cd ~/CastData/ExternCode/TimepixAnalysis/LogReader/
./cast_log_reader sc -p ../resources/LogFiles/SCLogs/2017_18 -s Version.idx

• [ ] SAVE A PLOT
• [ ] GET TABLE FROM JAIME's THESIS
• [ ] FIND REFERENCE OF JAIME's TABLE

The tilting angles of the CAST magnet are stored (among others, the tracking files also contain angle data, as well as the "angles" file {that existed at some point at least?} ) in the slow control log files.

We'll use our log file parser to parse all the log files between 2016 and

cd ~/CastData/ExternCode/TimepixAnalysis/LogReader/
./cast_log_reader sc -p ../resources/LogFiles/SCLogs -s Version.idx

This yields fig. 2 where we can see that the real angles are between \(\sim\SIrange{-7}{7.7}{°}\).

We also have all of the slow control logs in ./../CastData/ExternCode/TimepixAnalysis/resources/LogFiles/AllLogs/logfiles/. Feel free to run the command on this directory. But don't expect amazing performance given the amount of data!

A PNG of the full data in fig. 3 showing the same range as the figure only showing the data taking period discussed in this thesis.

The first X-ray telescope used at CAST as a focusing optics for the expected axion induced X-ray flux was a Wolter I type X-ray telescope (Wolter 1952) originally built for a proposed German space based X-ray telescope mission, ABRIXAS (Richter et al. 1995; Friedrich 1998). The telescope consists of 27 gold coated parabolic and hyperbolic shells and has a focal length of \(\SI{1.6}{m}\). Due to the small size of the dipole magnet's bores of only \(\SI{43}{mm}\) only a single section of the telescope can be exposed. The telescope is thus placed off-axis from the magnet bore to expose a single mirror section. An image of the mirror system with a rough indication of the exposed section is shown in fig. 4(b).

The telescope is owned by the 'Max Planck Institut für extraterrestrische Physik' in Garching. For that reason it will often be referred to as the 'MPE telescope' in the context of CAST.

The efficiency of the telescope reaches about \(\SI{48}{\%}\) as the peak at around \(\SI{1.5}{keV}\), drops sharply at around \(\SI{2.3}{keV}\) to only about \(\SI{30}{\%}\) up to about \(\SI{7}{keV}\). From there it continues to drop until about \(\SI{5}{\%}\) efficiency at \(\SI{10}{keV}\). The efficiency is shown in a comparison with another telescope in the next section 5.1.4 in fig. 7.

A picture of the telescope installed at CAST behind the magnet on the 'sunrise' side of the magnet is shown in fig. 4(a). ⁵ This telescope was used for the data taking campaign in 2014 and 2015 using a GridPix based detector discussed in (Christoph Krieger 2018) and serves as a comparison for certain aspects in this thesis.

Up to 2014 there was only a single X-ray telescope in use at CAST. In August 2014 a second X-ray optic was installed on the second bore next to the ABRIXAS telescope. This telescope, using technologies originally developed for the space based NuSTAR telescope by NASA (Harrison et al. 2013, 2006; Koglin et al. 2009; Craig et al. 2011; Hailey et al. 2010), was purpose built for axion searches and in particular the CAST experiment. Contrary to the ABRIXAS telescope only a single telescope section of \(\SI{30}{°}\) wide mirrors of the telescope was built as the small bore cannot expose more area anyway. It uses a cone approximation to a Wolter I optic, meaning the hyperbolic and parabolic mirrors are replaced by cone sections (Petre and Serlemitsos 1985). A side view and rear view of the open telescope after decommissioning at CAST are seen in fig. 5. It consists of 13 platinum / carbon coated glass shells in each telescope section, for a total of 26 mirrors. Each mirror uses one of four different depth graded multilayer (see sec. 6.1.2) coating recipes to improve reflectivity over a larger energy and angle range. Further, the focal length was shortened to \(\SI{1.5}{m}\). The telescope section is rotated such that the focal point is pointing away from the other magnet bore to make more space for two detectors side by side. ⁶ This can be seen in the render of the 2017/18 detector setup in fig. 6, seen from the top. The development process of the telescope is documented in the PhD thesis by A. Jakobsen (Jakobsen 2015). (Aznar et al. 2015) gives an overview and shows preliminary results from CAST. The telescope was characterized and calibrated at the PANTER X-ray test facility in Munich.

This telescope achieves a significantly higher effective area than the ABRIXAS telescope in the energy range between \(\SIrange{2}{3}{keV}\) fig. 7 (relevant for axion searches, compare with fig. #fig:theory:solar_axion_flux:differential_flux). But outside this range the efficiency is comparable or lower.

The precise understanding of the position, size and shape of the focal point as well as the effective area is essential for the limit calculation later in the thesis. In appendix 37 we discuss a raytracing simulation of this telescope. The aim is to simulate the expected distribution of axions from the Sun.

In the many years of data taking and countless detectors taking data at the CAST experiment, it has put the most stringent limits on different coupling constants over the years.

Specifically, CAST sets the current best helioscope limits on the:

• Axion-photon coupling \(g_{aγ}\)
• Axion-electron coupling \(g_{ae}\)
• Chameleon-photon coupling \(β_γ\)

For the axion-photon coupling the best limit is from (Collaboration and others 2017) in 2017 based on the full Micromegas dataset including the data behind the LLNL telescope and constricts the coupling to \(g_{aγ} < \SI{6.6e-11}{\GeV^{-1}}\).

For the axion-electron coupling the best limit is still from 2013 in (Barth et al. 2013) using the theoretical calculations for an expected solar axion flux done by J. Redondo in (Redondo 2013) for a limit on the product of the axion-electron and axion-photon coupling of \(g_{ae} · g_{aγ} < \SI{8.1e-23}{\GeV^{-1}}\). The limit calculation was based on data taken in CAST phase I in 2003 - 2005 with a pn-CCD detector behind the MPE telescope.

CAST was also used to set a limit on the hypothetical chameleon particle. The best current limit on the chameleon-photon coupling \(β_γ\) is based on a single GridPix based detector with data taken in 2014 and 2015 by C. Krieger in (Christoph Krieger 2018; Anastassopoulos et al. 2019), limiting the coupling to \(β_γ < \num{5.74e10}\), which is the first limit below the solar luminosity bound.

For more details on the figure of merit calculation, see sec. 3.1 in (Irastorza et al. 2011).

For completeness, the figure of merit is:

\[ f = f_M f_{\text{DO}} f_T = (B² L² A)_M (\frac{ε_d ε_o}{\sqrt{b a}})_{\text{DO}} (\sqrt{ε_t t})_T \]

The full relationship with the axion-photon coupling is:

So 10,000 more "produced" (i.e. not produced) photons due to f'/f = 10,000 for IAXO over CAST would imply the bounds on \(g\) could be improved by a factor of 10, one order of magnitude.

Let's calculate the figure of merit for the CAST magnet as well as the IAXO / BabyIAXO magnets:

import unchained

defUnit(T²•m⁴)
proc fMagnet(B: Tesla, L: Meter, d: CentiMeter): T²•m⁴ = B^2 * L^2 * (d / 2.0)^2 * π
let fCAST = fMagnet(8.8.T, 9.26.m, 4.3.cm)
echo "CAST magnet, single bore f_M = ", fCAST, " at 8.8 T"
echo "CAST, both bores f_M = ", fCAST * 2

let fIAXO = fMagnet(2.5.T, 20.m, 60.cm)
echo "IAXO magnet, single bore f_M = ", fIAXO, " at 2.5 T *average* field, 20 m length."
echo "IAXO, all bores f_M = ", fIAXO * 8

echo "IAXO FOM over CAST: ", fIAXO * 8 / (fCAST * 2)

Time scaling:

import unchained, math
let g = 8e-11
let g4 = g^4
let t = 1
# g⁴ = √t
# g⁴ / √t = g'⁴ / √t'
let tp = 2
let g4p = g4 * sqrt(2.0)
echo "New g for twice the time: ", pow(g4p, 0.25)

import unchained, math
let g = 8e-11
let g4 = g^4
let t = 1
# g⁴ · √t = N # <- some number of photons: we observe 0
# g⁴' · √t' = N' # <- new number of photons: we still observe 0
# So
# g⁴ · √t = g⁴' · √t'
# should hold, meaning
# g⁴ · √1 = g⁴' · √2
# g⁴' = g⁴ / √2
let g4p = g4 / sqrt(2.0)
echo "New g for twice the time: ", pow(g4p, 0.25)

The major difference between full grown IAXO and BabyIAXO is restricting the setup to 2 bores instead of 8 with a magnet length of only \(\SI{10}{m}\) to prove the magnet design works, before building a larger version of said design. Since the first conceptual design of IAXO (Armengaud et al. 2014) the bore diameter for the two bores of BabyIAXO has increased from \(\SI{60}{cm}\) to \(\SI{70}{cm}\). (Collaboration et al. 2021)

The BabyIAXO design was approved by the 'Deutsches Elektronen-Synchrotron' (DESY) for construction onsite. The project has suffered multiple delays most notably due to the magnet construction. First COVID19 due to its severe effects on supply chains and in 2022 the horrific Russian invasion of Ukraine have caused multi year delays. The latter in particular was problematic as the only two companies being able to supply the type of superconducting cable needed for the magnet are from Russia. The magnet situation is still in flow as of writing this thesis.

For the two bores two different X-ray telescopes are planned to be operated. One bore will be used with a flight spare of the XMM-Newton X-ray satellite mission with a focal length of \(\SI{7.5}{m}\). The second bore would receive a custom built X-ray optic based on a hybrid design of a NuSTAR-like optic for the inner part – similar to the LLNL telescope introduced in sec. 5.1.4 (just as a full telescope) – and a cold slumped glass design following (Civitani et al. 2016) for the outer part. This optic would have a focal length of only \(\SI{5}{m}\).

An annotaded schematic of the BabyIAXO design can be seen in fig. 8(b). The magnet figure of merit for BabyIAXO is aimed at being at least a factor 10 higher than for CAST, with (Collaboration et al. 2021) listing values between \(\SIrange{232}{326}{T^2.m^4}\) depending on how it is calculated.