# Search for Dark Matter Axions with CAST-CAPP

C. M. Adair  K. Altenmüller  V. Anastassopoulos  S. Arguedas Cuendis  J. Baier
K. Barth  A. Belov  D. Bozicevic  H. Bräuninger  G. Cantatore  F. Caspers  J.
F. Castel  S. A. Çetin  W. Chung  H. Choi  J. Choi  T. Dafni  M. Davenport  A.
Dermenev  K. Desch  B. Döbrich  H. Fischer  W. Funk  J. Galan  A. Gardikiotis
S. Gninenko  J. Golm  M. D. Hasinoff  D. H. H. Hoffmann  D. Díez Ibáñez  I. G.
Irastorza  K. Jakovčić  J. Kaminski  M. Karuza  C. Krieger  Ç. Kutlu  B. Lakić
222deceased J. M. Laurent  J. Lee  S. Lee  G. Luzón  C. Malbrunot  C.
Margalejo  M. Maroudas  L. Miceli  H. Mirallas  L. Obis  A. Özbey  K.
Özbozduman  M. J. Pivovaroff  M. Rosu  J. Ruz  E. Ruiz-Chóliz  S. Schmidt  M.
Schumann  Y. K. Semertzidis  S. K. Solanki  L. Stewart  I. Tsagris  T.
Vafeiadis  J. K. Vogel  M. Vretenar  S. Youn  K. Zioutas  Department of
Physics and Astronomy, University of British Columbia, V6T 1Z1 Vancouver,
Canada  Centro de Astropartículas y Física de Altas Energías (CAPA),
Universidad de Zaragoza, 50009 Zaragoza, Spain  Physics Department, University
of Patras, 26504 Patras, Greece  European Organization for Nuclear Research
(CERN), CH-1211 Genève, Switzerland  Physikalisches Institut, Albert-Ludwigs-
Universität Freiburg, 79104 Freiburg, Germany  Institute for Nuclear Research
(INR), Russian Academy of Sciences, 117312 Moscow, Russia  University of
Rijeka, Faculty of Engineering, 51000 Rijeka, Croatia  Max-Planck-Institut für
Extraterrestrische Physik, D-85741 Garching, Germany  Istituto Nazionale di
Fisica Nucleare (INFN), Sezione di Trieste, 34127 Trieste, Italy  Università
di Trieste, 34127 Trieste, Italy  European Scientific Institute (ESI), 74160
Archamps, France  Istinye University, Institute of Sciences, 34396 Sariyer,
Istanbul, Türkiye  Center for Axion and Precision Physics Research, Institute
for Basic Science (IBS), Daejeon 34141, Republic of Korea  Department of
Physics, Korea Advanced Institute of Science and Technology (KAIST), Daejeon
34141, Republic of Korea  Physikalisches Institut, University of Bonn, 53115
Bonn, Germany  Universität Hamburg, 22762 Hamburg, Germany  Institute for
Optics and Quantum Electronics, Friedrich Schiller University Jena, 07743
Jena, Germany  Xi’An Jiaotong University, School of Science, Xi’An, 710049,
China  Rudjer Bošković Institute, 10000 Zagreb, Croatia  University of Rijeka,
Faculty of Physics, 51000 Rijeka, Croatia  University of Rijeka, Photonics and
Quantum Optics Unit, Center of Excellence for Advanced Materials and Sensing
Devices, and Centre for Micro and Nano Sciences and Technologies, 51000
Rijeka, Croatia  Lawrence Livermore National Laboratory, Livermore, CA 94550,
USA  Extreme Light Infrastructure - Nuclear Physics (ELI-NP), 077125 Magurele,
Romania  Institut für Physik, Johannes Gutenberg Universität Mainz, 55128
Mainz, Germany  Max-Planck-Institut für Sonnensystemforschung, 37077
Göttingen, Germany  Present address: Bogazici University, Physics Department,
34342 Bebek, Istanbul, Türkiye  Present address: Institute of Experimental
Physics, University of Hamburg, 22761 Hamburg, Germany  Present address:
Istanbul University - Cerrahpasa, Department of Mechanical Engineering, 34320
Istanbul, Türkiye  Present address: SLAC National Accelerator Laboratory,
Menlo Park, CA 94025, U.S.A.  Present address: Adaptive Quantum Optics (AQO),
MESA+Institute for Nanotechnology, University of Twente, PO Box 217, 7500 AE
Enschede, The Netherlands

###### Abstract

The CAST-CAPP axion haloscope, operating at CERN inside the CAST dipole
magnet, has searched for axions in the
$19.74\text{\,}\mathrm{\SIUnitSymbolMicro
eV}22.47\text{\,}\mathrm{\SIUnitSymbolMicro eV}$ mass range. The detection
concept follows the Sikivie haloscope principle, where Dark Matter axions
convert into photons within a resonator immersed in a magnetic field. The
CAST-CAPP resonator is an array of four individual rectangular cavities
inserted in a strong dipole magnet, phase-matched to maximize the detection
sensitivity. Here we report on the data acquired for $4124\text{\,}\mathrm{h}$
from 2019 to 2021. Each cavity is equipped with a fast frequency tuning
mechanism of $10\text{\,}\mathrm{MHz}$ / min between
$4.774\text{\,}\mathrm{GHz}$ and $5.434\text{\,}\mathrm{GHz}$. In the present
work, we exclude axion-photon couplings for virialized galactic axions down to
$g_{a\gamma\gamma}=8\times 10^{-14}\,${\mathrm{GeV}}^{-1}$$ at the $90\%$
confidence level. The here implemented phase-matching technique also allows
for future large-scale upgrades.

###### keywords:

Axions , Dark Matter , Haloscopes

††journal: Nature Communications

##  1 Introduction

The quest to understand and identify the nature of Dark Matter (DM) is gaining
considerable momentum, and within this framework experimental searches for DM
axions have come to prominence. Axions are nearly massless pseudoscalar bosons
that appear in many extensions of the standard model [1, 2, 3, 4, 5, 6]. Of
particular interest is the case of the quantum chromodynamics (QCD) axion,
which arises from the Peccei–Quinn mechanism proposed as a solution to the
“strong CP problem” in QCD [1]. Because of their extremely feeble interactions
DM axions are often dubbed “invisible” and so far most search strategies rely
on their coupling to an external magnetic field and their conversion into
photons following the Lagrangian

$\mathcal{L}_{a\gamma\gamma}=g_{a\gamma\gamma}\,a\,\mathbf{E}\cdot\mathbf{B},$
(1)

where $g_{a\gamma\gamma}=\alpha g_{\gamma}/2\pi f_{a}$ is the axion-photon
coupling coefficient, $a$ the axion field, $\mathbf{E}\cdot\mathbf{B}$ the
scalar product of the electric and magnetic field strength, $\alpha$ the fine
structure constant, $f_{a}$ the axion decay constant and $g_{\gamma}$ a model
dependent dimensionless coupling constant [3]. Most widely quoted are the KSVZ
(Kim-Shifman-Vainshtein-Zakharov) [4, 5] and DFSZ (Dine-Fischler-Srednicki-
Zhitnitsky) [2, 6] models for which $g_{\gamma}$ varies between $-0.97$ and
$0.36$.

The main search method, used for over 30 years, is based on this coupling and
employs the concept of the Sikivie haloscope [3], searching for DM axions
converting to photons inside a high-quality resonant cavity immersed in a
strong magnetic field. The quality factor $Q_{\text{L}}$ of the cavity
enhances the conversion probability, provided that the axion mass matches the
resonant frequency of the cavity. Since the axion mass is unknown, haloscope
searches must be conducted by tuning the cavity in successive steps to scan
the expected axion mass range. The scanning speed is a function of several
parameters, but is mainly determined by choosing a suitably long integration
time such that at a given frequency the axion haloscope achieves sufficient
sensitivity to probe axion model predictions. Haloscope searches require an a
priori axion distribution model [7], and the common approach is to assume an
isotropic density of DM axions [8]. Under this assumption, relatively long
integration times are required for each step, while an assumption of
concentrated streams or flows of DM axions leads to reduced integration times.

The CERN Axion Solar Telescope (CAST) has been operating for two decades as an
experimental platform for axions and other exotic particles. Originally
developed as an axion helioscope capable of detecting axions produced in the
Sun, CAST has undergone several steps of upgrades to improve its sensitivity
for axions, axion-like particles (ALPs) and chameleons [9, 10, 11, 12, 13,
14]. With this new science program, CAST becomes unique amongst all axion
experiments employing the helioscope and haloscope techniques following a
suggestion from 2012 [15]. Several features were implemented for the first
time in an axion haloscope “à la Sikivie”: a dipole magnet with a high degree
of field homogeneity, four phase-matched resonant cavities, and a fast
frequency scanning technique. The fast scanning technique could become
decisive in the discovery of the DM axion, taking into account possible DM
axion transients such as streams [16] and Mini Clusters [17, 18].
Gravitational lensing effects of aligned DM streams [19, 20] by solar system
bodies can temporally increase the signal strength significantly [21, 22, 23].
In this work we report on the search for galactic DM axions while the here
introduced detection technique adapted for transient events will be the
subject of a forthcoming paper.

##  2 Results

###  2.1 Materials and methods

DM axions with velocity $v\sim 10^{-3}c$, where $c$ is the speed of light,
have negligible kinetic energy $\mathcal{O}(10^{-6})$ compared to their rest
mass. Thus, the frequency of the axion-converted photons is $\nu_{a}\approx
m_{a}c^{2}/h$, corresponding to the microwave domain for
$m_{a}\sim$\mathrm{\SIUnitSymbolMicro eV}$$. Microwave photons converted from
axions resonate inside a cavity when the photon frequency matches that of the
cavity resonance mode. The resonance mode frequencies $\nu$ for a rectangular
cavity are given by:

$\nu_{lmn}=\frac{c}{2}\sqrt{\left(\frac{l}{L_{x}}\right)^{2}+\left(\frac{m}{L_{y}}\right)^{2}+\left(\frac{n}{L_{z}}\right)^{2}}$
(2)

where $L_{x},L_{y},L_{z}$ are cavity side lengths and $l,m,n$ are the
corresponding mode indices which are defined by the separation condition. A
tuning mechanism inside the cavity is used to alter the boundary conditions
and change the electromagnetic field solutions to scan a range of photon
frequencies, i.e., axion masses. Not all resonance modes are axion sensitive
because axion-photon conversion requires the magnetic field to overlap the
electric field of the resonance mode. This condition favors transverse
electric (TE) modes where the radio frequency (RF) electric field is parallel
to the static magnetic field which fits the CAST-CAPP design. The selection of
the TE mode is through the maximization of the cavity form factor:

$C_{lmn}=\frac{\left|\int dV\
\mathbf{E}_{lmn}(x,y,z)\cdot\mathbf{B}\right|^{2}}{B^{2}V\int dV\
\varepsilon(x,y,z)\left|\textbf{E}_{lmn}(x,y,z)\right|^{2}}$ (3)

which is a dimensionless number between 0 and 1 as a measure of the overlap of
resonant electric and static magnetic fields. The optimum mode for axion
searches in CAST-CAPP is TE101 as it maximizes the form factor around 5 GHz at
$C_{101}=0.53\pm 0.05$, computed by numerical field simulations, where the
variation on the form factor is due to frequency-dependence. Here, $V$ and
$\mathbf{B}$ are the cavity volume and the static magnetic field value,
$E_{lmn}$ is the electric field associated with the resonance mode and
$\varepsilon(x,y,z)$ is the permittivity distribution inside the cavity.

Axion-photon conversion inside a resonant cavity can result in a voltage
signal at a cavity coupler. The power of the converted axion signal at
resonance for a single CAST-CAPP cavity is given by:

$\displaystyle P_{\text{axion}}=$ $\displaystyle 2.1\times 10^{-24}\hskip
2.84544pt\text{W}\times\left(\frac{\beta}{1+\beta}\right)\left(\frac{V}{224\hskip
2.84544pt\text{cm}^{3}}\right)\left(\frac{B}{8.8\hskip
2.84544pt\text{T}}\right)^{2}\left(\frac{C_{lmn}}{0.53}\right)$
$\displaystyle\times\left(\frac{g_{\gamma}}{0.97}\right)^{2}\left(\frac{\rho}{0.45\hskip
2.84544pt\text{GeV}/\text{cm}^{3}}\right)\left(\frac{Q_{\text{L}}}{2\times
10^{4}}\right)\left(\frac{\nu_{a}}{5\hskip 2.84544pt\text{GHz}}\right)$
$\displaystyle\times\left(1+(2Q_{\text{L}}(\nu-\nu_{0})/\nu_{0})^{2}\right)^{-1}$
(4)

The denominator values in most of the terms in Eq. (4) reflect CAST-CAPP
experimental parameters: $\beta$ is the coupling of the signal output coupler,
$g_{\gamma}$ is the model-dependent dimensionless coupling constant. The local
DM density $\rho$ is generally accepted to be about 0.45 GeV/cm3 which
corresponds to $\sim 10^{13}$ axion/cm3 in our axion mass range [8, 24] if the
axion is the only DM constituent. The loaded quality factor of the cavity
$Q_{\text{L}}$ is the ratio of the resonance mode frequency to the
$3\text{\,}\mathrm{dB}$ points of the resonance mode as measured by a Vector
Network Analyzer (VNA), which in our case is $Q_{\text{L}}\approx 2\times
10^{4}$(at around $5.3\text{\,}\mathrm{GHz}$), at cryogenic conditions with
magnetic field. The measured $Q_{\text{L}}$ variation between the four
cavities for the same frequency and in cryogenic conditions is below $10\%$,
whereas the difference is $5\%$ with or without static magnetic dipole field.
The uncertainty in each specific measurement of $Q_{\text{L}}$ is $<\pm
1.5\%$.

The resonance mode has a Lorentzian profile that affects the axion-photon
conversion power via the last term of Eq. (4) where $\nu_{0}$ is the center
frequency of the resonance. $f_{\text{Lab}}(\nu)$ is the probability
distribution function of the axion lineshape in lab frame [25]:

$f_{\text{Lab}}(\nu)=\frac{c^{2}\sqrt{6/\pi}}{r\nu_{a}\langle
v^{2}\rangle}\exp\left(-\frac{3r^{2}}{2}-\frac{3c^{2}(\nu-\nu_{a})}{\nu_{a}\langle
v^{2}\rangle}\right)\text{sinh}\left(3r\sqrt{\frac{2c^{2}(\nu-\nu_{a})}{\nu_{a}\langle
v^{2}\rangle}}\right)$ (5)

where r $\approx$ 0.85 is the ratio of the velocity of the Earth with respect
to the galactic rest frame to RMS velocity of galactic halo. The DM halo of
the Milky Way is virialized with RMS velocity $\sqrt{\langle
v^{2}\rangle}\approx 270$ km/s being Maxwell-Boltzmann distributed (Eq. (5))
with the quality factor $Q_{\text{axion}}\sim 10^{6}$. Hence the axion signal
linewidth is $\Delta\nu_{a}\approx 5$ kHz for axion mass $\sim 20\;\mu$eV.
These variables are modified for the laboratory frame considering the motion
of the Sun and the Earth through the galactic halo which yield $\sqrt{\langle
v^{2}\rangle}\approx 350$ km/s and linewidth $\Delta\nu_{a}\approx 7$ kHz
[26].

The signal-to-noise ratio (SNR) of an axion haloscope is a figure of merit
reflecting the sensitivity of the axion antenna and also determines the tuning
speed given a target sensitivity for the axion-photon coupling constant
$g_{a\gamma\gamma}$:

$\text{SNR}=\frac{P_{\text{axion}}}{\sigma_{\text{noise}}}=\frac{P_{\text{axion}}}{kT_{\text{sys}}}\sqrt{\frac{t}{\Delta\nu_{a}}}$
(6)

where $k$ is the Boltzmann constant, and $\sigma_{\text{noise}}$ is the
standard deviation of the mean noise power
$P_{\text{noise}}=kT_{\text{sys}}\Delta\nu$, which is reduced by a longer data
integration time $t$. The system temperature $T_{\text{sys}}$ is the sum of
the physical cavity temperature and the electronic noise temperature of the
receiver.

For a DM axion of $m_{a}\sim$20\text{\,}\mathrm{\SIUnitSymbolMicro eV}$$, the
minimum coherence length is $\sim$60\text{\,}\mathrm{m}$$ which is much larger
than the size of the cavity setup of $\sim$2\text{\,}\mathrm{m}$$ length.

CAST-CAPP consists of four tuneable $23\times 25\times 390$$\mathrm{mm}$
rectangular cavities. The volume of each cavity is
$V=$224\text{\,}{\mathrm{cm}}^{3}$$. Each cavity consists of two pieces of
stainless steel, coated with $30\text{\,}\mathrm{\SIUnitSymbolMicro m}$ of
copper. They are installed in series inside one of the two bores,
$43\text{\,}\mathrm{mm}$ $\varnothing$, of CAST’s superconducting dipole
magnet at CERN with the split plane parallel to the magnetic field along the
cavity’s small face. The CAST dipole magnet is an LHC prototype and has a
$9.25\text{\,}\mathrm{m}$ long uniform magnetic field of
$8.8\text{\,}\mathrm{T}$.

The cavity tuning mechanism consists of two sapphire strips with anisotropic
relative permittivity $\varepsilon_{\bot}\approx 9$ and
$\varepsilon_{\parallel}\approx 11$, relative to the crystallographic axis
defined as the reference. Their dimensions are $12\times 360\times
2.56$${\mathrm{mm}}^{3}$ and they are symmetrically placed parallel to the
longitudinal sides moving simultaneously towards the centre (see Fig. 1
bottom). These two parallel sapphire strips are displaced by a piezoelectric
motor through a locomotive mechanism delivering a tuning resolution of better
than $100\text{\,}\mathrm{Hz}$ in stable conditions (see Fig. 1 bottom). The
cavity frequency is changed by moving the sapphire strips towards or away from
the split plane, while maintaining the parallelism to each other. The maximum
tuning range for each cavity is about $400\text{\,}\mathrm{MHz}$ corresponding
to an axion mass range from $\sim$21\text{\,}\mathrm{\SIUnitSymbolMicro eV}$$
to $\sim$23\text{\,}\mathrm{\SIUnitSymbolMicro eV}$$. The cavity tuning system
including the electromagnetic impact from the locomotive mechanism situated
inside the cavity was designed to have no mode crossings for the axion mode
over the entire tuning range. The maximum achieved scanning speed of CAST-CAPP
is $10\text{\,}\mathrm{MHz}$ /
$\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{u}\mathrm{t}\mathrm{e}$ for each
cavity, and therefore, its full tuning range of $660\text{\,}\mathrm{MHz}$ can
be covered within $\sim$$1\text{\,}\mathrm{h}$. The maximum speed is limited
by the torque of the piezoelectric motors in cryogenic conditions. Following
the CAST-CAPP protocol a given frequency is revisited multiple times for
shorter periods rather than dwelling on it once for a long time interval. Thus
the axion mass range is scanned horizontally with the sensitivity improving
progressively. This gives us sensitivity not only to ALPs but also to axion
mini-clusters, caustics and streams. In this work, the fast tuning mechanism
allows primarily to quickly re-tune the cavities to a certain frequency in
order to cross-check the nature of an outlier.

The high mechanical $Q$-factor of the sapphire strips which are acting
accidentally as a mechanical tuning fork are leading to a frequency modulation
of the electromagnetic mode of interest. These ambient mechanical vibrations
were reduced, increasing the measured effective $Q_{\text{L}}$ by a few %, by
introducing a vibration damping mechanism consisting of two quartz glass tubes
filled with Teflon foils glued on the tuning sapphire strips.

Each cavity assembly includes the cavity, the sapphire strips tuner, two RF
couplers, one piezo-actuator, a locking device which fixes it to the CAST
magnet bore, and one cryogenic amplifier placed at a few $\mathrm{cm}$
distance from the edge of its cavity and with optimum orientation to the
static B-field (see Fig. 1 top). In addition, three out of the four cavities
are equipped with Cernox temperature sensors. More specifically, one
temperature sensor is installed in cavity 1, two in cavity 2 and one more in
cavity 4. Each cavity is equipped with a weak coupler called “injection port”
and a near-critical coupler which we call “main port”. The near-critical
coupling at cryo, for all four cavities was adopted in order to have optimum
power transfer. The main port which is connected to a Low Noise Amplifier
(LNA), is significantly under-critically coupled at room temperature in order
to achieve near critical coupling at cryogenic temperatures with magnetic
field within the available tuning range. This procedure was adopted because it
was not possible to measure the coupling of the cavity directly and in situ
under cryogenic conditions due to the permanently connected pre-amplifier. The
strong coupling criterion is based on the experimentally-done observation that
the coupling factor $\beta$ increases by a factor of $\sim 4$ for a tuneable
cavity going from room to cryogenic temperatures. The coupling was
characterized at warm by doing a reflection measurement at various frequencies
around the resonance for both the very weakly coupled injection port and the
strongly coupled main port. The length of the main coupler was adjusted
accordingly in order to have four times less coupling than the critical one
which is required in data-taking conditions neglecting the coupling at the
injection port which was kept below $3\%$ both at cold and warm. The overall
estimated uncertainty on the coupling from several performed measurements is
below $10\%$.

For cryogenic temperatures, the $Q_{\text{L}}$ measured in transmission is
about 20000 (at $5.3\text{\,}\mathrm{GHz}$) which for near-critical coupling
returns an unloaded Q of about 40000. However, this value of the unloaded Q
could not be measured directly in our case since the near-critical coupled
port was permanently connected to the low-noise pre-amplifier (no RF relay
operating in a strong magnetic field is available). Thus, we are relying on
the extrapolation from the $Q_{\text{L}}$ from warm to cold taking into
account the Q-dependent change in the coupling factor $\beta$ and assuming
negligible coupling on the other side (injection port) of the cavity. In
addition, as a cross-check, we have the shape and height of the noise bump at
cryo.

Figure 1: A photograph of the elements of a single cavity assembly (top) and a
technical drawing of CAST-CAPP tuning mechanism with the two sapphire strips
(bottom). The static B-field is shown by the arrow and is parallel to the two
axes of the tuning mechanism.

The signal of each cavity at the cryogenic stage is amplified using an LNA
with a gain of $39\text{\,}\mathrm{dB}$ and then it is transferred from the
cryogenic environment to room temperature through RF cables. Of course, these
cables have certain frequency-dependent losses which have to be taken into
account for the overall gain. An external signal amplification of about
$22\text{\,}\mathrm{dB}$ is made for each one of the four cavities with four
room temperature amplifiers. The signals from the individual cavities are
combined with a power combiner and transitioned to an RF switch sending the
coherent signal to the measuring instruments. The simplified schematic of the
setup both inside and outside the CAST magnet, is shown in Fig. 2.

Figure 2: Top: Simplified outline of the CAST-CAPP setup. The dashed and solid
lines correspond to connections in each cavity input and output port
respectively. The cavities are actually aligned along the axis of their length
as one after the other. Bottom: Detailed schematic of room temperature
hardware connections. The numbers for the picture on the bottom refer also to
the top.

Using $N$ cavities, the SNR can be enhanced through hardware-implemented
phase-matching, where, simultaneously acquired signals from several frequency-
tracking cavities are combined coherently. In our case, the first stage
amplification takes place before the signal combination, thus the SNR is
improved linearly with the number of cavities [27]. This makes phase-matching
the optimum configuration when using multiple cavities resulting in a much
better performance compared to signal summation with undefined phases. A
challenging part of the phase-matching of multiple cavities is the frequency
alignment of all the cavities to the same resonant frequency. This has been
achieved by adjusting the frequency of the cavities via tuning with the
sapphire strips within $10\text{\,}\mathrm{kHz}$, which is well below the
allowed frequency matching tolerance of $\sim$100\text{\,}\mathrm{kHz}$$ [27].
The amplitude of the resonance of the individual cavities was also adjusted
within $0.25\text{\,}\mathrm{dB}$ using programmable phase-independent
variable attenuators. The adjustment procedure uses the weakest signal as a
reference and then the rest of the signals are adjusted via the phase-
independent programmable step attenuators for each cavity path. The procedure
of the frequency and amplitude alignment between the cavities has been
performed for each data-taking step of $200\text{\,}\mathrm{kHz}$. Finally,
the output signals of each cavity have been adjusted using low-loss delay
lines aiming for phase matching of the axion signal. The delay line is a
frequency dependent phase shifter with a linear relation of phase-shift vs.
frequency. This is what we are aiming at in order to achieve tracking of the
phase-matching conditions over our frequency range without re-tuning the
phase-shifting elements at each frequency step. More specifically, the phases
were adjusted for coarse tuning by using short cable sections below
$5\text{\,}\mathrm{cm}$ length and for the remaining difference continuously
adjustable coaxial line stretchers. The hardware-based signal combination
procedure is done at room temperature outside the magnet. By injecting to each
cavity a pure sine-wave signal from a synthesizer and doing a complex addition
of signals while taking into account the signal combiner properties, the
linear increase on the SNR is observed in agreement with theory [27].

The cavities’ average physical temperature is about $8\text{\,}\mathrm{K}$ or
less, while the ambient temperature of the CAST magnet is
$1.7\text{\,}\mathrm{K}$. The cavities are cooled along with the CAST magnet
bores using liquid He ($\sim$1.7\text{\,}\mathrm{K}$$). This difference is due
to contributions from the local heat dissipation by the LNAs being
$1.5\text{\,}\mathrm{mW}$ [28] aggravated by the non-perfect thermal contact
with the magnet bore. The temperature difference between LNA ON/OFF is
$\sim$2\text{\,}\mathrm{K}$$. Piezo movement constitutes an additional heat
source, however, impacting the overall cavity temperature by less than
$0.4\text{\,}\mathrm{K}$.

The noise temperature was measured through the $3\text{\,}\mathrm{dB}$ signal
generator method where a signal generator is used to inject a defined signal
into the cavities aiming for a $3\text{\,}\mathrm{dB}$ difference between
signal and no signal. It is noted that the LNA noise temperature is about
$2\text{\,}\mathrm{K}$ for our frequency range in cryogenic conditions and
with proper orientation of the LNA with respect to the magnetic field. With
this method, and considering a number of uncertainties for the losses from the
cavities, we estimate an upper limit of the system noise temperature of
$10\text{\,}\mathrm{K}$. Following our evaluation the system noise temperature
is $(9\pm 1$) K. Additionally, the loss of the connecting cable between the
input of the amplifier and the output of the cavity at cryo was evaluated and
is below $0.1\text{\,}\mathrm{dB}$. Since this cable is also at cryo, its
contribution to the system noise temperature is estimated to be safely below
$0.2\text{\,}\mathrm{K}$.

Several “intended” emitters in the experimental area, such as the
$5\text{\,}\mathrm{GHz}$ Wireless Local Area Network (WLAN), were observed in
our frequency range of operation. The path of the infiltration was tracked
down as going via the RF amplifiers outside the cryostat. Two measures were
taken: turning off part of the WLAN system in the $5\text{\,}\mathrm{GHz}$
band, and setting up a witness “veto” channel to measure those time dependent
signals online. The witness channel is made out of an additional Vector Signal
Analyzer (SA) which is connected to an external quasi-omnidirectional antenna
placed next to the CAST magnet. It is operating simultaneously with the SA
connected to the cavities and at the same frequency band. Therefore, if a
signal appears both in the cavities and in the witness channel at the same
frequency it is rejected since an axion-related signal would only be generated
inside the cavities which are permeated with magnetic field.

The magnet vacuum vessel itself acts as a nearly-perfect Faraday cage.
However, several vacuum coaxial feedthroughs reduce this “perfect” shielding.
In addition, an amount of electromagnetic interferences can make their way in
the data acquisition (DAQ) chain though external amplifiers and electronics.
However, there is a safety margin of $30\text{\,}\mathrm{dB}$, i.e., as along
as the Electromagnetic Interference (EMI)/Electromagnetic Compatibility (EMC)
signals in the witness channel are less than $30\text{\,}\mathrm{dB}$ above
the noise floor outside the magnet vessel, they can be excluded with the
margin mentioned above. This limit comes from a measurement. We have
intentionally radiated a well-defined signal in the CAST area via an
additional antenna using the VNA as a signal generator. By analyzing the
background through regular analysis we have verified that only strong signals
beyond this amplitude may make their way into the cavity DAQ system.
Therefore, the comparison between the two measuring channels allows us to
directly control the impact of EMI/EMC parasites (see Fig. 3).

Figure 3: An example of comparison of daily combined spectra between cavity
(upper figure) and EMI/EMC channel (lower figure) both being equally
processed. If a parasitic signal appears in both channels it is excluded from
further consideration as an axion candidate.

###  2.2 Data taking and analysis

The DAQ chain is shown in Fig. 2. The first part of the DAQ procedure is the
measurement of all characteristic parameters required for analysis such as
temperature, amplitude of resonant peak, Q-factor and center frequency for the
cavity(ies). The data-recording from the SA begins with a streaming transfer
of $60\text{\,}\mathrm{s}$ data blocks formatted as a real and imaginary part
time domain trace. After each block the aforementioned parameters are re-
measured in order to be used for quality checks as well as for averaging.

A calibration peak from a signal generator is regularly injected in order to
verify that the whole DAQ chain and the cavities themselves are responsive to
an actual axion signal, as well as to verify the analysis procedure.

During data-taking, 4 TB of data are produced per day, processed and uploaded
to CERN’s tape archiving system.

Both single and phase-matched cavity configurations are used in order to cover
the maximum parameter space. More specifically, $62\%$ of the data were
recorded with single cavities while $38\%$ with phase-matched cavities. The
ideal tuning step size is of the order of the cavity frequency mode peak width
$\sim\nu_{0}/Q_{\text{L}}$. For our setup with
${\nu_{0}}\sim$5\text{\,}\mathrm{GHz}$$ and $Q_{\text{L}}\sim 20000$, this
results in a width of $\sim$250\text{\,}\mathrm{kHz}$$. In order to account
for possible variations in ${\nu_{0}}$ and $Q_{\text{L}}$ due to mechanical
vibrations, the tuning step was set to $200\text{\,}\mathrm{kHz}$ whereas the
maximum scanning speed of CAST-CAPP is about
$$10\text{\,}\mathrm{MHz}$/$\mathrm{min}$$. An integration time of
$60\text{\,}\mathrm{s}$ was chosen for each of the $200\text{\,}\mathrm{kHz}$
data taking steps in every run.

From 12 September 2019 to 21 June 2021, it was scanned a total frequency range
of $660\text{\,}\mathrm{MHz}$, from $4.774\text{\,}\mathrm{GHz}$ to
$5.434\text{\,}\mathrm{GHz}$, in steps of $200\text{\,}\mathrm{kHz}$ for a
total acquisition time of $4123.8\text{\,}\mathrm{h}$. The total frequency
range corresponds to axion masses between
$19.74\text{\,}\mathrm{\SIUnitSymbolMicro eV}$ and
$22.47\text{\,}\mathrm{\SIUnitSymbolMicro eV}$. The duty cycle of the data-
taking campaigns was approximately $20\text{\,}\mathrm{h}$ per day. Background
measurements were also performed for a total of $394.6\text{\,}\mathrm{h}$
without magnetic field.

From 18 November 2020 and on, a parallel channel has been used to measure
EMI/EMC ubiquitous parasites yielding $2140\text{\,}\mathrm{h}$ of data
between $4.798\text{\,}\mathrm{GHz}$ and $5.402\text{\,}\mathrm{GHz}$.

The raw data consist of in-phase (I) and quadrature (Q) components of time-
domain (TD) voltage samples. In order to detect a potential axion signal the
TD data are converted by a Fast Fourier Transformation (FFT) [29] into
frequency-domain (FD), where a peak is expected as the manifestation of a
potential axion signal. The TD data are split into chunks and then are
converted to FD by applying FFT to each individual chunk. Thus, we obtain I
and Q samples in FD which are related to the RMS power via
$P_{\text{rms}}=\left({{I^{2}}+{Q^{2}}}\right)/\left({2{Z_{0}}}\right)$, where
$Z_{0}=$50\text{\,}\mathrm{\SIUnitSymbolOhm}$$ is the SA input impedance. The
number of samples in each FFT chunk is determined by the desired resolution
bandwidth (RBW) $\delta\nu$ of the resulting processed spectra. The storage of
the data allows a re-processing with FFT choosing a different RBW according to
the needs of the analysis. We recall here that streaming axions should have a
much smaller linewidth than the standard halo axions (of 5-7kHz) due to their
very small velocity dispersion. At the same time, this format allows searching
for short spikes and transient signals directly in the time domain trace in
contrast with the frequency-domain which washes out any small and short-
lasting signal.

To adjust $\delta\nu=$50\text{\,}\mathrm{Hz}$$, we set the time length of each
chunk as $\tau=1/\delta\nu=0.02\,\text{s}$, which corresponds to
$N=0.02\,\text{s}\times 5\text{ Mega samples/s}=10^{5}$ samples per FFT chunk,
given the sampling rate of 5 complex Mega samples/s. In order to obtain the
processed spectra out of each $t=$60\text{\,}\mathrm{s}$$ measurement
$t/\tau=3000$ FFT chunks are averaged. The acquisition bandwidth of each
processed spectrum is $5\text{\,}\mathrm{MHz}$, being deliberately much wider
compared to the $\approx$250\text{\,}\mathrm{kHz}$$ cavity resonance width.

A number of selection criteria, as shown in Table 1, are applied on each
processed block before the analysis procedure takes place. These criteria are
applied to ensure exclusion of undesired non-systematic effects from
mechanical vibrations or possible EMI/EMC interferences, which could otherwise
influence the center frequency of the resonant peak, its amplitude and the
measured $Q_{\text{L}}$. These characteristic parameters are measured by the
VNA before and after each single $60\text{\,}\mathrm{s}$ measurement block.

For the data taken with $B=$8.8\text{\,}\mathrm{T}$$, the total number of
processed blocks is 262491 out of which $\sim 4.4\%$ did not pass the quality
checks. For the data without magnetic field, 461 blocks out of 24138 were
discarded corresponding to a rejection factor of $\sim 1.9\%$.

Table 1: Data qualification criteria. “Before” and “after” labels indicate the measurements before and after each measurement block, respectively. Criteria 1-4 apply to all measurements while 5-8 refer only to phase-matched data taking. Nr. | Parameters | Criteria
---|---|---
1 | Resonance frequency stability |  $\Delta\nu_{0}<$ $100\text{\,}\mathrm{kHz}$
2 | Resonance amplitude variation |  $\Delta A_{0}<$ $3\text{\,}\mathrm{dB}$
3 | Loaded quality factor | $10^{3}<Q_{\text{L}}<4\times 10^{4}$
4 | Loaded quality factor shift | $\Delta Q_{\text{L}}<7\times 10^{3}$
5 | Frequency mismatch |  $<$ $20\text{\,}\mathrm{kHz}$ (before)
6 | Frequency mismatch |  $<$ $80\text{\,}\mathrm{kHz}$ (after)
7 | Amplitude mismatch |  $<$ $1\text{\,}\mathrm{dB}$
8 | Temperature mismatch |  $<$ $3\text{\,}\mathrm{K}$

The analysis procedure is mainly based on widely accepted methods [24, 25,
30]. Nevertheless, we make a few modifications to adapt this procedure to our
experimental conditions. We start with the removal of the noise baseline of
the processed spectra using a Savitzky-Golay (SG) smoothing filter [31] with
window length $W=1000$ bins and a polynomial of order $d=4$. The processed
spectra are divided by their SG filter output and subtracted 1 to obtain a
mean $\mu=0$ with standard deviation $\sigma=(\delta\nu\cdot t)^{-1/2}\approx
0.018$ of a Gaussian distribution. This sample distribution is a result of
averaging 3000 FFT chunks as dictated by the central limit theorem, whereas
the samples of each chunk, in power units, obey a $\chi^{2}$ distribution. We
remove the intermediate frequency (IF) filter roll-off from the two edges of
these flattened spectra which correspond to 20% of the samples in total.
Therefore, each flattened spectrum has $10^{5}$ bins.

The flattened spectra are scanned for IF interferences which occur as
unexpectedly high-amplitude bins on the same index of most of the flattened
spectra regardless of the cavity resonance frequency. First, all flattened
spectra are divided into three groups, and each group is averaged according to
the IF bin index. Second, we flag the bins that exceed 5$\sigma$ with
$\sigma=(M\,\delta\nu_{P}\,t)^{-1/2}$, where M is the number of averaged
spectra in each group. Finally, we compare the flagged IF bin index list. If
an IF bin is flagged in at least 2 groups, we discard that particular IF bin
plus the 2 adjacent bins of all flattened spectra from the subsequent steps of
the analysis procedure, this is the case for 6 out of the $10^{5}$ bins.

Each flattened spectrum is scaled by $P_{\text{noise}}/P_{\text{axion}}$ in
order to attain an axion SNR as given in Eq. (6), where $P_{\text{axion}}$ is
the axion signal power curve across the bandwidth of each spectrum as defined
by Eq. (4).

The combined spectrum is generated by aligning the scaled spectra on the RF
axis and taking the weighted average of the scaled spectra bin amplitudes that
correspond to the same RF bin of the combined spectrum with weights equal to
inverse bin variances, as determined by maximum likelihood (ML) estimation.
The amplitude $p_{k}$ of each combined spectrum bin of index $k$ is normalized
by dividing it by its standard deviation $\sigma_{k}$, resulting to normalized
samples with a normal distribution of mean $\mu=0$ and standard deviation
$\sigma=1$, except for the prospective bin that contains axion power which
must be a sample of a normal distribution with mean $(\sigma_{k})^{-1}$ and
$\sigma=1$. The resolution bandwidth of the combined spectrum remains
$\delta\nu_{C}=50$ Hz.

In order to increase the SNR of an axion signal of linewidth
$\Delta\nu\approx$7\text{\,}\mathrm{k}\mathrm{H}\mathrm{z}$$ in the lab frame,
the adjacent 28 bins in the combined spectrum are averaged with their ML
weights, obtaining a rebinned spectrum with increased bandwidth resolution
$\delta\nu_{R}=$1.4\text{\,}\mathrm{k}\mathrm{H}\mathrm{z}$$.

Finally, the “grand spectrum” is computed by convolving the rebinned spectrum
with the kernel equal to the axion lineshape in lab frame defined by Eq. (5).
This leads to an unchanged bandwidth resolution and number of samples of the
grand spectrum. The normalized grand spectrum is generated by dividing each
bin’s power by its standard deviation $p_{k}^{G}/\sigma_{k}^{G}$, where the
noise distribution should have $\mu=0$ and $\sigma=1$. However, the standard
deviation is reduced to $\sigma=0.74$, due to the negative correlations among
adjacent bins introduced by the SG filter. To quantify the covariance among
consecutive grand spectrum bins, a Monte Carlo simulation of $10^{4}$
processed spectra has been constructed using sample noise baselines from real
data. Elements of the covariance matrix resulting from this simulation are
used to compute the ML estimate of the standard deviation of the grand
spectrum bins. The so derived normalized grand spectrum is described by
$\sigma=0.96$. Fig. 4 shows the grand spectrum and its noise distribution.

Figure 4: Grand spectrum (left) and its projected noise distribution (right).
All the grand spectrum bins are below the selection threshold (red dashed
line) after the rescanning procedure which shows that all the axion candidates
are excluded.

###  2.3 Analysis results

We search the grand spectrum for bins that could show an axion DM signal
indicated by a positive power excess. Applying the SG filter on the analysis
procedure reduces the grand spectrum SNR by $\eta=0.717$ as derived by Monte
Carlo simulations of $10^{4}$ experiments with axion signal injections. To
search for the KSVZ axion, accepting the target SNR${}_{\text{T}}=5\sigma$ and
confidence level of 90%, the candidate selection threshold is set accordingly
to $3.72\sigma$. The grand spectrum bins which exceed this threshold are then
flagged as rescan candidates. We have in total 60 bins out of $\approx$ 472k
that are flagged for rescanning.

Following a predefined procedure, every candidate spectrum is compared to the
simultaneously and independently measured spectrum from the second channel
with the external antenna which is sensitive to the same frequency and
searches for ambient EMI/EMC parasites. A total of nine out of the $60$
outliers were discarded from further consideration with three of them being
rejected following background measurements without a magnetic field.
Furthermore, 11 outliers were blind calibration signals deliberately injected
into the cavities. The next step is to rescan a narrow band around each of the
40 remaining outliers with the same and different cavities to increase
statistics, but also for consistency checks. If a candidate is persistent
enough, an extra rescanning is performed by tuning to a higher order resonant
mode that does not couple to axions. Finally, if an outlier also passes this
elimination step, a rescan at a different magnetic field strength takes place.

No outlier has reached these two last predefined steps because all 40 outliers
were discarded during rescanning. We can thus compute the excluded coupling
strength $|g_{a\gamma\gamma}|$ for each bin of the grand spectrum
$|g_{{a\gamma\gamma}}|=|g_{{a\gamma\gamma}}^{\text{KSVZ}}|\,\sqrt{\text{SNR}_{\text{T}}/\text{SNR}}$.

The exclusion of axion-photon coupling at 90% confidence is shown in Fig. 5,
where the estimated overall uncertainty calculated from the individual
uncertainties shown in Table 2, is $10\%$. We exclude previously unexplored
new parameter space for axion masses between
$19.74\text{\,}\mathrm{\SIUnitSymbolMicro eV}$ and
$22.47\text{\,}\mathrm{\SIUnitSymbolMicro eV}$.

Table 2: CAST-CAPP parameters and related uncertainties used for the analysis. Note that the loaded quality factor is given for the frequency of $5.3\text{\,}\mathrm{GHz}$. Parameters | Explanation | Values | Uncertainty
---|---|---|---
$B$ | Static dipole magnetic field | $8.8\text{\,}\mathrm{T}$ | $10^{-3}$
$V$ | Cavity volume | $224\text{\,}{\mathrm{cm}}^{3}$ | $0.1\text{\,}{\mathrm{cm}}^{3}$
$C$ | Form factor | 0.53 | $10\%$
$\beta$ | Main port coupling factor | 1 | $0.3$
$Q_{L}$ | Loaded quality factor | 20000 | $3\%$
$T_{S}$ | System noise temperature | $9\text{\,}\mathrm{K}$ | $1\text{\,}\mathrm{K}$
$\eta$ | Signal attenuation coefficient | 0.717 | 0.01
Figure 5: CAST-CAPP exclusion limit on the axion-photon coupling as a function
of axion mass at $90\%$ confidence level (left), and compared to other axion
search results [32, 33, 10, 25, 34, 35, 36, 30, 37, 38, 39] within the mass
range 1-25 $\mathrm{\SIUnitSymbolMicro eV}$ (right). The higher sensitivity
around the $22\text{\,}\mathrm{\SIUnitSymbolMicro eV}$ region, is due to the
predominant use of phase-matching around this mass range.

##  3 Discussion

We report here the first results of the CAST-CAPP detector searching for
galactic DM axions. CAST-CAPP is a haloscope consisting of four individual
resonant cavities inserted in one bore of the CAST dipole magnet.

A previously unexplored parameter space has been scanned to extend the axion
search towards larger rest mass values from
$19.74\text{\,}\mathrm{\SIUnitSymbolMicro
eV}22.47\text{\,}\mathrm{\SIUnitSymbolMicro eV}$. This required higher
frequencies and thus a smaller cavity size and a tuning mechanism with no
mode-crossings for the mode of interest over the entire frequency range. This
is a particular strength of the cavity design. In this mass range, we exclude
axion-photon coupling for virialized galactic axions down to
$g_{a\gamma\gamma}=8\cdot 10^{-14}~{}\text{GeV}^{-1}$ at 90% confidence level.

In addition, the following novelties, of potential importance also for future
DM axion searches, have been instrumented:

  * 1.

Four identical cavities have been coherently combined through the phase-
matching technique increasing significantly the SNR. Combining signals from
individual cavities is shown to be feasible and still unique in DM axion
search. This can be extended in future large-scale axion haloscopes with a
large number of small cavities.

  * 2.

The successful scan of a significant mass range showed that this experiment is
at the cutting-edge of cavity tunability in axion research. This was achieved
thanks to the unique design of the locomotive tuning mechanism and the cavity
geometry. With an upgrade of the piezoelectric motors at cryo, the tuning
range can even further be extended to $1\text{\,}\mathrm{GHz}$ and slightly
beyond ($4.6\text{\,}\mathrm{GHz}$ \- $5.8\text{\,}\mathrm{GHz}$), shown by
simulation [40] and also demonstrated on the bench at room temperature.

  * 3.

The fast-scanning technique includes a fast change of resonance frequencies
(10 MHz / min) between $4.774\text{\,}\mathrm{GHz}$ and
$5.434\text{\,}\mathrm{GHz}$, which, combined with a high sensitivity, allows
for $60\text{\,}\mathrm{s}$ short acquisition intervals for each
$200\text{\,}\mathrm{kHz}$ tuning step. This also permits to quickly re-tune
the cavities to a frequency of interest, for instance to investigate a stable
and reproducible outlier.

  * 4.

The raw data which are recorded in each interval consist of a “real and
imaginary part” time domain trace allowing for easy analysis of the traces for
transient event search. Together with the fast-scanning technique, it permits
a simultaneous search for halo DM axions and axion-caused electromagnetic
transients originating for example from mini-clusters or streams [16, 17, 18].
It is challenging to separate non-stationary signals from axion streams
against transient-type EMI/EMC perturbations. The very first adequate approach
in this case is the comparison with the reference antenna output in the hall.

Note added in Proof:
During the review process another publication [41] appeared overlapping partly
with our low axion mass range.

## Data availability

The source data and code underlying the plots in this paper are available from
the corresponding authors upon request.

## References

  * Peccei and Quinn [1977] R. D. Peccei, H. R. Quinn,  Constraints imposed by $\mathrm{CP}$ conservation in the presence of pseudoparticles,  Phys. Rev. 16 (1977) 1791–1797. doi:10.1103/PhysRevD.16.1791.
  * Zhitnitsky [1980] A. R. Zhitnitsky,  On Possible Suppression of the Axion Hadron Interactions.,  Sov. J. Nucl. Phys. 31 (1980) 260.
  * Sikivie [1983] P. Sikivie,  Experimental tests of the ”invisible” axion,  Phys. Rev. Lett. 51 (1983) 1415–1417. doi:10.1103/PhysRevLett.51.1415.
  * Kim [1979] J. E. Kim,  Weak-interaction singlet and strong $\mathrm{CP}$ invariance,  Phys. Rev. Lett. 43 (1979) 103–107. doi:10.1103/PhysRevLett.43.103.
  * Shifman et al. [1980] M. Shifman, A. Vainshtein, V. Zakharov,  Can confinement ensure natural $\mathrm{CP}$ invariance of strong interactions?,  Nuclear Physics B 166 (1980) 493–506. doi:10.1016/0550-3213(80)90209-6.
  * Dine et al. [1981] M. Dine, W. Fischler, M. Srednicki,  A simple solution to the strong $\mathrm{CP}$ problem with a harmless axion,  Physics Letters B 104 (1981) 199–202. doi:10.1016/0370-2693(81)90590-6.
  * Di Luzio et al. [2020] L. Di Luzio, et al.,  The landscape of qcd axion models,  Physics Reports 870 (2020) 1–117. doi:10.1016/j.physrep.2020.06.002, the landscape of QCD axion models.
  * Read [2014] J. I. Read,  The local dark matter density,  Journal of Physics G: Nuclear and Particle Physics 41 (2014) 063101. doi:10.1088/0954-3899/41/6/063101.
  * G. Cantatore, et al., (2010) [CAST Collaboration] G. Cantatore, et al., (CAST Collaboration) (CAST),  Search for solar Axion Like Particles in the low energy range at CAST,  Nucl. Instrum. Meth. A 617 (2010) 502–504. doi:10.1016/j.nima.2009.10.098.
  * V. Anastassopoulos, et al., (2017) [CAST Collaboration] V. Anastassopoulos, et al., (CAST Collaboration) (CAST),  New CAST Limit on the Axion-Photon Interaction,  Nature Phys. 13 (2017) 584–590. doi:10.1038/nphys4109.
  * V. Anastassopoulos, et al., (2015) [CAST Collaboration] V. Anastassopoulos, et al., (CAST Collaboration) (CAST),  Search for chameleons with CAST,  Physics Letters B 749 (2015) 172–180. doi:{10.1016/j.physletb.2015.07.049}.
  * V. Anastassopoulos, et al., (2019) [CAST Collaboration] V. Anastassopoulos, et al., (CAST Collaboration) (CAST),  Improved search for solar chameleons with a GridPix detector at CAST,  Journal of Cosmology and Astroparticle Physics (2019). doi:{10.1088/1475-7516/2019/01/032}.
  * S. Arguedas Cuendis, et al., (2019) [CAST Collaboration] S. Arguedas Cuendis, et al., (CAST Collaboration) (CAST),  First results on the search for chameleons with the KWISP detector at CAST,  Physics of the Dark Universe 26 (2019). doi:{10.1016/j.dark.2019.100367}.
  * A. Álvarez Melcón, et al., (2021) [CAST Collaboration] A. Álvarez Melcón, et al., (CAST Collaboration) (CAST),  First results of the cast-rades haloscope search for axions at 34.67 $\mu$ev,  Journal of High Energy Physics 2021 (2021). doi:10.1007/JHEP10(2021)075.
  * Baker et al. [2012] O. K. Baker, et al.,  Prospects for searching axionlike particle dark matter with dipole, toroidal, and wiggler magnets,  Phys. Rev. D 85 (2012) 035018. doi:10.1103/PhysRevD.85.035018.
  * Vogelsberger and White [2011] M. Vogelsberger, S. D. M. White,  Streams and caustics: the fine-grained structure of $\Lambda$ cold dark matter haloes,  Monthly Notices of the Royal Astronomical Society 413 (2011) 1419–1438. doi:10.1111/j.1365-2966.2011.18224.x.
  * Tkachev [1991] I. Tkachev,  On the possibility of bose-star formation,  Physics Letters B 261 (1991) 289–293. doi:10.1016/0370-2693(91)90330-S.
  * Kolb and Tkachev [1993] E. W. Kolb, I. I. Tkachev,  Axion miniclusters and bose stars,  Phys. Rev. Lett. 71 (1993) 3051–3054. doi:10.1103/PhysRevLett.71.3051.
  * Hoffmann et al. [2003] D. Hoffmann, J. Jacoby, K. Zioutas,  Gravitational lensing by the sun of non-relativistic penetrating particles,  Astroparticle Physics 20 (2003) 73–78. doi:10.1016/S0927-6505(03)00138-5.
  * Patla et al. [2013] B. R. Patla, et al.,  Flux enhancement of slow-moving particles by sun or jupiter: Can they be detected on earth?,  The Astrophysical Journal 780 (2013) 158. doi:10.1088/0004-637x/780/2/158.
  * Zioutas et al. [2017] K. Zioutas, et al.,  Search for axions in streaming dark matter (2017). arXiv:1703.01436.
  * Kryemadhi et al. [2021] A. Kryemadhi, M. Vogelsberger, K. Zioutas,  Gravitational Focusing of Dark Matter Streams in Solar Neighborhood and Implications for Detection,  in: 16th Patras Workshop on Axions, WIMPs and WISPs, 2021. URL: https://agenda.infn.it/event/20431/contributions/137662/attachments/82466/108343/DM_Streams_Talk_PatrasWorkshop2021.pdf.
  * Fischer et al. [2017] H. Fischer, Y. Semertzidis, K. Zioutas, Search for axions in streaming dark matter, 2017. URL: https://ep-news.web.cern.ch/content/search-axions-streaming-dark-matter.
  * S. Asztalos, et al., (2001) [ADMX Collaboration] S. Asztalos, et al., (ADMX Collaboration),  Large-scale microwave cavity search for dark-matter axions,  Phys. Rev. D 64 (2001) 092003. doi:10.1103/PhysRevD.64.092003.
  * B. M. Brubaker, et al., (2017) [HAYSTAC Collaboration] B. M. Brubaker, et al., (HAYSTAC Collaboration),  Haystac axion search analysis procedure,  Phys. Rev. D 96 (2017) 123008. doi:10.1103/PhysRevD.96.123008.
  * Turner [1990] M. S. Turner,  Periodic signatures for the detection of cosmic axions,  Phys. Rev. D 42 (1990) 3572–3575. doi:10.1103/PhysRevD.42.3572.
  * Jeong et al. [2018] J. Jeong, et al.,  Phase-matching of multiple-cavity detectors for dark matter axion search,  Astroparticle Physics 97 (2018) 33–37. doi:10.1016/j.astropartphys.2017.10.012.
  * Factory [2020] L. N. Factory, Lnf-lnc4_8d, 2020\. URL: https://www.lownoisefactory.com/.
  * Cooley and Tukey [1965] J. W. Cooley, J. W. Tukey,  An algorithm for the machine calculation of complex fourier series,  Mathematics of Computation 19 (1965) 297–301.
  * C. Bartram, et al., (2021) [ADMX Collaboration] C. Bartram, et al., (ADMX Collaboration) (ADMX Collaboration),  Axion dark matter experiment: Run 1b analysis details,  Phys. Rev. D 103 (2021) 032002. doi:10.1103/PhysRevD.103.032002.
  * A. Savitzky and M.J.E. Golay [1964] A. Savitzky and M.J.E. Golay,  Smoothing and Differentiation of Data by Simplified Least Squares Procedures,  Analytical Chemistry 36 (1964) 1627–1639. doi:{10.1021/ac60214a047}.
  * De Panfilis et al. [1987] S. De Panfilis, et al.,  Limits on the abundance and coupling of cosmic axions at 4.5$<{m}_{a}<$5.0 $\mu$$\mathrm{eV}$,  Phys. Rev. Lett. 59 (1987) 839–842. doi:10.1103/PhysRevLett.59.839.
  * Hagmann et al. [1990] C. Hagmann, et al.,  Results from a search for cosmic axions,  Phys. Rev. D 42 (1990) 1297–1300. doi:10.1103/PhysRevD.42.1297.
  * C. Boutan, et al., (2018) [ADMX Collaboration] C. Boutan, et al., (ADMX Collaboration) (ADMX Collaboration),  Piezoelectrically tuned multimode cavity search for axion dark matter,  Phys. Rev. Lett. 121 (2018) 261302. doi:10.1103/PhysRevLett.121.261302.
  * Lee et al. [2020] S. Lee, et al.,  Axion dark matter search around $6.7\text{ }\text{ }\mu\mathrm{eV}$,  Phys. Rev. Lett. 124 (2020) 101802. doi:10.1103/PhysRevLett.124.101802.
  * Jeong et al. [2020] J. Jeong, et al.,  Search for invisible axion dark matter with a multiple-cell haloscope,  Phys. Rev. Lett. 125 (2020) 221302. doi:10.1103/PhysRevLett.125.221302.
  * C. Bartram, et al., (2021) [ADMX Collaboration] C. Bartram, et al., (ADMX Collaboration),  Dark matter axion search using a josephson traveling wave parametric amplifier (2021). arXiv:2110.10262.
  * Backes et al. [2021] K. M. Backes, et al.,  A quantum enhanced search for dark matter axions,  Nature 590 (2021) 238–242. doi:10.1038/s41586-021-03226-7.
  * Kwon et al. [2021] O. Kwon, et al.,  First results from an axion haloscope at CAPP around $10.7\text{ }\text{ }\mu\mathrm{eV}$,  Phys. Rev. Lett. 126 (2021) 191802. doi:10.1103/PhysRevLett.126.191802.
  * Miceli [2015] L. Miceli,  Haloscope axion searches with the cast dipole magnet: the CAST-CAPP/IBS detector,  in: Proceedings, 11th Patras Workshop on Axions, WIMPs and WISPs (Axion-WIMP 2015): Zaragoza, Spain, June 22-26, 2015, 2015, pp. 164–168. doi:10.3204/DESY-PROC-2015-02/miceli\\_lino.
  * Lee et al. [2022] Y. Lee, B. Yang, H. Yoon, M. Ahn, H. Park, B. Min, D. Kim, J. Yoo,  Searching for invisible axion dark matter with an 18 t magnet haloscope,  Phys. Rev. Lett. 128 (2022) 241805. doi:10.1103/PhysRevLett.128.241805.

## Acknowledgements

We wish to thank our colleagues at CERN, in particular Thomas Schneider and
Miranda Van Stenis from the glass lab, as well as Manfred Wendt and the whole
team of the CERN Central Cryogenic Laboratory for their help and overall
support. We highly appreciate the help of the dental expert Dr. Sebastian
Engelhardt, Satigny in a post data taking repair / upgrade. We would also like
to thank Spyridon Maroudas for creating the first two figures of this paper.
This work has been supported by the Greek General Secretariat for Research
Innovation (GSRI), the Institute for Basic Science (IBS) under the Project
Code No. IBS-R017-D1 of the Republic of Korea, the Spanish Agencia Estatal de
Investigacion (AEI) and Fondo Europeo de Desarrollo Regional (FEDER) under
project FPA-2016-76978-C3-2-P and PID2019-108122GB-C33, by the CERN Doctoral
Studentship programme, the European Research Council (ERC), the DFG Research
Training Group Programme 2044 “Mass and Symmetry after the Discovery of the
Higgs Particle at LHC”, MSE (Croatia) and Natural Sciences and Engineering
Research Council of Canada. We acknowledge support through the ERC under grant
ERC2018-StG-802836 (AxScale project) and ERC-2017-AdG-788781 (IAXO+ project).
Part of this research is co-financed by Greece and the European Union
(European Social Fund - ESF) through the Operational Programme “Human
Resources Development, Education and Lifelong Learning” in the context of the
project “Strengthening Human Resources Research Potential via Doctorate
Research – 2nd Cycle” (MIS-5000432), implemented by the State Scholarships
Foundation (IKY). Part of this work was performed under the auspices of the US
Department of Energy by Lawrence Livermore National Laboratory under Contract
No. DE-AC52-07NA27344.

## Author contributions

G.C., F.C., S.A.C., W.C., H.C., J.C., H.F., W.F., M.K., C.K., J.L., S.L. M.M.,
L.M., K.O., Y.K.S., T.V., S.Y. and K.Z. conceived, designed and built the
CAST-CAPP detector. F.C., A.G., J.M.L., M.M., L.M., K.O., Y.K.S. and T.V.
installed, and operated the detector. F.C., H.F., W.F., M.M., K.O., T.V., K.Z.
organized the data-taking runs and general operation of the experiment,
coordinated, monitored, processed and analysed the detector data. F.C.,
S.A.C., H.F., W.F., M.K. M.M., K.O., G.C., Y.K.S., K.Z. wrote the manuscript.
All authors contributed to the data-taking shifts or the operation and
maintenance of the experiment at a whole.

## Competing interests

The authors declare no competing interests.