1 Axion Searches and the IAXO Experiment

The absence of observed charge-conjugation and parity ($\text{CP}$) 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 $\text{CP}$ 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 $\text{CP}$:

Here, ${𝐺}_{𝜇𝜈}^{𝑎}$ is the gluon field-strength tensor and ${\widetilde{𝐺}}^{𝑎,𝜇𝜈}={𝜀}^{𝜇𝜈𝜆𝜌}{𝐺}_{𝜆𝜌}^{𝑎}/2$ is its dual. The remaining quantities are the strong coupling ${𝛼}_{\mathrm{s}}$ and the quark mass matrix ${𝑀}_{𝑞}$. The physical angle $\overline{𝜃}$ combines the bare QCD angle $𝜃$ with a phase from the quark masses. It describes a source of $\text{CP}$ 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 ${𝑑}_{𝑛}/\overline{𝜃}$ of order ${10}^{-16}𝑒\text{cm}$, with a coefficient that depends on the calculation method [10, 20, 21]. The measured limit therefore requires $|\overline{𝜃}|\lesssim \mathrm{𝒪︀}({10}^{-10})$. 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 $\text{CP}$ problem. Proposed solutions include imposing fundamental $\text{CP}$ 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 $𝑈(1{)}_{\text{PQ}}$ 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 Equation (1.1) by a field-dependent quantity:

Nonperturbative QCD generates a potential whose minimum satisfies $⟨𝑎⟩/{𝑓}_{𝑎}=\overline{𝜃}$. As the field relaxes to this minimum, the effective strong $\text{CP}$ 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 $\text{CP}$ 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 ${𝑓}_{𝑎}\gg {𝑣}_{\text{EW}}$ 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 $\text{CP}$ 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, ${𝐹}_{𝜇𝜈}$ and ${\widetilde{𝐹}}^{𝜇𝜈}$ are the electromagnetic field-strength tensor and its dual. The constant $𝛼$ 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 ${𝑔}_{𝑎𝛾}$ has dimensions of inverse energy. Together with Equation (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 $({𝑚}_{𝑎},{𝑔}_{𝑎𝛾})$ 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, $\hslash =𝑐=1$, the decay width and lifetime are

The lifetime increases rapidly as the mass and coupling decrease. For the illustrative values ${𝑚}_{𝑎}=1\text{meV}$ and ${𝑔}_{𝑎𝛾}=1\times {10}^{-14}{\text{GeV}}^{-1}$, it is approximately $4\times {10}^{34}\text{yr}$. 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

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 $\text{CP}$ 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 $3𝐻({𝑇}_{\text{osc}})\simeq {𝑚}_{𝑎}({𝑇}_{\text{osc}})$, it begins coherent oscillations. Here, $𝐻(𝑇)$ is the Hubble expansion rate and ${𝑇}_{\text{osc}}$ 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 ${𝑔}_{𝑎𝛾}$, 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 ${𝑔}_{𝑎𝛾}^4$. The Any Light Particle Search II (ALPS II) campaign of February–May 2024 found no signal and set a 95% upper limit of $|{𝑔}_{𝑎𝛾}|<1.5\times {10}^{-9}{\text{GeV}}^{-1}$ for pseudoscalar masses below approximately $0.1\text{meV}$ [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 ${𝑔}_{𝑎𝛾}^2$, giving a signal rate proportional to ${𝑔}_{𝑎𝛾}^4$. For ABC axions, the rate is proportional to ${𝑔}_{𝑎𝑒}^2{𝑔}_{𝑎𝛾}^2$. A helioscope therefore constrains $|{𝑔}_{𝑎𝛾}|$ through the Primakoff component and $|{𝑔}_{𝑎𝑒}{𝑔}_{𝑎𝛾}|$ 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 $1\text{–}10\text{keV}$. 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 $0.01\text{–}20\text{keV}$ gives a total flux ${\mathrm{\Phi }}_{𝑎}=3.46\times {10}^{11}{\text{cm}}^{-2}{\mathrm{s}}^{-1}$ and a mean energy of $4.14\text{keV}$.

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 ${𝑔}_{𝑎𝛾}$-dependent component and may dominate below approximately $200\text{eV}$, 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 ${𝐵}_{⟂}$ of length $𝐿$, neglecting photon absorption and using natural units $\hslash =𝑐=1$, it is

The factor $\mathrm{ℱ︀}$ describes the loss of coherence caused by the momentum mismatch $𝑞$:

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, $\mathrm{ℱ︀}\simeq 1$, and the conversion probability grows as ${𝐵}_{⟂}^2{𝐿}^2$. 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 ${𝑚}_{𝛾}$. The mismatch becomes $𝑞\simeq |{𝑚}_{𝑎}^2-{𝑚}_{𝛾}^2|/(2𝐸)$, which vanishes near ${𝑚}_{𝑎}={𝑚}_{𝛾}$; the vacuum expression follows by setting ${𝑚}_{𝛾}=0$. Equation (1.8) and Equation (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,

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 ${𝑚}_{𝑎}\simeq {𝑚}_{𝛾}$. 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

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 ${𝜖}_{𝑜}$ and ${𝜖}_{𝑑}$, and the effective tracking exposure is ${𝜖}_{𝑡}𝑡$. For a selected focal region, ${𝜖}_{𝑜}$ 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 ${𝑚}_{𝑎}^2-{𝑚}_{𝛾}^2$. 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 ${𝑚}_{𝛾}^2$. 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 ${𝑚}_{𝑎}=0.10\text{eV}$. 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

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 ${𝑇}_{\text{scan}}$. 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 Equation (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 Equation (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]:

The magnetic, detector–optics, and tracking contributions are

The magnetic factor contains the total instrumented aperture $𝐴$ and its effective transverse field ${𝐵}_{\text{eff}}$. For a uniform field, ${𝐵}_{\text{eff}}={𝐵}_{⟂}$; for a nonuniform magnet, the coherent-limit quantity ${𝐵}_{\text{eff}}^2{𝐿}^2𝐴$ represents ${\int }_{𝐴}|{\int }_0^{𝐿}{𝐁}_{⟂}\mathrm{d}\ell {|}^2\mathrm{d}𝐴$. The detector–optics factor balances the detector efficiency ${𝜖}_{𝑑}$ and optics throughput ${𝜖}_{𝑜}$ 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 ${𝜖}_{𝑡}$ 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 ${𝑔}_{𝑎𝛾}^4$, these gains translate into an approximate coupling sensitivity $|{𝑔}_{𝑎𝛾}|\propto {𝑓}^{-1/4}$. 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 $\mathrm{\Delta }𝐸$ and total selected focal area $𝑎$, the expected count is

where $𝑇$ is the effective tracking exposure. For illustration, the full-IAXO targets in Table 1.1, an energy window of $2\text{–}7\text{keV}$, and $3\text{yr}$ of elapsed operation give ${𝜇}_{𝑏}=2.84$ when ${𝜖}_{𝑡}=0.5$. 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

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 ${\mathrm{ℒ︀}}_{\text{aux}}$ and nuisance parameters $𝝂$. 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 ${𝜇}_{𝑏}$. For $𝑛$ observed events and a prior uniform in the nonnegative signal mean $𝑠$, the 95% Bayesian upper bound satisfies

For a fixed Primakoff response, this prior is uniform in ${𝑔}_{𝑎𝛾}^4$, 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 $𝑛\sim \text{Pois}({𝜇}_{𝑏})$. At ${𝜇}_{𝑏}=2.84$ 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 ${𝑔}_{𝑎𝛾}^{\text{lim}}\propto {𝑏}^{1/8}{𝑇}^{-1/8}$. When the median outcome is zero events, further background reduction leaves the median counting limit unchanged, whereas increasing the accepted exposure gives ${𝑔}_{𝑎𝛾}^{\text{lim}}\propto {𝑇}^{-1/4}$. 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 ${𝑚}_{𝑎}\lesssim 0.02\text{eV}$. The first buffer-gas campaign used ${}^4\text{He}$ at $1.8\mathrm{K}$, scanning 160 density settings to cover $0.02\text{–}0.39\text{eV}$. The pressure increments were approximately $0.08\text{mbar}$, reaching $13.4\text{mbar}$; the saturated-vapor pressure limited the attainable ${}^4\text{He}$ density. Subsequent ${}^3\text{He}$ campaigns reached higher densities at the same temperature and covered $0.39\text{–}1.17\text{eV}$. 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 $|{𝑔}_{𝑎𝛾}|<5.8\times {10}^{-11}{\text{GeV}}^{-1}$ at 95% confidence for ${𝑚}_{𝑎}\lesssim 0.02\text{eV}$ [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.

Background level $𝑏$ is given in $\text{counts}{\text{keV}}^{-1}{\text{cm}}^{-2}{\mathrm{s}}^{-1}$.

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 $|{𝑔}_{𝑎𝛾}|\sim 3\times {10}^{-12}{\text{GeV}}^{-1}$, 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.

1.4.3.1 Magnet

The 2014 reference design uses an approximately $20\mathrm{m}$-long superconducting toroid with eight coils and eight bores of approximately $60\text{cm}$ 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].

1.4.3.2 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 $0.15{\text{cm}}^2$ 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 Equation (1.14).

1.4.3.3 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 ${𝜖}_{𝑡}\simeq 0.5$ [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 $1.5\text{yr}$ of effective exposure for each of the vacuum and buffer-gas campaigns. Under those assumptions, the projected vacuum sensitivity is $|{𝑔}_{𝑎𝛾}|\simeq 1.5\times {10}^{-11}{\text{GeV}}^{-1}$ for ${𝑚}_{𝑎}\lesssim 0.02\text{eV}$. A subsequent buffer-gas scan would extend the mass coverage and probe the KSVZ benchmark approximately over $0.06\text{–}0.25\text{eV}$ [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 $6\text{kA}$ [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 $0.2{\text{cm}}^2$ for the custom telescope and $0.3\text{–}0.7{\text{cm}}^2$ 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. Section 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 $1\text{–}10\text{keV}$ 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; Section 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. Section 4 and Section 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 $1\text{–}10\text{keV}$ band while suppressing events that can mimic the signal. The conceptual background targets are $1\times {10}^{-7}\text{counts}{\text{keV}}^{-1}{\text{cm}}^{-2}{\mathrm{s}}^{-1}$ for BabyIAXO and $1\times {10}^{-8}\text{counts}{\text{keV}}^{-1}{\text{cm}}^{-2}{\mathrm{s}}^{-1}$ 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.