Development of axion haloscopes for high-mass search at CAPP

The multi-cell cavity is one of the haloscope concepts developed by CAPP as a volume-efficient approach for high-mass axion search (Jeong et al., 2018b). It is characterized by multiple identical cells divided by equidistant thin metal partitions placed in a conventional cylindrical cavity. This design is superior to the traditional multiple-cavity concept in terms of volume usage, as visually compared in figure 1. In particular, the key idea is to introduce a partition gap in the center of the cavity. This allows all cells to be spatially connected to each other, enabling a single antenna to capture signals across the entire volume, simplifying the readout chain design. Due to the symmetric structure, the pick-up antenna can be located at the cavity center, where only the TM₀₁₀ mode is detected when the system exhibits perfect symmetry. Imperfect symmetry leads to asymmetric field distribution across the cavity volume, degrading the form factor. This can be indicated by a non-vanishing electric field for the higher TM_0n0 (with $n>1$) modes, and the corresponding field strength estimates the form factor degradation.

Similar to the traditional mechanism for cylindrical cavities, frequency tuning can be achieved by introducing identical dielectric rods, one for each cell, and translating them along the azimuthal direction with respect to the cavity center. Each tuning rod is extended out of the cavity through an arch-shaped opening made at the top and bottom of the cell. The set of tuning rods is gripped at each end outside the cavity by a pair of multi-arm structures that rotate in a carousel configuration, allowing all the rods to move simultaneously. The radius of the rod and the tuning path are optimized based on simulations using COMSOL Multiphysics (COMSOL, 1998) by maximizing the figure of merit defined as ${\rm F.O.M.}\equiv{\int}_{{\rm{\Delta}}\nu}({V}^{2}{C}^{2}Q)d\nu$ to obtain high cavity performance over a reasonable tuning range $\Delta\nu$. An extended study has shown that the optimal rod size for multi-cell cavities matches that for cylindrical cavities of the same frequency and that the corresponding F.O.M. values are approximately the same regardless of the cell multiplicity (Jeong et al., 2023b).

A potential issue of the multi-cell cavity design is related to field localization owing to geometric asymmetry, mainly arising from tolerances in cavity fabrication, including machining and assembly. This gives rise to different field distributions in individual cells and eventually degrades the overall form factor. The original cavity design consists of multiple identical bodies, each machined as a single piece with a central divider (partition) to form a multi-cell structure when assembled (Jeong et al., 2018b). The monolithic structure makes precision machining difficult and thus the assembled cavity becomes vulnerable to forming a symmetric configuration. We found that increasing the partition gap at the center of the cavity causes the individual cells to become more strongly coupled, effectively relieving field localization. However, a large gap draws more field into the center of the cavity and eventually reduces the resonant frequency, losing the desired benefit for high-frequency searches. To compromise between these two aspects, an extensive simulation study was performed to find the optimal size of the gap. The general behavior is that higher cell multiplicity requires larger gap to maximize the F.O.M. The simulation results were validated for several multi-cell (2-, 4-, and 6-cell) cavities of commercially available oxygen-free copper. With the tuning structure taken into account, the effects can be further reduced by introducing a thinner (thicker) rod in the cell with the highest (lowest) field strength. From an experimental perspective, the field localization effect can be estimated from the degree of imbalance in the distribution of electric (magnetic) field strength measured for the individual cells at relatively the same location using a mono-pole (loop) antenna.

The effectiveness of this unique design was successfully demonstrated by performing a series of axion search experiments at CAPP each with a multi-cell cavity implemented. The first experiment was conducted using a double-cell cavity to prove the superiority of the multi-cell concept over the conventional one (Jeong et al., 2020). The high performance and reliability enabled the search four times faster than a single cavity at the same frequency region and set new exclusion limits on the axion-photon coupling in the mass range between 13.0 and 13.9 $\mu$eV. Another experiment employed a larger cavity consisting of eight cells to search for higher-mass axion dark matter. The high multiplicity increased the search frequency by a factor of 4 and the full use of a given magnet volume improved sensitivity, allowing the experiment to reach the KSVZ model at masses around 24.5 $\mu$eV (Kutlu et al., 2022). Both experiments employed a set of alumina rods to tune the search frequency. The resonant cavities used in these experiments are shown in figure 2. These results demonstrated that this new design could make considerable contributions to the next-generation searches for high-mass axions.

A modified version can be considered in which the partitions are detached from the monolithic structure and placed separately within the cavity, as shown in Fig. 3. This configuration reduces the complexity of cavity machining and thus improves the precision of cavity fabrication and assembly. Each partition is slightly longer (about 100 $\mu$m) than the cavity wall to create stronger contacts with the cavity end-caps. Moreover, the additional space between the partition and cavity wall causes the individual cells to be more strongly coupled, making the field configuration more symmetrical, naturally reducing the field localization effect. A simulation study has shown that despite a slight reduction in cavity quality factor, this design enhances the form factor and thus improves the overall performance of haloscope searches. An experiment using a modified three-cell cavity is currently underway to search for axion dark matter in the mass range around 5.3 GHz.

Higher-order resonant modes, as specified in table 1, are beneficial for increasing search frequency. However, there are two major issues that need to be addressed: 1) the field structure contains counter-oscillating component(s) that reduces the form factor in a uniform external magnetic field and 2) there is difficulty in tuning the resonant frequency while maintaining the form factor at a reasonable level. The former issue can be resolved by properly arranging a structure of dielectric material to suppress the counter-oscillating electric field component(s) and thereby restore the form factor (McAllister et al., 2018; Alesini et al., 2021). For the TM₀₃₀ mode of a cylindrical cavity, for example, a layer of cylindrical dielectric hollow can be considered for this purpose.

For frequency tuning, there are several schemes to be considered depending on the direction in which the field symmetry is broken (e.g., axial, radial, and azimuthal directions for a cylindrical geometry). Breaking axial symmetry can be achieved by splitting the dielectric hollow into two parts horizontally and moving them along the axial direction. This was studied in Ref. (McAllister et al., 2018), especially for the TM₀₃₀ mode. Similarly, the transverse symmetry can be broken by splitting the dielectric hollow into several pieces vertically and separating them along the radial direction. The scheme is described in Ref. (Alesini et al., 2021). Symmetry breaking along the azimuthal direction relies on the EM characteristic in that the resonant frequency is strongly dependent on the thickness of the dielectric hollow. Based on this property, we designed a new tuning mechanism consisting of a double layer of concentrically segmented dielectric hollow pieces in which one layer of the segments rotates with respect to the other (Kim et al., 2020), effectively varying the thickness of the structure, as visualized in figure 4. For each scheme, the optimal dimensions of the tuning structure that maximize the F.O.M. were obtained based on extensive simulation studies. Among them, the one involving the symmetry breaking along the azimuthal direction showed the high sensitivity over a reasonable tuning range. In this study, we did not consider the effects of non-minimal coupling between electromagnetism and gravity motivated by quantum phenomena such as vacuum polarization in extreme gravitational environments (Ravi et al., 2023). While they could induce azimuthal dependence in axion-photon coupling (Chen et al., 2022; Sakurai et al., 2023), their impact was estimated to be negligible for laboratory axion haloscope experiments.

The third tuning scheme essentially relies on the transformation of continuous rotational symmetry into discrete rotation symmetry to create the tuning capability. Since simultaneous rotation of the segments within a layer can be achieved using a single rotor, this mechanism is highly reliable and easy to implement. The optimal number of segments and thickness/position of the layers for the ${\rm TM}_{030}$ mode were obtained through numerical simulations. Using a model of a copper cylindrical cavity and dielectric segments of $\epsilon=10$, it was found that a pair of six-segment layers with thickness and inner radius of $\lambda/2\sqrt{\epsilon}$ ($\lambda$ is the wavelength of the EM wave) and $0.37R$ ($R$ is the cavity radius), respectively, gives the best performance. We observed that the TM₀₃₀ resonant frequency can be tuned about 5% and the form factor was estimated to be greater than 0.33 (compared to 0.05 for an empty cavity) over the entire tuning range, allowing reasonable sensitivity to be achievable.

The feasibility of this tuning mechanism was demonstrated using a copper cavity and a double-layer of alumina segments. The cavity consisted of three identical pieces, each of which had two outer alumina (99.7% Al₂O₃) segments placed at internal fixed positions. Six smaller alumina segments supported by a pair of wheel-shaped structures at the top and bottom made up the inner layer of the tuning system. The overall structure of the cavity and tuning system is shown in figure 5. The cavity assembly was brought to a temperature of about 4 K to test the tuning mechanism in a cryogenic environment. By rotating the inner layer of the tuning system using a piezoelectric actuator, a mode map was drawn as a function of rotation angle. We observed periodic patterns of the resonance modes during the continuous tuning process. Figure 5 shows the mode map over a single cycle achieved with a rotation angle of 60$\degree$. The bell-shaped curve corresponds to our desired TM₀₃₀ mode with its frequency spanning from 6.9 to 7.2 GHz, which is approximately three times higher than the TM₀₁₀ resonant frequency of the same cavity ($\nu_{010}=2.5$ GHz). The smooth and symmetrical curve over $\sim 300$ MHz indicates the stability and reliability of the tuning mechanism with a reasonable tuning range. The measured quality factors ranged from 90,000 in the high-frequency region to 110,000 in the low-frequency region. This confirmed that this unique design provides a practical search method for high-mass axion search that leverage the high-order resonant modes of cavity haloscopes.

As discussed earlier, periodic (lattice) structures of dielectric or metallic materials can provide volume-efficient searches suitable for high-frequency regimes. Motivated by the plasma haloscope scheme (Lawson et al., 2019), we explored a cavity design that incorporates an array of dielectric rods instead of thin conducting wires. This approach anticipates the use of low-loss dielectric materials to enhance the quality factor and make more efficient use of a given volume. The two schemes, conducting wires vs. dielectric rods, were compared in terms of EM field properties using two-dimensional simulations. A lattice structure was modeled by considering a square unit cell with the base material centered, as shown in figure 6, and arranging it in a two-dimensional repeating pattern with periodic boundary conditions imposed. The dimensions of the unit cells and base materials were determined to have the same resonant frequency. For the dielectric unit cell, the desired mode corresponds to the monopole mode of photonic crystals with a field component oscillating in opposite directions within the dielectric, resulting in a relatively low form factor. However, the dielectric properties greatly improve the cavity quality factor in experimental environments, i.e., at low temperatures and high magnetic fields. Additionally, the larger size of the unit cell reduces the number density of the base material, facilitating cavity assembly and frequency tuning and reducing the mode population.

To evaluate the performance, a three-dimensional simulation study was performed with the lattice structures implemented in a common resonant cavity of $100\times 100\times 100$ mm³. The wire metamaterial was simulated using a $10\times 10$ array of 2 mm-thick copper wires following the same structure as in Ref. (Millar et al., 2023), which gives the resonant frequency of 11.42 GHz. On the other hand, the photonic crystal was designed using a $6\times 6$ array of 7.45mm-thick dielectric rods with $\epsilon=9.7$ to produce a similar resonant frequency. The key quantity $V^{2}C^{2}Q$ was calculated numerically for various values of electrical conductivity ($\sigma$) and dielectric loss ($\tan\delta$), which are summarized in table 2. A 16-cell pizza cavity was also considered as reference.

Similar to the wire metamaterial haloscope, the resonant frequency of the photonic crystal haloscope can be tuned by varying the space between adjacent rods. Therefore, an ideal frequency tuning mechanism requires expansion or contraction of the rod array at equidistant intervals in two dimensions. We engaged the auxetic behavior of rotating rigid polygons to stretch or compress the array structure (Grima and Evans, 2000). In particular, regular tessellation preserves a highly symmetrical pattern while rotating the unit cell to isotropically deform the structure. For a realistic design, we modeled an array of 3x3 square blocks forming a regular tessellation with a dielectric rod anchored in the center of each block. Each block has a different number of ears on the edges that connect it to adjacent blocks such that the overall structure expands when stretched and contracts when compressed, as illustrated in figure 7. It is noteworthy that 1) the structure can be expanded or contracted by rotating the central block, allowing frequency tuning with a single rotating device, and 2) all the tuning rods move linearly in the radial direction with respect to the center, offering a straightforward way to guide them. The size and spacing of the rods are determined to match the desired frequency, while the number of layers is chosen to accommodate the given cavity volume.

The concept of the photonic crystal haloscope was demonstrated using a cylindrical copper cavity and a set of alumina tuning rods. The cavity had a conventional cylindrical shape with internal dimensions of $\O 78\,{\rm mm}\times 100\,{\rm mm}$. The frequency tuning structure consisted of a $3\times 3$ array of PEEK square blocks with a rod fixed at the center of each block. A piezoelectric rotator was attached to the center block to induce auxetic motion of the array structure. Since the tuning rods move only radially, as mentioned earlier, the end caps have slotted openings along the radial direction to guide their movement. The overall structure of this demo cavity design can be seen in figure 8. To test the tuning mechanism in an experimental environment, the cavity assembly was installed in a vacuum chamber immersed in a reservoir of liquid helium. Helium exchange gas was used to cool down the assembly to 4.5 K. A mode map was drawn by rotating the central block of the tuning structure through a full rotation angle (40$\degree$), as shown in figure 8. The desired mode corresponding to the lowest curve shows a frequency range of 10.9–9.6 GHz, which is in good agreement with the simulations. The cavity quality factor was measured during the tuning process, reaching the highest value of approximately 210,000 near 10.1 GHz and slowly declining in both low and high frequency regions. Additionally, we observed a 5% increase in quality factor with a magnetic fields $\gtrsim 1$ T, which is likely due to the similar dielectric property reported in Ref. (Di Vora et al., 2022). This demonstrated the experimental feasibility of the photonic crystal cavity design along with the newly invented tuning mechanism.

The cavity-based axion haloscopes, including those described in this text, would face considerable challenges when extending the search frequency well beyond several tens of GHz. Entering this region demands a significant increase in multiplicity, which in turn leads to complexity and subtlety in building and operating systems, making them vulnerable to mode mixing and field localization. A new technique was proposed to search for weakly interacting light particles with dish antennas relying on the detection principle that a reflective metal surface in a strong magnetic field effectively converts these particles into EM radiation emitted perpendicular to the surface (Jaeckel and Redondo, 2013; Horns et al., 2013). The scheme is broadband and allows to explore a wide range of masses in a single measurement. The axion-photon conversion power per unit area is given by

where $A$ is the area of the metal surface and $B_{\parallel}$ is the parallel component of the magnetic field to the metal surface. Focusing these radiated photons enhances the experimental sensitivity in searching for dark matter axions over a broad frequency range (Bajjali et al., 2023). Another research group proposed an interesting design that involves an outwardly focused parabolic mirror inserted in the center of a cylindrical conductor (Liu et al., 2022). This unique geometry allows the dish antenna principle to be realized in standard cryostats and high-field solenoids and enables sensitive searches in the THz region that is difficult to access by cavity haloscopes.

One advantage of the dish antenna haloscope is that the radiation power is proportional to the surface area, making it easy to scale up. Building upon this concept, CAPP has introduced an advanced geometric design for the dish antenna haloscope, aiming for volume-efficient searches for a given experimental setup (Jeong et al., 2023c). This design aimed to insert an “array” of horn antennas, effectively increasing the surface area within the solenoid bore. When low-aspect-ratio conical horn antennas are aligned parallel to the solenoid field, each antenna serves to convert dark matter axions into photons, thereby enhancing the total radiation power. The size of the horn dictates both the minimum frequency and surface area of axion-photon conversion; a smaller aperture shifts the search frequency towards higher regions while accommodating more antennas. The converted photons continue to reflect off the inner surface of each antenna until they eventually escape. By positioning a dielectric lens at the antenna opening, the escaped photons can be deflected and aligned along the antenna axis. These highly directional photons can be reflected by a parabolic mirror placed outside the solenoid magnet and then focused at a single point where a photo sensor is located. A schematic of this proposed design is shown in figure 9.

As the conversion power is directly related to the surface area within a magnetic field, the total power increases proportionally to the number of antennas inside the magnet volume. For an array of $N$ identical conical horn antennas packed in a solenoid with bore radius $R$, the total radiation power is calculated as

where $P_{\rm sgl}$ is the conversion power by a single antenna and $\Gamma$ is the packing efficiency. We assume antennas dimensions with $a=10$ mm and $b=1$ mm, and allow a space of 1 mm between adjacent antennas. This conversion power level is comparable with that of typical cavity haloscopes. We conducted a simulation study of axion electrodynamics using COMSOL Multiphysics to verify that the analytical approximation given by equation 5 is consistent with the numerical results, even at sufficiently high frequencies (Jeong et al., 2023a). Furthermore, we found that a simple hemispherical dielectric lens is adequate for aligning the emitted photons in the desired direction. Determining the optimal focusing geometry is left as a topic for future study. The study also showed that a horn antenna with an aperture radius of 10 mm is effective for experimental searches above 50 GHz, and the proposed array design increases sensitivity to the axion-photon coupling by a factor of 30 compared to a single antenna configuration for the same magnet.