The copper box provides a cleaner inner barrier: it stops escaping charged particles and attenuates lead fluorescence and low-energy bremsstrahlung. Copper can itself fluoresce near 8 keV, so its presence does not eliminate the need to model secondary radiation [16]. Its intrinsic radioactivity is included separately in the detector-material inventory.

The copper benefit is evaluated by comparing the nominal geometry with a control in which the box is replaced by air, leaving the lead source and all other detector components unchanged. Both samples use the common TPC baseline and simulation BDT, without veto rejection. After the baseline selection, the copper reduces this contribution by a factor of 3.0 (two-sided 90% interval: 1.3–6.3). This comparison includes the actual openings and unequal wall thicknesses, rather than treating copper as a uniform absorber.

After the BDT, the smaller air-control sample has no surviving events and gives an individual 90% upper limit of \(\relax \leq 1.54\,\times \,\)\(\relax 10^{-8}{}^{\dagger }\) \(\mathrm {counts\,keV^{-1}\,cm^{-2}\,s^{-1}}\). The nominal copper result is \(\relax (6.02\pm 1.90)\,\times \,\)\(\relax 10^{-9}{}^{}\) in the same units. The samples therefore demonstrate a benefit before the BDT, but do not resolve the reduction after it; the baseline factor must not be applied again to the final background budget.

The remaining lead contribution can also be reduced at its source. For a Roman-lead sample, Pattavina et al. report a \(\ce {^{210}Pb}\) activity below 0.715 mBq kg⁻¹ at 90% confidence [148]. Using that assay ceiling as a fixed design benchmark, rather than as a measurement of the proposed shield, Table 5.18 compares ordinary and archaeological lead in the same inner 10-mm shell. This changes the source activity, not the attenuation properties or event selection. It does not rescale the ordinary lead behind the replacement layer, or the independent U/Th/K contributions.

The useful thickness depends on how far into the lead the radiation reaching the detector originates. A complementary planar transport study varies the thickness and position of the low-activity layer, retaining ordinary lead elsewhere and the copper on the detector side. It compares a detector-facing layer with the same amount of low-activity lead buried deeper in the shield. The preferred ordering, from outside towards the TPC, is ordinary lead, low-activity lead, then copper: placing ordinary radioactive lead inside the clean layer would leave an unprotected nearby source. The thickness at which the remaining photon flux is reduced by 90% is about 8.6 mm for a 10-mm copper layer. Replacing the first 10, 20 and 30 mm of lead leaves, respectively, \(7.5\pm 0.3\)%, \(1.7\pm 0.2\)% and \(0.5\pm 0.1\)% of the ordinary-lead photon flux. These flux reductions guide the material choice, but are not substitutes for background rates after TPC selection.

On this basis, 1 cm of low-activity lead immediately outside the copper is a useful initial design benchmark; 2 cm provides further suppression where space and material availability permit. These are not demonstrated optima for the finite shield. Their benefit concerns lead-induced electromagnetic background, not a demonstrated reduction of the complete background budget or the neutron component. The reference budget therefore retains ordinary lead; the low-activity configuration is an alternative, not an additional contribution.

Other lead contaminants. The reference specific activities are \(3.3\times 10^{-4}~\mathrm {Bq\,kg^{-1}}\) for \(\ce {^{238}U}\), \(1.0\times 10^{-4}~\mathrm {Bq\,kg^{-1}}\) for \(\ce {^{232}Th}\), and \(1.2\times 10^{-3}~\mathrm {Bq\,kg^{-1}}\) for \(\ce {^{40}K}\). For the same 38.8624 kg shell these correspond to 12.8 mBq, 3.89 mBq, and 46.6 mBq, respectively. Their historical selected rates cannot be converted into final-chain results by changing the normalization area: the archived response used a different gas configuration and selection, and unfiltered source files were not located. Fixed-parent replacement productions retain the complete radioactive-decay physics and apply the same response and BDT as the \(\ce {^{210}Pb}\) calculation. Table 5.19 gives the results from \(8\times 10^7\) parents for each of \(\ce {^{238}U}\) and \(\ce {^{232}Th}\), and \(8\times 10^8\) for \(\ce {^{40}K}\). These contributions enter the radioactive-inventory subtotals in Section 5.5. Failed attempts are excluded; their complete replacements supply the corresponding exposure exactly once. No absolute \(\ce {^{235}U}\) or \(\ce {^{60}Co}\) contribution is inferred without an adopted activity.