Dielectric-Boosted Sensitivity to Cylindrical Azimuthally Varying Transverse-Magnetic Resonant Modes in an Axion Haloscope
Aaron P. Quiskamp, Ben T. McAllister, Gray Rybka, Michael E. Tobar
DDielectric Boosted Axion Haloscope Sensitivity In Cylindrical Azimuthally VaryingTransverse Magnetic Resonant Modes
Aaron P. Quiskamp, Ben T. McAllister, Gray Rybka, and Michael E. Tobar ∗ ARC Centre of Excellence for Engineered Quantum Systems,Department of Physics, University of Western Australia,35 Stirling Highway, Crawley, WA 6009, Australia. Centre for Experimental Nuclear Physics and Astrophysics,University of Washington, 1410 NE Campus Parkway, Seattle, WA 98195, USA. (Dated: June 11, 2020)Axions are a popular dark matter candidate which are often searched for in experiments known as“haloscopes” which exploit a putative axion-photon coupling. These experiments typically rely onTransverse Magnetic (TM) modes in resonant cavities to capture and detect photons generated viaaxion conversion. We present a study of a novel resonant cavity design for application in haloscopesearches, of particular use in the push to higher mass axion searches (above ∼ µ eV). In particular,we take advantage of azimuthally varying TM m modes which, whilst typically insensitive to axionsdue to field non-uniformity, can be made axion sensitive (and frequency tunable) through strategicplacement of dielectric wedges, becoming a type of resonator known as a Dielectric Boosted AxionSensitivity (DBAS) resonator. Results from Finite Element Modelling (FEM) are presented, andcompared with a simple proof-of-concept experiment. The results show a significant increase in axionsensitivity for these DBAS resonators over their empty cavity counterparts, and high potential forapplication in high mass axion searches when benchmarked against simpler, more traditional designsrelying on fundamental TM modes. I. INTRODUCTION
The composition and nature of dark matter continuesto elude physicists, despite decades of observations im-plying its existence [1–3]. However, the search for com-pelling candidates is narrowing through various experi-mental and theoretical efforts. In particular, the class ofparticles know as WISPs (weakly interacting sub-eV par-ticles) are becoming increasingly favoured as dark mattercandidates [4]. The axion is one such particle, widely con-sidered amongst the most compelling dark matter candi-dates, which arises as a consequence of an elegant solu-tion to the strong CP problem in QCD [5].The proposal of the axion haloscope by Sikivie in 1983was one of the first plausible methods of detecting ax-ions in the lab by way of exploiting their expected cou-pling with photons [6]. The inverse Primakoff effect is themechanism by which an axion decays into a real photonthrough the absorption of another photon. Tradition-ally, a strong DC magnetic field is used to saturate aresonant cavity in a sea of virtual photons. Dark mat-ter axions may scatter off these virtual photons, produc-ing detectable photons with a frequency corresponding tothe mass of the axion. If the cavity contains a geometri-cally appropriate resonant mode at the correct frequency,these photons will be captured in the cavity and the sig-nal will be resonantly enhanced. The power in the cavitycan then be read out via a low-noise receiver chain. How-ever, because the axion mass and the strength of its cou-pling to photons is unconstrained by theory, there exists ∗ [email protected] a very large parameter space to be searched, and manyexperiments are required to span the range. Several suchexperiments exist [7, 8], with many focused around themicrowave frequency band (corresponding to masses inthe µ eV range). However, many experiments are increas-ingly interested in lower [9] and higher [10] mass axions.The majority of the physics of the axion is determinedby a parameter known as the Peccei-Quinn symmetrybreaking scale, f a , which arises in the solution to thestrong CP problem which motivates the axions. f a iswhat most axion experiments ultimately hope to measureor constrain. This parameter is unconstrained by theory(although some cosmological constraints exist [11, 12]). f a determines the axion mass and the strength of its cou-pling to photons according tom a ∼ . × f a eV g aγγ = g γ αf a π . (1)Here, m a is the mass of the axion, g aγγ is the twophoton coupling constant of the axion and α is the finestructure constant [13–15]. The dimensionless axion-model dependent parameter g γ is of order one, andtakes different values in different axion models. In themost popular two models, the KimShifmanVainshtein-Zakharov (KSVZ), and DineFisher-SrednickiZhitnisky(DFSZ) models, g γ takes values of -0.97 and 0.36 respec-tively [13–15].To date, The Axion Dark Matter eXperiment (ADMX)is the most sensitive and mature haloscope experiment,placing impressive exclusion limits on the searchable pa- a r X i v : . [ phy s i c s . i n s - d e t ] J un rameter space [16–18]. However, current ADMX cavitydesigns are limited to probing masses of the order of afew µ eV at KSVZ and DFSZ sensitivity.Currently, the high axion mass regime ( > µ eV or15GHz) is largely inaccessible using traditional haloscopedesigns, attributed to the substantial decrease in sensitiv-ity in this mass range owing to a range of technical factorswhich will be discussed below. Interestingly, despite thelack of sensitive experimental constraints, this high massregion has benefited from a recent surge in theoreticaland observational motivation [19–22]. For example, theSMASH model favours axions with mass ∼ µ eV [21].As discussed, haloscopes operate on the principle thataxions from the galactic dark matter halo are resonantlyconverted into detectable photons in a cavity. The signalpower due to axion-photon conversion for a critically-coupled cavity, with axion conversion occurring on reso-nance is given by [23] P a ∝ g aγγ B CV Q L ρ a m a . (2)The parameters g aγγ , m a and the local axion halo darkmatter density ρ a are beyond experimental control. How-ever the external magnetic field strength B , cavity vol-ume V , mode dependent form factor (of order 1) C , andloaded quality factor Q L are parameters within experi-mental control [24]. The form factor for a given mode ina cylindrical cavity, with a homogeneous static magneticfield aligned in the ˆ z direction can be defined as C = (cid:12)(cid:12)(cid:12)(cid:82) dV c (cid:126)E c · (cid:126) ˆ z (cid:12)(cid:12)(cid:12) V (cid:82) dV c (cid:15) r | E c | . (3)Here (cid:126)E c is the cavity electric field and (cid:15) r is relativedielectric constant of the medium. For a non-zero formfactor, there must exist some degree of overlap betweenthe electromagnetic field of the axion induced photonand electromagnetic field of the resonant cavity mode,and the integral of this overlap must be non-zero. Thus,in an empty cylindrical cavity, only TM n modes willcouple to axions in the experimental context outlinedabove. The highest form factor belongs to the TM mode, which is consequently the mode of choice for mosthaloscope searches.The mode quality factor Q can be calculated throughthe mode dependent geometry factor G . Q = GR s G = ωµ (cid:82) | (cid:126)H | dV (cid:82) | (cid:126)H | dS (4)Here R s is the surface resistance of the material, (cid:126)H thecavity magnetic field, ω the resonant angular frequencyof the cavity mode and µ the vacuum permeability. It isassumed throughout this work that resistive wall lossesare the dominant loss mechanism, far greater than any losses in low-loss dielectric materials.As mentioned, poor constraints on the axion mass andphoton coupling strength create a large searchable pa-rameter space. This places a high premium on axion-sensitive haloscopes with frequency tuning mechanisms.We therefore define the scanning rate of a haloscope as[25] dfdt ∝ SN R goal g aγγ B C V ρ a Q L Q a m a ( k B T S ) . (5)Where SN R goal denotes the chosen signal-to-noise ra-tio, T s represents the total system noise temperature,largely due to the noise of the first stage amplifier, and Q a ∼ is the effective axion signal quality factor, ow-ing to the velocity distribution of dark matter. The sen-sitivity of an experiment is therefore measured by therate at which a haloscope can scan through a frequencyrange, at a desired level of axion-photon coupling andsignal-to-noise ratio. The figure of merit for resonatordesign is then given by the quantity C V Q L , or equiv-alently C V G , as these are the controllable parameterswhich explicitly depend on the chosen resonator.Now we can see why axion haloscopes become increas-ingly difficult at high masses. The volume, V of resonantcavities scales by V ∝ f − , and the expression containsan explicit dependence on m a − . Furthermore, the noisetemperature, T S of amplifiers increases at higher fre-quency, and the surface resistances of materials increaseleading to a decrease in Q L . All of these factors con-spire to decrease dfdt rapidly with increasing axion mass,making haloscope searches extremely difficult, requiringcareful resonator design. Some suggestions on how tomitigate this problem at high frequencies include multi-ple cavity designs [8, 10]. II. DIELECTRIC HALOSCOPES
Dielectric embedded haloscopes have been of growinginterest in recent times. Since axion conversion has a highdependence on field geometry, the addition of dielectricin suitable regions can alter the geometry to favour axionconversion. Experiments such as The Electric Tiger [26],Orpheus [27] and MADMAX [28] incorporate dielectricsto facilitate their axion searches, for various reasons.Traditional, tuning rod cavity haloscope designs, likethe ones used by ADMX [16, 17], exploit the TM mode for its superior form factor of ∼ .
69. However,resonators that utilise lower order modes are ineffectiveat higher frequencies due to the dramatic decrease in vol-ume, since the cavity dimensions must be of order λ/ λ is the axion‘s Compton wavelength (which de-creases with mass). Higher order resonances are thusattractive in the push to probe higher axion frequencies,allowing for higher cavity volumes at a given frequency.The cost of using higher order modes is the large de- → FIG. 1: The E z ( φ ) field of a TM m mode shown before and after the addition of dielectric wedges (blue regions), asviewed in the azimuthal direction.gree of field variation, resulting in degraded form factors,cancelling out the sensitivity benefit from the increasedvolume. For example, compared to a TM mode in anempty cavity, a TM has a significant portion of its E z field out of phase with the applied B field, reducing thecoupling between the cavity mode and the axion, and de-grading the form factor to ∼ .
13. However, this issuecan be addressed with the use of carefully placed dielec-tric materials to alter the field structure of the higherorder modes, as has been previously considered for thecase of TM n modes with n > z field of higher order TM n modes successfullymitigates this loss in form factor, while keeping the cavityvolume high. This is possible due to the fact that dielec-tric structures effectively suppress electric field. Addi-tionally, TM modes are highly uniform, which makesfrequency tuning difficult due to the high degree of sym-metry. The use of dielectrics can be exploited to cre-ate “built-in” tuning mechanisms as a result of morefree parameters and broken symmetries in the cavity.Such resonators were named Dielectric Boosted AxionSensitivity (DBAS) resonators in the context of TM n modes. This has been further confirmed by some recentexperiments by Kim et. al. [30], who introduced fur-ther ways to tune such TM n modes with reasonablefrequency tunability. Also, Alesini et. al. [31] recentlyrealised a fixed frequency prototype for axion searches,with boosted quality factor. In this work we consider anew type of DBAS resonator, in the context of TM m modes with m >
0, and will refer to them as the WedgeDBAS resonators. This resonator appears visually simi-lar to a dielectric equivalent to the multiple cell “Pizza”resonator proposed recently [32]. In this case, the wedgesact like the boundaries of the individual “Pizza” cells.
III. WEDGE DBAS RESONATORS
The cavity mode electric field, (cid:126)E c for a given TM m mode inside a hollow cylindrical resonator of radius R ,parametrised in cylindrical coordinates r , φ and z is de-fined as (cid:126)E c = E e iωt J m (cid:18) ς m, R r (cid:19) cos( mφ ) ˆ z. (6)Where E is some constant denoting the amplitude ofthe field, J m is a Bessel J function of order m , with ς m, denoting its 1 st root (ie. the cavity wall). The field isin one phase in the r direction, but alternates in phase m times in the φ direction over the 2 π range. There-fore implementing the DBAS method for a given TM m mode would require placement of m dielectric wedges inthe m lobes of one of the phases, suppressing their con-tribution to the form factor integral shown in equation 3by suppressing the field amplitude in these regions.Maximising the out of phase E z field confinement in-side the dielectric wedges is done by placing the dielectricboundaries of the wedges between nodes of the field. Fora TM m mode, each of the m total azimuthal variationsoccurs over a range of πm radians, in this range the fieldmust alternate between maxima in both phases. We de-note the optimal dielectric region size by θ (the angularsize of each wedge) and the region without dielectric by¯ θ (vacuum). Hence we can find θ by demanding that θ + ¯ θ = 2 πm . (7)Introducing dielectric material reduces the speed of lightwithin it by a factor of √ (cid:15) r . This is tantamount to thespace inside the dielectric increasing by a factor of √ (cid:15) r ,and so the physical size of the dielectric wedge must bedecreased by this factor to meet our optimal condition.In the empty cavity structure, the angular size of thetwo phases is equal, and here we are reducing only one ofthem, such that θ = ¯ θ/ √ (cid:15) r . Considering (7), the optimaldielectric wedge thickness, θ , can then found to be θ = 2 πm (1 + √ (cid:15) r ) . (8)Figure 1 shows the implementation of the WedgeDBAS method by placing dielectric (blue regions) of ap-propriate thickness in the out of phase parts of the E z field. It should be noted that this sketch is not to scaleand only serves to show the effects of adding dielectric;namely the suppressed amplitude of the E z field and thereduced size of the dielectric region as compared to theempty region (vacuum). Integrating E z · (cid:126) ˆ z over the en-tire range now produces a non-zero value, and hence anon-zero form factor. IV. MODELLINGA. 4 Wedge DBAS cavity
Using Finite Element Modelling (FEM) in COMSOLMultiphysics, we investigated the axion sensitive TMmodes in a 4 wedge resonator, with sapphire chosen asthe dielectric, and wedge sizes as per (8) with m = 4. Po-tential axion haloscope mode candidates must be highlytunable whilst retaining a sufficiently high scan rate,as indicated by the product C V G , computed via theFEM. The “built-in” frequency tuning mechanism for thewedge-type cavities explored in this work relies on tuningvia the relative angular separation of the wedges from oneanother. This can be achieved in an m -wedge cavity with m/ m/ φ and define φ = 0 as the starting symmetric position where the an-gular separation between all wedges is the same. Themaximum possible tuning is given by ¯ θ radians, definedfrom φ = 0 to the angular position where the wedges aretouching. We find ¯ θ ∼ .
21 using equation 8, where forsapphire, (cid:15) r ∼ .
1. The TM mode
Shown in the top panel of figure 2 is the field structureof the TM mode as the wedges tune together fromleft to right. Although resemblant of a TM mode,strictly speaking, this mode is not a true TM due tothe intruding dielectric. Using the results from FEM andequation 3, we determine the form factor for this mode ateach φ position. We find that the TM mode success-fully confines out of phase lobes of the E z field to producea non-zero form factor, C ∼ .
37 at the φ = 0 position,decreasing to C ∼ . φ = 1 .
2. The TM -like mode
In an empty cavity, there exist degenerate doubletTM m modes that are a quarter period out of phase,or π m . However, when dielectric is added and azimuthalsymmetry is broken, the modes break degeneracy andmove to different frequencies. Through FEM, we find theformerly degenerate doublet of the TM mode, with asimilar but distinctly different field structure. This modeis therefore referred to as the TM -like mode, whosefield structure is shown in the second panel of figure 2. Itshould be noted from our discussion on form factor that itis only after perfect symmetry between the wedges breaks( φ (cid:54) = 0), that this mode becomes axion sensitive. Pastthis initial position, the form factor gradually increasesto ∼ . φ = 1 .
3. The TM mode
DBAS m -wedge resonators that have m ≥ m modes, that tune in the same way as the previ-ous two modes. These fractional modes only show sig-nificant sensitivity when the wedges are close together.This is an intuitive result, since we can think of an m -wedge resonator with its wedges tuned together as effec-tively being a m -wedge resonator, with an axion sensitiveTM m mode. Indeed, the optimal wedge angle for theTM m mode is exactly double that of the TM m mode.Through FEM we find the field structure of the TM mode in a 4 wedge cavity as shown in the bottom panelof figure 2. It is clear that this mode begins with a formfactor of zero and gradually becomes more sensitive astuning progresses, increasing to have C ∼ .
13 at the φ = 1 .
4. Sensitivity
The relevant axion sensitivity and frequency tuning re-sults of FEM for a 4 wedge DBAS cavity with a radiusof 20mm, a height of 60mm, and an angular wedge thick-ness ( θ ) of ∼ .
36 rads are shown in fig. 3. Althoughthe total tuning range is shown, it is useful to define aso called “sensitive” tuning range, which only considersa given mode when it is within an order of magnitudeof the maximum C V G . The TM mode shows thegreatest peak sensitivity, however tuning of this mode ispoor, with a starting frequency of ∼ ∼
720 and ∼ -like mode however isa much more promising candidate for axion searches, of-fering substantial sensitivity over a broad tuning range,with a total and sensitive tuning of ∼ . ∼ mode, the TM ,although sensitive to axion detection, also suffers from aFIG. 2: The E z profile of the TM (upper), TM -like (middle) and TM (lower) modes in a 4 sapphire wedgecavity as the wedges move together. It should be noted that the dielectric cylinder at the center acts only toincrease the minimum mesh size in that area and has little to no impact on the field structure. Each mode is shownat tuning angles of φ = 0 , . , . ( rads ) F r equen cy ( G H z )
10 11 12 1310 - - - - - Frequency ( GHz ) C V G ( m Ω ) FIG. 3: Left: Resonant frequencies of the TM (blue), TM -like (orange) and TM (green) modes shown as afunction of tuning angle ( φ ). Right: C V G product as a function of frequency for the three modes of interest.poor degree of tuning, reporting only a total and sensitivetuning of ∼
340 and ∼ B. 8 Wedge DBAS cavity
Successfully finding 3 axion sensitive modes in the 4wedge configuration, we now investigate higher order TMmodes in an 8 wedge configuration, whilst using the samecavity dimensions. The angular size of each wedge willthen be exactly half the size used in the 4 wedge res-onator, as shown from equation 8. The results of FEMin an 8 wedge DBAS cavity are shown in figures 4 and5. Whilst not surprising, it is clear from the field pro-files, that the same three modes of interest (with twicethe number of azimuthal variations) also exist in the 8 wedge cavity. Where the fractional TM m mode is nowa TM , as shown in the bottom panel of figure 4. Wecan then think of the TM mode as having two tun-ing regimes; one in the earlier presented 4 wedge cavityand another in the 8 wedge configuration. Importantly,this mode is axion sensitive across different regions offrequency space for the two tuning regimes, effectivelyextending the mode’s sensitive tuning range. Again, thefractional TM mode starts with a form factor of zero,increasing to have C ∼ .
37 at the φ = 1 . φ = 0 position in the 4 wedge cav-ity. Interestingly, the TM mode performs better inthe 8 wedge configuration when it comes to the total( ∼ . ∼ . has C ∼ .
33 to be maximalFIG. 4: The E z profile of the TM (upper), TM -like (middle) and TM (lower) modes in a 8 sapphire wedgecavity as the wedges move together. Each mode is shown at tuning angles of φ = 0 , . , . ( rads ) F r equen cy ( G H z )
14 16 18 2010 - - - - - Frequency ( GHz ) C V G ( m Ω ) FIG. 5: Left: Resonant frequencies of the TM (brown), TM -like (purple) and TM (red) modes shown as afunction of tuning angle ( φ ) in an 8 sapphire wedge cavity. Right: C V G product as a function of frequency for thethree modes of interest.at the starting φ = 0 position, whereas the TM -likemode is completely axion insensitive at this position. Astuning progresses, the TM becomes less sensitive with C decreasing to ∼ . -like mode in-creases to have a maximum C ∼ .
11. The total and sen-sitive tuning for the TM mode is poor, with ∼
740 and340MHz respectively. In contrast the TM -like modehas a more impressive tuning of ∼ ∼ C. Practicalities and Mode Crossings
As previously discussed, novel cavity design is an es-sential step in the push towards searching the higher fre-quency axion parameter space. However, there is an inherent trade off between cavity volume and the useof higher order modes. The DBAS method seeks torectify this by mitigating the downside of higher ordermodes (reduction in form factor), whilst keeping the cav-ity volume high. However, higher order modes shouldbe approached with caution, as they introduce signifi-cant mode crowding and risk “avoided level crossings”,resulting in degraded axion sensitivity in those regionsof frequency space. To combat this, we opted for a rela-tively low aspect ratio of 3, thus preventing higher orderlength dependent mode crowding.
10 12 14 16 18 2010 - - - - - Frequency ( GHz ) C V G ( m Ω ) FIG. 6: C V G product as a function of frequency forthe TM (brown), TM -like (purple), TM (red),TM (blue), TM -like (orange) and TM (green)modes. Shown in black (dashed) are a series oftraditional conducting rod-tuned resonators, centred indifferent frequency regions for comparison. V. POSSIBLE IMPLEMENTATION ANDCOMPARISON
In principle, it would be possible to combine the 8 and4 wedge cavities discussed here. If we we began withthe 8 wedge configuration, and tuned the wedges untilthey were touching, each pair of 2 wedges would be thesame size as the wedges in the 4 wedge cavity. We couldthen tune 2 of these new, thicker wedges relative to theother 2, and recreate the tuning of the 4 wedge cavity.In this way, all 6 axion sensitive modes would becomeaccessible within a single cavity. Since FEM modellingfor both configurations was done using the same cavitydimensions, we plot C V G against frequency for all 6modes, as shown in fig. 6. Although possible in prin-ciple, a modular Wedge DBAS design is highly concep-tual and would face significant practical challenges in itsimplementation. Foremost of which is an intricate tun-ing mechanism such that the 8 wedge configuration can“fold” into 4 wedges, and then be tunable after. Al-ternatively, one could avoid significant engineering andcomplexity by simply inserting the desired wedge con-figuration, since the cavity radius is the same for bothregimes.To assess the viability of new haloscope designs, it iscommon practice to compare against a reference cavitythat tunes in the same frequency range. We have chosento benchmark against a TM mode tuned by radiallymoving a conducting rod, resulting in subtle changes tothe mode geometry, thus altering the resonant frequency,this is the type of resonator used by world-class halo-scopes, and thus a good comparison for a novel design.Overlaid in black (dashed) in fig. 6 is the C V G datafor this benchmark cavity, constructed and additionallyscaled such that the frequency tuning ranges are compa-rable with the other wedge cavity designs presented. Tocreate a clear comparison, an aspect ratio of 3 was also
10 12 14 16 18 20 22 2410 - - - - - Frequency ( GHz ) C V G ( m Ω ) FIG. 7: C V G product as a function of frequency forthe relevant modes of interest with a scaled 2 nd cavity(dashed orange) presented containing the same modesat higher frequencies.chosen for the benchmark cavity. There are ultimatelymany free parameters, and much optimisation possiblein the design of both schemes, and thus the compareddesigns should be thought of as a relatively simple one.However it should be noted that the benchmark cavity,although comparable in sensitivity in these regions, be-comes increasingly impractical to implement in the highfrequency regime, attributed to the significantly reducedcavity and tuning rod dimensions.As shown, almost all of the modes of interest have apeak C V G greater than the benchmark cavity, withsome modes sustaining an improved scan rate over theirentire sensitive tuning range. If implemented, this modu-lar cavity design is very attractive as an axion haloscopein the hard to reach but well motivated high mass regime,due to its broadband tuning and high sensitivity, but wecan take it even further.Using the inverse relationship between radius and fre-quency ( ω ∝ R − ), we can simply scale the results fromthe modelled cavity to imitate the results of a second cav-ity with a slightly different radius, so that the gaps in theprevious sensitivity plot (fig. 6) are filled by a second res-onator of the same type. As a result, 2 cavities of slightlydifferent radii can be used to almost completely cover afrequency range between 9.5-21.5GHz with a high degreeof sensitivity. In the case of uniform rescaling, the volumechanges with the cube of the radius, whereas mode de-pendent factors C and G remain unchanged. Thereforeincreasing the resonant frequency of a particular modeby a factor f results in C V G decreasing by factor f .The second cavity was scaled such that the resonant fre-quencies for the modes of interest increased by a factor f = 1 .
11, degrading C V G by f − ∼ .
53. Once againit is clear why many experiments have so far been unableto probe the higher frequency parameter space. As shownin figure 7, the combination of two multi-stage cavitiescan almost completely cover a 12GHz region with C V G greater than 10 − .FIG. 8: The E z profile of the TM -like (upper) and TM (lower) modes in a 4 teflon wedge cavity as the wedgesmove together. Each mode is shown at tuning angles of φ = 0 , . , . ∼ VI. PROOF OF CONCEPT EXPERIMENT
To assess the viability of a Wedge DBAS type res-onator, a prototype with 4 teflon wedges was first con-sidered. As a proof of concept this cavity was expectedto tune the TM and doublet TM -like modes in linewith expectations from the COMSOL modelling (withinexperimental uncertainty). Teflon wedges were an idealchoice due to their relatively low cost and ease of produc-tion, unlike more expensive, harder to machine, low-losscrystals such as sapphire. Based on the success of theteflon proof of concept, a sapphire resonator will be con-structed and tested.We use equation 8 to once again find the optimal teflonwedge thickness. The copper cavity had a radius of13.47mm and a height of 22.5mm. The field profiles forthe modes of interest in the teflon cavity are shown infig. 8 and closely resemble what is seen in the sapphireiteration, albeit with a significant reduction in the de-gree of out of phase field suppression and the presence ofFIG. 9: The teflon Wedge DBAS cavity used in theproof of concept experiment. As discussed in the text, apair of diametrically opposed wedges are mounted to themoveable lid, while another pair are affixed to the base. a central lobe, attributed to teflon’s comparatively lowpermittivity, (cid:15) r ∼ .
1. The TM mode is not shownhere and was not further investigated due to an absenceof tuning, as indicated by the initial FEM results.The proof of concept measurements were done at roomtemperature using a Thorlabs stepper motor and rota-tion stage. The lid of the cavity was clamped down,such that the base of the cavity was able to rotate rel-ative to the lid. Two of the wedges were affixed to thebase, and two to the lid, meaning that as the base tunedwith respect to the lid, two of the wedges tuned. Thecavity was coupled to with coaxial antennae, and trans-mission measurements were made with a Vector NetworkAnalyzer as a function of wedge angular position. TheFIG. 10: Colour density plot of the transmissioncoefficient as a function of resonant frequency andtuning angle φ . Of specific interest are the TM (lower) and T M -like modes (upper), identified byhand-taken measurements (orange) and the predictedtuning from FEM (blue). Darker regions represent lesstransmission while lighter regions represent greatertransmission.two modes were first tracked by hand using a step size of0.02 radians, and later via automated transmission coeffi-cient measurements that used a 0.0087 rad step size. Themodelled and measured frequencies are shown as a func-tion of tuning angle in figure 10. Horizontal error barsplaced on the measured data are due to the Thorlabs ro-tation stage quoting an accuracy in angular position of ± µ rad. This being an open-loop system, the horizon-tal error compounds for each subsequent measurement.Additionally, deviations from perfect symmetry can sig-nificantly perturb the mode field structure and hence fre-quency. Unequal wedge sizes, wedge tilt, crude measure-ments of their thickness (within ± .
02 rad) and the addi-tion of probes greatly effect the resonant frequency of themode. Modelling these small perturbations in COMSOLin conjunction with other uncertainties resulted in a totaluncertainty of approximately ± <
1% of the central starting frequency). Thevertical error bars on the FEM data represent this un-certainty.Importantly, the overall shape of the two modelledmodes match almost perfectly what is seen experimen-tally. We also observe highly responsive frequency tuningas a result of the novel “built-in” tuning mechanism. Fur-thermore, the modes in the proof of concept cavity wereat even higher frequencies than the modelled sapphirecavity, owing to the diameter of the available teflon stock- and very few avoided level crossings were observed overthe experimental tuning range. These factors demon-strate the viability of this promising resonator design.
VII. CONCLUSION
This work presents a theoretical and experimentalstudy of a novel Wedge DBAS cavity resonator for usein high mass axion haloscopes. Through strategic place-ment of dielectric structures, these resonator designs wereshown to significantly boost the form factors of variousTM m modes. The results of FEM for both 8 and 4-wedge cavity configurations are presented, and show 6axion sensitive modes with varying levels of frequencytuning. We compare their performance with a conven-tional conducting rod resonator, and find the DBAS cav-ity modes to boast superior C V G products, albeit eachover reduced tuning ranges. 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