A Polarization Modulator Unit for the Mid- and High-Frequency Telescopes of the LiteBIRD mission
Fabio Columbro, Paolo de Bernardis, Luca Lamagna, Silvia Masi, Alessandro Paiella, Francesco Piacentini, Giampaolo Pisano
AA Polarization Modulator Unit for the Mid- andHigh-Frequency Telescopes of the LiteBIRD mission
Fabio Columbro a, b , Paolo de Bernardis a, b , Luca Lamagna a, b , Silvia Masi a, b , AlessandroPaiella a, b , Francesco Piacentini a, b , and Giampaolo Pisano a,c , for the Litebird Joint StudyGroup da Dipartimento di Fisica, Sapienza Universit`a di Roma, P.le A. Moro 5, 00185, Roma, Italy b INFN–Sezione di Roma1, P.le A. Moro 5, 00185, Roma, Italy c School of Physics and Astronomy, Cardiff University, Queens Buildings, The Parade, Cardiff,CF24 3AA, U.K. d LiteBIRD Joint Study Group Members are listed at this link
ABSTRACT
The LiteBIRD mission is a JAXA strategic L-class mission for all sky CMB surveys which will be launched inthe 2020s. The main target of the mission is the detection of primordial gravitational waves with a sensitivity ofthe tensor-to-scalar ratio δr < . /f noise contribution and mitigate systematic uncertainties induced by detector gaindrift, both for the high-frequency telescope (HFT) and for the mid-frequency telescope (MFT). Each PMUis based on a continuously-rotating transmissive half-wave plate (HWP) held by a superconducting magneticbearing in a 5 K environment. In this proceeding we will present the design and expected performance of theLiteBIRD PMUs and testing performed on every PMU subsystem with a room-temperature rotating disk usedas a stand-in for the cryogenic HWP rotor. Keywords:
Cosmology, polarimeter, cryogenic, HWP
1. INTRODUCTION
The
Lite (Light) satellite for the studies of B-mode polarization and Inflation from cosmic background RadiationDetection (LiteBIRD) mission is the successor of the CMB space missions COBE, WMAP, and Planck, eachof which has given landmark scientific discoveries. A detection of primordial gravitational waves with LiteBIRD(at a level δr < . Additionally,the energy scale of inflation has important implications for other aspects of fundamental physics, such as axionsand neutrinos. LiteBIRD’s ability to measure the entire sky at the largest angular scales with 15 frequencybands is complementary to ground-based experiments. Ground-based experiments can also improve LiteBIRDobservations with high-resolution lensing data.A key component of LiteBIRD is its polarization modulator unit (PMU), an essential feature to suppress the1 /f noise contribution (low-frequency system drifts induced by thermal variations or detector gain drift) and andmitigate systematics uncertainties induced by detector gain drifts. The polarization modulation methodologybased on HWP is already used by a large number of experiments and can be divided in two families: a step-and-integrate strategy (SPIDER, QUBIC
8, 9 ) and a continuously-rotating HWP (ABS, EBEX, ACT-pol, POLARBEAR-2,
13, 14
LSPE/SWIPE
15, 16 ). Each of the 3 telescopes (high, mid and low frequency: HFT, MFT,LFT) is equipped with a cryogenic continuously-rotating half-wave plate (HWP) based on a superconductingmagnetic bearing (SMB), an emerging technology with a low technology readiness level (TRL).In this contribution we present the baseline design (Sec. 2) of the MHFT (mid- and high-frequency telescope)PMUs, which use the metal-mesh filter technology, while the LFT PMU uses of an achromatic 9-layer sapphire
Further author information: (Send correspondence to Fabio Columbro)E-mail: [email protected] a r X i v : . [ a s t r o - ph . I M ] J a n WP. The MHFT design takes inspiration from the LSPE/SWIPE one which is under testing (Sec. 3). Aroom-temperature mockup was used to develop and validate the eddy current model and to develop the driverand readout electronics (Sec. 3.1). The expected performance of the LiteBIRD PMUs is discussed in Sec. 4 andwill be confirmed during the first test of the breadboard model.
2. BASELINE DESIGN
In this section, we present the baseline design of the LiteBIRD MHFT PMU. Since both modulators will bemounted on a space mission, the design is driven by stringent requirements on mass, dimensions, stiffness,power dissipation, and TRL for the levitation, driving, gripping, and position encoding mechanisms. The mostimportant requirements for both PMUs are summarized in Tab. 1.Table 1: MHFT-PMU main requirements.
Parameter RequirementMFT HFT
Spin rate 39 rpm (0 .
65 Hz) 61 rpm (1 .
02 Hz)HWP diameter 320 mm 220 mmHWP temperature <
20 KLoad on the 5 K stage < < (cid:48) < (cid:48) Total mass <
20 kgThe modulator is conceptually similar to the EBEX,
11, 18
POLARBEAR-2 and LSPE/SWIPE designs,but is more challenging and ambitious because of the space application. The HWP diameters of MFT and HFTare 320 mm and 220 mm, respectively. The concept of the design is shown in Fig. 1 and is the same for bothmodulators with a scaling of the components.In contrast to the most common design of a superconducting magnetic bearing (SMB), we chose a differentconfiguration: the magnet ring and the superconductor are not stacked up but the internal rotating ring is themagnetic one and the external is the superconducting one, in order to obtain a side face to face interaction andminimize horizontal displacement.The selected superconductor, YBCO (Yttrium barium copper oxide), is the type-II superconductor with thehighest pinning force and critical current density ( ∼ A mm − ), and was chosen because higher critical currentmeans lower hysteresis losses. The rotor is composed of three rings stacked along the optical axis, startingfrom the bottom: • Groove ring: used to clamp the plate above the YBCO transition temperature. • Magnetic ring: composed of 2 Samarium-Cobalt magnetic rings sandwiched between 3 thin iron rings toproduce a more uniform magnetic field. • Aluminum ring with three different functions: to align the HWP in the center, to measure the angularposition of the rotor with the encoder and to hold the motor magnets used in the driver system.The drive mechanism is conceptually similar to an electromagnetic motor. We use 8 SmCo magnets (2 mmthick, 9 mm diameter) coupled with 2 rings of 32 coils each, on the top and on the bottom of the rotor to obtaina larger and more uniform force. The coils are connected in series (4 series of 16 coils each). The geometricparameters chosen are reported in Tab. 2, and the average force produced by the motor during operation (16coils) is 280 mN A − /414 mN A − for MFT/HFT. 2igure 1: Left panel : Overview of the polarization modulator unit design. The concept of the design is thesame with a scaling of the geometry (320 mm and 220 mm diameter HWPs are mounted in the center, for MFTand HFT, respectively).
Right panel : Section view of the modulator: a nearly frictionless bearing is obtainedwith the magnetic levitation of rotor composed by a permanent magnet rotor ring (cream grey) sandwitchedbetween an encoder ring and a groove ring. The stator ring hosts an array of superconducting bulks (black) andthe electromagnetic motor composed of 2 sets of 32 coils each coupled with 8 small motor magnets hosted in therotor.Table 2: Coil parameters for the MFT and HFT. The diameter of the copper wire is 0 . Parameter Unit HFT MFTCoil diameter mm 6 5
Coil length mm 10 10
Turn density mm −
25 25
Resistance (16 coils)
Ω 103 87During the launch, the rotor is held above the stator at room temperature by 3 pin pullers ∗ , radially orientedtowards the center of the HWP ring. After the launch, the pin pullers are released and 3 linear actuators holdthe rotor in position during the cooldown process, until the YBCO is superconducting and the magnetic field isfrozen. Hereafter the rotor is kept in place by the flux pinning and the clamps are released.We developed a frictionless electromagnetic clamp/release system suitable for any experiment equippedwith a large cryogenic HWP rotator based on a SMB. The main features of this system are: • large rotor mass compliance ( ∼
10 kg); • zero power dissipation while holding the rotor; • fast ( ∼
40 ms) release with low power dissipation ( ∼
30 J) during each operation; • low cost and high reliability over hundreds of operation cycles.This system is intended to be used only once but if needed it can clamp the rotor as needed throughout theflight. ∗ The temperature sensor is a thermistor, physically mounted on the rotating device and biased withan AC current, which is transferred from the stationary electronics to the rotating device via capacitive coupling.The levitation height sensor is a network of capacitors, similar to the one used for the capacitive coupling of thethermistor. The system reaches an accuracy better than 3% for the measurement of the thermistor resistance,and an accuracy of ∼ µ m for the measurement of its levitation height. The baseline designs for the MFT and HFT HWPs are mesh-HWPs.
23, 24
These quasi-optical components arebased on the mesh-filter technology, which has been adapted to mimic anisotropic behaviour. A mesh-HWPis based on two stacks of anisotropic metal grids embedded into polypropylene. The two stacks, one inductiveand one capacitive, are designed in such a way that two electromagnetic waves passing through them, polarisedin orthogonal directions, will experience 180 ° phase-shift. Each stack has different grids, designed with specificgeometries, located at optimised distances. The combination of all the grids, in our case 5 capacitive and 5inductive, provides a differential phase-shift around 180 ° across the frequency of operation. The design and themanufacture of mesh-HWPs are described in detail elsewhere. The expected performance of the MFT andHFT mesh-HWPs are reported in Fig. 2. The transmission coefficients and the modulation efficiencies acrossthe MFT and HFT bands are on average greater than 95%.
115 135 155 175 195 2150.90.920.940.960.981.0
Tx-CapTx-Inf
115 135 155 175 195 215
Frequency [
GHz ] Ax-CapAx-Ind
200 250 300 350 4000.90.920.940.960.981.0
Tx-CapTx-Inf
200 250 300 350 400
Frequency [
GHz ] Ax-CapAx-Ind
Figure 2: MFT (
Left ) and HFT (
Right ) mesh-HWP preliminary designs expected performances as a functionof frequency: transmissions, absorptions for the capacitive and inductive axes. Vertical dashed lines representthe central frequency of MHFT bands.
3. ROOM-TEMPERATURE MOCKUP
We developed a room-temperature mockup to validate the motor, the driver and readout electronics, the eddycurrent model, the main magnet inhomogeneities and the spinning frequency stablity. The size of the mockup issimilar to the LSPE/SWIPE polarization modulator (500 mm diameter), but the performance in terms of the fric-tion can be scaled because of the well known diameter dependence (see Sec. 4.1). In place of the superconductingmagnetic bearing, we used a low-friction ball bearing † .The top panel of Fig. 3 shows a CAD cross section of the mockup: in the center there are 2 ball bearings(yellow) separated by an aluminum spacer. The umbrella support in the center positions a dummy HWP, whichis composed of a lightened aluminum disk ( ∼ † Top ) CAD section of the room-temperature mockup, composed by 2 ball bearings (yellow) separatedby an aluminum spacer allowing to rotate an umbrella support which keeps in position a lightened aluminum disk( ∼ Left ) Picture of the room-temperature mockup rotating. The rotation is driven by a set of 64 coilsmounted on the upper aluminum ring coupled with 8 small Neodymium motor magnets hosted in the rotatingdisk. The YBCO holder is removed to show the magnet ring (top right). (
Right ) Detail of the Polyether etherketone (PEEK) encoder holder coupled with 64 evenly spaced slits on the rotor.the top of the external part of the main disk and is coupled with 8 small Neodymium motor magnets (8 mmdiameter) on the rotating disk. On the same diameter there are 64 evenly spaced slits for the encoder readoutsystem. The left bottom panel of Fig. 3 shows the assembled system without the stator while right bottom panel of Fig 3 shows a of the Polyether ether ketone (PEEK) encoder holder which is coupled with 64 evenly spacedslits on the rotor.
In the prototype implementation, the coils mounted on the stator are powered in 8 groups. Together with thesmall magnets on the rotor, they form an 8-phase low-torque motor, optimized to minimize the heat losses in thesystem. A sampled, smoothed trapezoidal-wave, stored in permanent memory, is used to drive eight independentmultiplying DACs and current generators. These produce 8 suitably phased currents, flowing in the 8 groups ofcoils. The phasing is such that when the current through a given coil is at the positive maximum, the currentin the next coil is at the negative minimum, so that the first coil pushes the magnet while the next one pullsit. The rotation is sensed by an optical encoder, consisting of 64 precision machined, equally spaced slits, in theperiphery of the rotor. Their position is read by means of LED emitters, optical fibers, and photodiodes, in thesame way as in the Pilot experiment cryogenic WP rotator. The measured rotation speed is compared to thedesired rotation speed to produce an error signal, which is PID-processed and used to modulate the referenceof the multiplying DACs, and thus the amplitude of the driving currents. For synchronization with the rest5f the instrument, each transit of a slit below a fixed reference position is time-stamped with the value of awide-counter, driven by the 5 MHz master clock of the instrument. An additional single slit, placed on a largerradius in the periphery of the rotor, is read in the same way. Its transit below the reference position resets aposition counter, updated by the transit of each of the 64 slits. The position counter is then output togetherwith its master clock time-stamp.
We first mounted only the bearing and the encoder in order to quantify the friction of the bearing with andwithout the driver motor magnets. The friction is quantified in terms of power loss and measured by spinningthe rotor up to ∼ . τ ( i ) − τ f ( ω ) = I dωdt , (1)where τ is the external torque applied to spin the rotor, τ f is the torque of friction forces, I is the moment ofinertia of the rotating system and ω the angular velocity of the rotor we measure. When the bearing is free toslow down (applied torque τ a = 0) we can convert Eq. 1 into an equation for the dissipated power: τ f ( ω ) = P f ( ω ) ω → P f ( ω ) = − ωI dωdt . (2)Fig. 4 shows the spin down test performed for different configurations of the system in order to quantifythe magnitude of each contribution to the total power budget. The first configuration we tested consists onlyin the rotor. All conductive materials and the motor magnets are removed in order to measure the frictionproduced by the bearings (P ). Than the whole system was assembled except for the motor magnets. Thisconfiguration allows us to quantify the eddy currents produced by the inhomogeneities ( ∼ mag ). This value sets only an upper limit for the eddy currents in the cryo environment because themost of this contribution comes from the aluminum holder of the YBCO which will be mostly shielded by thesuperconductors at cryo temperature. At the end we add the 8 motor magnets to determine their losses (P ). The Proportional-Integrated-Derivative (PID) feedback controls both the frequency of pulses (allowing to spinup the rotor) and the magnitude of the current 32 times per round, to stabilize the rotation when the rightfrequency is reached. The user specifies the target frequency of the rotor which should be changed during theoperation. Knowing the position of the 8 magnets (one every 8 slits), the relative phase of current in each seriesof coils is determined. The maximum value of the current is reached when the magnets are in the middle of twocoils. Due to the inertia of the system, an additional small phase that is dependent on frequency is inserted tooptimize system performance. Fig. 5 shows a sample test performed with a target frequency of 0 . σ θ [ (cid:48) ] = ¯ σ · · f · , (3)where f is the mean frequency expressed in Hz and ¯ σ is the mean value expressed in seconds of the standarddeviations of the Gaussian distribution for each interval ∆ t i − ∆ t , while ∆ t i and ∆ t are the time in second reads64 times per round by the relative encoder and only one time per round by the absolute encoder, respectively.The right panel of Fig. 5 shows the histogram of the data taken in the second half of the test shown in the leftpanel of Fig. 5.Due to the high inertia of the system, all measurements of the position are correlated. We introduce aKalman filter, which uses the dynamic model, the physical properties of the system, and multiple sequential6 -1 P o w e r [ m W ] P -1 P o w e r [ m W ] P mag Frequency [ Hz ] -1 P o w e r [ m W ] P Figure 4: Undersampled data of spin down tests calculated according to Eq. 2. The power loss from frictionis measured as a function of frequency for different contributions: ball bearings (P in the top panel ), mainmagnet (P mag in the central panel ) and 8 motor magnets (P in the bottom panel: ). The main magnet and motormagnets contributions are differential measurements from the ball bearings contribution.measurements to make an estimate of the varying quantities that is better than the estimate obtained by usingonly one measurement alone. The input parameters of the filter are the error on the readout data retrievedwith the previous estimation and the uncertainty on the acceleration of the system estimated using the rotorinertia and the variation of the coil torque. The accuracy improvement obtained by means of the Kalman filterranges from a factor 3 at 0 . . µ s). Thecurrent configuration is not limited by the electronic readout resolution but only by the stability of the rotation.This stability is limited by the current generator resolution which uses a 12-bit DAC. An improvement (from12-bit to 16-bit) of the resolution is already planned but is not required for the SWIPE/LSPE modulator whichhas a requirement of 0 . (cid:48) at 0 .
50 100 150 200Time [ min ]0.00.20.40.60.81.0 F r e q u e n c y [ H z ]
40 20 0 20 40 ∆t i − ∆t [ µ s] C o un t s Figure 5:
Left panel:
Relative encoder data acquired with a target frequency of 0 . Right panel:
Histogramof the data during the stable rotation period ( ∼
100 min, ∼ Hz ]10 -2 -1 A n g u l a r a cc u r a c y [ a r c m i n ] EncoderKalmanReadout resolution
Figure 6: The raw accuracy of the encoder data (blue dots), the accuracy resulting from the use of a Kalmanfilter (red squares) and the accuracy corresponding to the electronic readout resolution (1 µ s).
4. EXPECTED PERFORMANCE4.1 Losses
The tests performed with the LSPE/SWIPE prototype show that when the ball bearing friction is removed, themost important friction contribution comes from the inhomogeneities of the main magnet. The uniformity of themain magnet magnetic field should be improved by the help of the manufacturer up to 1%. This is not so easybut seems feasible because of the smaller dimension of the permanent magnets with respect to the LSPE/SWIPEone. A further solution for HFT (due to the small radius of HFT magnet ∼
200 mm) consists in the use ofa single magnet with only one magnetization which will guarantee more uniformity. By assuming the RRR =2.8 for aluminum 6061-T6, the dependence on frequency and magnetic dipole, we can estimate the expected8ower loss produced by the rotor eddy currents: 1 .
10 mW for MFT and 1 .
45 mW for HFT ‡ We expect hysteresis losses to be very small. This is due both to the absence of gravity which keeps inposition the rotor after the release and to the high homogeneity of the magnetic field which minimizes hysteresisin the superconductor. We estimate a contribution (cid:28) . − (414 mN A − ). Assuming the same radius R ∗ for all drag forces, we can find a rough estimate for the requiredforce to spin the rotor: F drag = Pv = P πf R ∗ , (5)which gives a required force of 1 .
98 mN (2 .
26 mN), meaning that the current required is ∼ ∼ .
09 mW (0 .
05 mW).As for the harness we decide to use manganin wires for the sensors and CuBe (0 .
25 mm diameter) for themotor and actuator wires in order to minimize the total heat load produced by the harness (0 .
22 mW for eachtelescope). Table 3: Contribution to the power budget. The total expected heat load is < .
19 mW.
MFT HFT [mW] [mW] .
59 0 . Main magnet < . < . Hysteresis < . < . Joule .
09 0 . Harness .
22 0 . Rotor emission .
09 0 . Total < . < . .
19 mW which isof the order of the total power budget for both PMUs (4 mW). Because this estimate was made by using theupper limit both of the main magnet and hysteresis contributions, there are margins to be within the budget.The main contribution to the motor eddy currents comes from the aluminum holder of the YBCO. Making theholder of electrical insulator like G10 will remove eddy currents but will thermally insulate the superconductorring. This may make the cooldown time of the superconductor too long. The possibility of using an electricalinsulator for the upper part of the holder and a thermal conductor (aluminum) for the lower part is under study.
The temperature of both HWPs must be <
20 K to reduce the radiative loading on the detector and minimizethe amplitude of spurious signals.
27, 32, 33
We use Comsol Multiphysics to build a thermal model of the rotorsurrounded by a 5 K environment. The rotor is made by Aluminum for the encoder and the groove rings, whilethe material assumed for the magnetic ring is the iron. This choice is driven by the lack of SmCo measured ‡ Starting from Fig. 4, the power loss was estimated at the operating frequencies for both telescopes and by scaling thediameter values. For example the HFT (equivalent radius 150 mW) eddy currents were estimated as: P HFT = P (1 .
02 Hz) × d HFT d mock × RRR = 1 .
25 mW × × . .
88 mW . (4) .
02 and 0 .
03 for MFT and HFT (see Fig. 2), respectively, while theemissivity outside the instrument bands is 0 .
03. The assumed emissivity of aluminum is 0 . ∼ . . . µ W, which is negligible with respect to the heating from thecoils. Combined with a HWP thermal time constant of about 10-20 h (from simulation of Fig. 7) this produces anegligible sky-synchronous variation of the HWP temperature, resulting in a negligible loading variation on thedetectors.Fig. 7 shows that the rotor (HFT solid lines, MFT dashed lines) reaches the equilibrium temperature of <
20 Kwithin a few days under all scenarios that were modeled, minimizing the impact on the detector background andinstrument sensitivity. -1 Time [ h ]4681012141618 H W P T e m p e r a t u r e [ K ] P = 0.5 mW P = 0.2 mW P = 0.1 mW Figure 7: Temperature of the HWPs as a function of time for different values of power load on the rotor (0 . The LiteBIRD total angular error budget corresponds to 1 (cid:48) for MFT and 5 (cid:48) for HFT and is equally split in 3error contributions: angle reconstruction, positioning of the HWP reference, margin.As stated before, the angular accuracy of the system is related to the inertia of the rotor, to its speed and to thewarm readout resolution. The main parameters and expected performance of LiteBIRD PMUs are summarizedin Tab. 4. The MFT modulator is very similar to the prototype tested configuration and a similar performance isexpected. The faster rotation and lower inertia of the HFT modulator reduce rotational stabilization, resultingin a reduced angular accuracy. All the same, the HFT raw encoder accuracy is nearly sufficient to meet therequirement and can be readily improved to perform well below the requirement by use of a Kalman filter. Theimprovement can be achieved by increasing the current generator resolution to have a finer control of the motorcurrent in the PID feedback loop. 10able 4: Main parameters of LSPE/SWIPE, MFT and HFT configurations. The encoding accuracy of LiteBIRDmodulators is estimated using the same configuration used in LSPE/SWIPE.
SWIPE MFT HFTHWP diameter mm 500 320 220
Frequency rpm 30 39 71
Encoder speed m s − . . . Moment of inertia kgm . ∼ . ∼ . Encoding accuracy (cid:48) . ∼ . ∼ . Kalman accuracy (cid:48) . ∼ . ∼ .
5. CONCLUSIONS
We presented the baseline design of LiteBIRD PMUs for the mid and high frequency telescopes. Both PMUare located at 5 K and based on a continuously transmissive rotating HWP which has a transmission across thebands on average greater than 95%. We discussed the tests performed on a room-temperature rotating disk usedas stand-in for the cryogenic HWP rotor which helped in the confirmation of the models used for the LiteBIRDdesign. The expected total load on the 5 K stage is < .
19 mW which is close to the requirement of 4 mW.The angular accuracy in the angle reconstruction is 0 . (cid:48) (5 . (cid:48) ) for MFT (HFT). The introduction of a Kalmanfilter improves the accuracy of angle reconstruction down to 0 . (cid:48) and 0 . (cid:48) for MFT and HFT, both values lowerthan the requirements of 1 (cid:48) and 5 (cid:48) , respectively. Both HWP temperatures are expected to be below 20 K, themaximum value to minimize the impact on the detector background and on instrument sensitivity. In conclusion,all values are close to the requirement. In any case, they represent the worst case for the expected performance,giving us some design margin. 11 CKNOWLEDGMENTS
This work is supported in
Japan by ISAS/JAXA for Pre-Phase A2 studies, by the acceleration program of JAXAresearch and development directorate, by the World Premier International Research Center Initiative (WPI)of MEXT, by the JSPS Core-to-Core Program of A. Advanced Research Networks, and by JSPS KAKENHIGrant Numbers JP15H05891, JP17H01115, and JP17H01125. The
Italian
LiteBIRD phase A contributionis supported by the Italian Space Agency (ASI Grants No. 2020-9-HH.0 and 2016-24-H.1-2018), the NationalInstitute for Nuclear Physics (INFN) and the National Institute for Astrophysics (INAF). The
French
LiteBIRDphase A contribution is supported by the Centre National d’Etudes Spatiale (CNES), by the Centre Nationalde la Recherche Scientifique (CNRS), and by the Commissariat `a l’Energie Atomique (CEA). The
Canadian contribution is supported by the Canadian Space Agency. The US contribution is supported by NASA grantno. 80NSSC18K0132. Norwegian participation in LiteBIRD is supported by the Research Council of Norway(Grant No. 263011). The
Spanish
LiteBIRD phase A contribution is supported by the Spanish Agencia Estatalde Investigaci´on (AEI), project refs. PID2019-110610RB-C21 and AYA2017-84185-P. Funds that support the
Swedish contributions come from the Swedish National Space Agency (SNSA/Rymdstyrelsen) and the SwedishResearch Council (Reg. no. 2019-03959). The
German participation in LiteBIRD is supported in part bythe Excellence Cluster ORIGINS, which is funded by the Deutsche Forschungsgemeinschaft (DFG, GermanResearch Foundation) under Germany’s Excellence Strategy (Grant No. EXC-2094 - 390783311). This researchused resources of the Central Computing System owned and operated by the Computing Research Center atKEK, as well as resources of the National Energy Research Scientific Computing Center, a DOE Office of ScienceUser Facility supported by the Office of Science of the U.S. Department of Energy.
REFERENCES [1] Sugai, H., Ade, P. A. R., Akiba, Y., Alonso, D., Arnold, K., Aumont, J., Austermann, J., Baccigalupi, C.,Banday, A. J., Banerji, R., Barreiro, R. B., Basak, S., Beall, J., Beckman, S., Bersanelli, M., Borrill, J.,Boulanger, F., Brown, M. L., Bucher, M., Buzzelli, A., Calabrese, E., Casas, F. J., Challinor, A., Chan, V.,Chinone, Y., Cliche, J. F., Columbro, F., Cukierman, A., Curtis, D., Danto, P., de Bernardis, P., de Haan,T., De Petris, M., Dickinson, C., Dobbs, M., Dotani, T., Duband, L., Ducout, A., Duff, S., Duivenvoorden,A., Duval, J. M., Ebisawa, K., Elleflot, T., Enokida, H., Eriksen, H. K., Errard, J., Essinger-Hileman, T.,Finelli, F., Flauger, R., Franceschet, C., Fuskeland , U., Ganga, K., Gao, J. R., G´enova-Santos, R., Ghigna,T., Gomez, A., Gradziel, M. L., Grain, J., Grupp, F., Gruppuso, A., Gudmundsson, J. E., Halverson, N. W.,Hargrave, P., Hasebe, T., Hasegawa, M., Hattori, M., Hazumi, M., Henrot-Versille, S., Herranz, D., Hill,C., Hilton, G., Hirota, Y., Hivon, E., Hlozek, R., Hoang, D. T., Hubmayr, J., Ichiki, K., Iida, T., Imada,H., Ishimura, K., Ishino, H., Jaehnig, G. C., Jones, M., Kaga, T., Kashima, S., Kataoka, Y., Katayama, N.,Kawasaki, T., Keskitalo, R., Kibayashi, A., Kikuchi, T., Kimura, K., Kisner, T., Kobayashi, Y., Kogiso, N.,Kogut, A., Kohri, K., Komatsu, E., Komatsu, K., Konishi, K., Krachmalnicoff, N., Kuo, C. L., Kurinsky,N., Kushino, A., Kuwata-Gonokami, M., Lamagna, L., Lattanzi, M., Lee, A. T., Linder, E., Maffei, B.,Maino, D., Maki, M., Mangilli, A., Mart´ınez-Gonz´alez, E., Masi, S., Mathon, R., Matsumura, T., Mennella,A., Migliaccio, M., Minami, Y., Mistuda, K., Molinari, D., Montier, L., Morgante, G., Mot, B., Murata,Y., Murphy, J. A., Nagai, M., Nagata, R., Nakamura, S., Namikawa, T., Natoli, P., Nerval, S., Nishibori,T., Nishino, H., Nomura, Y., Noviello, F., O’Sullivan, C., Ochi, H., Ogawa, H., Ogawa, H., Ohsaki, H.,Ohta, I., Okada, N., Okada, N., Pagano, L., Paiella, A., Paoletti, D., Patanchon, G., Piacentini, F., Pisano,G., Polenta, G., Poletti, D., Prouv´e, T., Puglisi, G., Rambaud, D., Raum, C., Realini, S., Remazeilles, M.,Roudil, G., Rubi˜no-Mart´ın, J. A., Russell, M., Sakurai, H., Sakurai, Y., Sandri, M., Savini, G., Scott, D.,Sekimoto, Y., Sherwin, B. D., Shinozaki, K., Shiraishi, M., Shirron, P., Signorelli, G., Smecher, G., Spizzi,P., Stever, S. L., Stompor, R., Sugiyama, S., Suzuki, A., Suzuki, J., Switzer, E., Takaku, R., Takakura,H., Takakura, S., Takeda, Y., Taylor, A., Taylor, E., Terao, Y., Thompson, K. L., Thorne, B., Tomasi,M., Tomida, H., Trappe, N., Tristram, M., Tsuji, M., Tsujimoto, M., Tucker, C., Ullom, J., Uozumi, S.,Utsunomiya, S., Van Lanen, J., Vermeulen, G., Vielva, P., Villa, F., Vissers, M., Vittorio, N., Voisin, F.,Walker, I., Watanabe, N., Wehus, I., Weller, J., Westbrook, B., Winter, B., Wollack, E., Yamamoto, R.,Yamasaki, N. Y., Yanagisawa, M., Yoshida, T., Yumoto, J., Zannoni, M., and Zonca, A., “Updated Designof the CMB Polarization Experiment Satellite LiteBIRD,”
Journal of Low Temperature Physics , 1107–1117 (Jan. 2020). 122] Boggess, N. W., Mather, J. C., Weiss, R., Bennett, C. L., Cheng, E. S., Dwek, E., Gulkis, S., Hauser, M. G.,Janssen, M. A., Kelsall, T., Meyer, S. S., Moseley, S. H., Murdock, T. L., Shafer, R. A., Silverberg, R. F.,Smoot, G. F., Wilkinson, D. T., and Wright, E. L., “The COBE Mission: Its Design and Performance TwoYears after Launch,”
The Astrophysical Journal , 420 (Oct. 1992).[3] Bennett, C. L., Larson, D., Weiland, J. L., Jarosik, N., Hinshaw, G., Odegard, N., Smith, K. M., Hill,R. S., Gold, B., Halpern, M., Komatsu, E., Nolta, M. R., Page, L., Spergel, D. N., Wollack, E., Dunkley,J., Kogut, A., Limon, M., Meyer, S. S., Tucker, G. S., and Wright, E. L., “Nine-year Wilkinson MicrowaveAnisotropy Probe (WMAP) Observations: Final Maps and Results,”
The Astrophysical Journal SupplementSeries , 20 (Oct. 2013).[4] Planck Collaboration, Aghanim, N., Arnaud, M., Ashdown, M., Aumont, J., Baccigalupi, C., Band ay,A. J., Barreiro, R. B., Bartlett, J. G., Bartolo, N., Battaner, E., Benabed, K., Benoˆıt, A., Benoit-L´evy, A.,Bernard, J. P., Bersanelli, M., Bielewicz, P., Bock, J. J., Bonaldi, A., Bonavera, L., Bond, J. R., Borrill,J., Bouchet, F. R., Boulanger, F., Bucher, M., Burigana, C., Butler, R. C., Calabrese, E., Cardoso, J. F.,Catalano, A., Challinor, A., Chiang, H. C., Christensen, P. R., Clements, D. L., Colombo, L. P. L., Combet,C., Coulais, A., Crill, B. P., Curto, A., Cuttaia, F., Danese, L., Davies, R. D., Davis, R. J., de Bernardis, P.,de Rosa, A., de Zotti, G., Delabrouille, J., D´esert, F. X., Di Valentino, E., Dickinson, C., Diego, J. M., Dolag,K., Dole, H., Donzelli, S., Dor´e, O., Douspis, M., Ducout, A., Dunkley, J., Dupac, X., Efstathiou, G., Elsner,F., Enßlin, T. A., Eriksen, H. K., Fergusson, J., Finelli, F., Forni, O., Frailis, M., Fraisse, A. A., Franceschi,E., Frejsel, A., Galeotta, S., Galli, S., Ganga, K., Gauthier, C., Gerbino, M., Giard, M., Gjerløw, E.,Gonz´alez-Nuevo, J., G´orski, K. M., Gratton, S., Gregorio, A., Gruppuso, A., Gudmundsson, J. E., Hamann,J., Hansen, F. K., Harrison, D. L., Helou, G., Henrot-Versill´e, S., Hern´andez-Monteagudo, C., Herranz, D.,Hildebrand t, S. R., Hivon, E., Holmes, W. A., Hornstrup, A., Huffenberger, K. M., Hurier, G., Jaffe, A. H.,Jones, W. C., Juvela, M., Keih¨anen, E., Keskitalo, R., Kiiveri, K., Knoche, J., Knox, L., Kunz, M., Kurki-Suonio, H., Lagache, G., L¨ahteenm¨aki, A., Lamarre, J. M., Lasenby, A., Lattanzi, M., Lawrence, C. R.,Le Jeune, M., Leonardi, R., Lesgourgues, J., Levrier, F., Lewis, A., Liguori, M., Lilje, P. B., Lilley, M.,Linden-Vørnle, M., Lindholm, V., L´opez-Caniego, M., Mac´ıas-P´erez, J. F., Maffei, B., Maggio, G., Maino,D., Mandolesi, N., Mangilli, A., Maris, M., Martin, P. G., Mart´ınez-Gonz´alez, E., Masi, S., Matarrese, S.,Meinhold, P. R., Melchiorri, A., Migliaccio, M., Millea, M., Mitra, S., Miville-Deschˆenes, M. A., Moneti, A.,Montier, L., Morgante, G., Mortlock, D., Mottet, S., Munshi, D., Murphy, J. A., Narimani, A., Naselsky,P., Nati, F., Natoli, P., Noviello, F., Novikov, D., Novikov, I., Oxborrow, C. A., Paci, F., Pagano, L.,Pajot, F., Paoletti, D., Partridge, B., Pasian, F., Patanchon, G., Pearson, T. J., Perdereau, O., Perotto,L., Pettorino, V., Piacentini, F., Piat, M., Pierpaoli, E., Pietrobon, D., Plaszczynski, S., Pointecouteau, E.,Polenta, G., Ponthieu, N., Pratt, G. W., Prunet, S., Puget, J. L., Rachen, J. P., Reinecke, M., Remazeilles,M., Renault, C., Renzi, A., Ristorcelli, I., Rocha, G., Rossetti, M., Roudier, G., Rouill´e d’Orfeuil, B.,Rubi˜no-Mart´ın, J. A., Rusholme, B., Salvati, L., Sandri, M., Santos, D., Savelainen, M., Savini, G., Scott,D., Serra, P., Spencer, L. D., Spinelli, M., Stolyarov, V., Stompor, R., Sunyaev, R., Sutton, D., Suur-Uski,A. S., Sygnet, J. F., Tauber, J. A., Terenzi, L., Toffolatti, L., Tomasi, M., Tristram, M., Trombetti, T.,Tucci, M., Tuovinen, J., Umana, G., Valenziano, L., Valiviita, J., Van Tent, F., Vielva, P., Villa, F., Wade,L. A., Wandelt, B. D., Wehus, I. K., Yvon, D., Zacchei, A., and Zonca, A., “Planck 2015 results. XI. CMBpower spectra, likelihoods, and robustness of parameters,” A & A , A11 (Sept. 2016).[5] Kamionkowski, M. and Kovetz, E. D., “The Quest for B Modes from Inflationary Gravitational Waves,” Annual Review of Astron. and Astrophys. , 227–269 (Sept. 2016).[6] LiteBIRD Collaboration, “Probing Cosmic Inflation with the LiteBIRD Cosmic Microwave BackgroundPolarization Survey,” PTEP (2021).[7] Gualtieri, R., Filippini, J. P., Ade, P. A. R., Amiri, M., Benton, S. J., Bergman, A. S., Bihary, R., Bock,J. J., Bond, J. R., Bryan, S. A., Chiang, H. C., Contaldi, C. R., Dor´e, O., Duivenvoorden, A. J., Eriksen,H. K., Farhang, M., Fissel, L. M., Fraisse, A. A., Freese, K., Galloway, M., Gambrel, A. E., Gandilo, N. N.,Ganga, K., Gramillano, R. V., Gudmundsson, J. E., Halpern, M., Hartley, J., Hasselfield, M., Hilton, G.,Holmes, W., Hristov, V. V., Huang, Z., Irwin, K. D., Jones, W. C., Kuo, C. L., Kermish, Z. D., Li, S.,Mason, P. V., Megerian, K., Moncelsi, L., Morford, T. A., Nagy, J. M., Netterfield, C. B., Nolta, M.,Osherson, B., Padilla, I. L., Racine, B., Rahlin, A. S., Reintsema, C., Ruhl, J. E., Runyan, M. C., Ruud,T. M., Shariff, J. A., Soler, J. D., Song, X., Trangsrud, A., Tucker, C., Tucker, R. S., Turner, A. D., List,13. F. v. d., Weber, A. C., Wehus, I. K., Wiebe, D. V., and Young, E. Y., “SPIDER: CMB Polarimetry fromthe Edge of Space,”
Journal of Low Temperature Physics , 1112–1121 (Dec. 2018).[8] D’Alessandro, G., Mele, L., Columbro, F., Amico, G., Battistelli, E. S., de Bernardis, P., Coppolecchia,A., De Petris, M., Grandsire, L., Hamilton, J. C., Lamagna, L., Marnieros, S., Masi, S., Mennella, A.,O’Sullivan, C., Paiella, A., Piacentini, F., Piat, M., Pisano, G., Presta, G., Tartari, A., Torchinsky, S. A.,Voisin, F., Zannoni, M., Ade, P., Alberro, J. G., Almela, A., Arnaldi, L. H., Auguste, D., Aumont, J.,Azzoni, S., Banfi, S., B´elier, B., Ba`u, A., Bennett, D., Berg´e, L., Bernard, J. P., Bersanelli, M., Bigot-Sazy,M. A., Bonaparte, J., Bonis, J., Bunn, E., Burke, D., Buzi, D., Cavaliere, F., Chanial, P., Chapron, C.,Charlassier, R., Cobos Cerutti, A. C., De Gasperis, G., De Leo, M., Dheilly, S., Duca, C., Dumoulin, L.,Etchegoyen, A., Fasciszewski, A., Ferreyro, L. P., Fracchia, D., Franceschet, C., Gamboa Lerena, M. M.,Ganga, K. M., Garc´ıa, B., Garc´ıa Redondo, M. E., Gaspard, M., Gayer, D., Gervasi, M., Giard, M., Gilles,V., Giraud-Heraud, Y., G´omez Berisso, M., Gonz´alez, M., Gradziel, M., Hampel, M. R., Harari, D., Henrot-Versill´e, S., Incardona, F., Jules, E., Kaplan, J., Kristukat, C., Loucatos, S., Louis, T., Maffei, B., Marty,W., Mattei, A., May, A., McCulloch, M., Melo, D., Montier, L., Mousset, L., Mundo, L. M., Murphy, J. A.,Murphy, J. D., Nati, F., Olivieri, E., Oriol, C., Pajot, F., Passerini, A., Pastoriza, H., Pelosi, A., Perbost,C., Perciballi, M., Pezzotta, F., Piccirillo, L., Platino, M., Polenta, G., Prˆele, D., Puddu, R., Rambaud, D.,Rasztocky, E., Ringegni, P., Romero, G. E., Salum, J. M., Schillaci, A., Sc´occola, C. G., Scully, S., Spinelli,S., Stankowiak, G., Stolpovskiy, M., Supanitsky, A. D., Thermeau, J. P., Timbie, P., Tomasi, M., Tucker,G., Tucker, C., Vigan`o, D., Vittorio, N., Wicek, F., Wright, M., and Zullo, A., “QUBIC VI: cryogenic halfwave platerotator, design and performances,” arXiv e-prints , arXiv:2008.10667 (Aug. 2020).[9] Mennella, A., Ade, P., Amico, G., Auguste, D., Aumont, J., Banfi, S., Barbar`an, G., Battaglia, P., Battistelli,E., Ba`u, A., B´elier, B., Bennett, D., Berg´e, L., Bernard, J., Bersanelli, M., Sazy, M., Bleurvacq, N.,Bonaparte, J., Bonis, J., Bunn, E., Burke, D., Buzi, D., Buzzelli, A., Cavaliere, F., Chanial, P., Chapron, C.,Charlassier, R., Columbro, F., Coppi, G., Coppolecchia, A., D’Agostino, R., D’Alessandro, G., Bernardis, P.,Gasperis, G., Leo, M., Petris, M., Donato, A., Dumoulin, L., Etchegoyen, A., Fasciszewski, A., Franceschet,C., Lerena, M., Garcia, B., Garrido, X., Gaspard, M., Gault, A., Gayer, D., Gervasi, M., Giard, M., H´eraud,Y., Berisso, M., Gonz´alez, M., Gradziel, M., Grandsire, L., Guerard, E., Hamilton, J., Harari, D., Haynes,V., Versill´e, S., Hoang, D., Holtzer, N., Incardona, F., Jules, E., Kaplan, J., Korotkov, A., Kristukat, C.,Lamagna, L., Loucatos, S., Louis, T., Lowitz, A., Lukovic, V., Luterstein, R., Maffei, B., Marnieros, S.,Masi, S., Mattei, A., May, A., McCulloch, M., Medina, M., Mele, L., Melhuish, S., Montier, L., Mousset,L., Mundo, L., Murphy, J., Murphy, J., O’Sullivan, C., Olivieri, E., Paiella, A., Pajot, F., Passerini, A.,Pastoriza, H., Pelosi, A., Perbost, C., Perciballi, M., Pezzotta, F., Piacentini, F., Piat, M., Piccirillo, L.,Pisano, G., Polenta, G., Prˆele, D., Puddu, R., Rambaud, D., Ringegni, P., Romero, G., Salatino, M.,Schillaci, A., Sc´occola, C., Scully, S., Spinelli, S., Stankowiak, G., Stolpovskiy, M., Suarez, F., Tartari, A.,Thermeau, J., Timbie, P., Tomasi, M., Torchinsky, S., Tristram, M., Tucker, C., Tucker, G., Vanneste, S.,Vigan`o, D., Vittorio, N., Voisin, F., Watson, R., Wicek, F., Zannoni, M., and Zullo, A., “QUBIC: Exploringthe Primordial Universe with the Q&U Bolometric Interferometer,”
Universe , 42 (Jan. 2019).[10] Kusaka, A., Essinger-Hileman, T., Appel, J. W., Gallardo, P., Irwin, K. D., Jarosik, N., Nolta, M. R.,Page, L. A., Parker, L. P., Raghunathan, S., Sievers, J. L., Simon, S. M., Staggs, S. T., and Visnjic, K.,“Publisher’s Note: “Modulation of cosmic microwave background polarization with a warm rapidly rotatinghalf-wave plate on the Atacama B-Mode Search instrument” [Rev. Sci. Instrum. 85, 024501 (2014)],” Reviewof Scientific Instruments , 039901 (Mar. 2014).[11] The EBEX collaboration, Aboobaker, A. M., Ade, P., Araujo, D., Aubin, F., Baccigalupi, C., Bao, C.,Chapman, D., Didier, J., Dobbs, M., Geach, C., Grainger, W., Hanany, S., Helson, K., Hillbrand, S.,Hubmayr, J., Jaffe, A., Johnson, B., Jones, T., Klein, J., Korotkov, A., Lee, A., Levinson, L., Limon,M., MacDermid, K., Matsumura, T., Miller, A. D., Milligan, M., Raach, K., Reichborn-Kjennerud, B.,Sagiv, I., Savini, G., Spencer, L., Tucker, C., Tucker, G. S., Westbrook, B., Young, K., and Zilic, K., “TheEBEX balloon-borne experiment—optics, receiver, and polarimetry,” The Astrophysical Journal SupplementSeries , 7 (nov 2018).[12] Henderson, S. W., Allison, R., Austermann, J., Baildon, T., Battaglia, N., Beall, J. A., Becker, D., DeBernardis, F., Bond, J. R., Calabrese, E., Choi, S. K., Coughlin, K. P., Crowley, K. T., Datta, R., Devlin,M. J., Duff, S. M., Dunkley, J., D¨unner, R., van Engelen, A., Gallardo, P. A., Grace, E., Hasselfield, M.,14ills, F., Hilton, G. C., Hincks, A. D., Hlozek, R., Ho, S. P., Hubmayr, J., Huffenberger, K., Hughes, J. P.,Irwin, K. D., Koopman, B. J., Kosowsky, A. B., Li, D., McMahon, J., Munson, C., Nati, F., Newburgh, L.,Niemack, M. D., Niraula, P., Page, L. A., Pappas, C. G., Salatino, M., Schillaci, A., Schmitt, B. L., Sehgal,N., Sherwin, B. D., Sievers, J. L., Simon, S. M., Spergel, D. N., Staggs, S. T., Stevens, J. R., Thornton, R.,Van Lanen, J., Vavagiakis, E. M., Ward, J. T., and Wollack, E. J., “Advanced ACTPol Cryogenic DetectorArrays and Readout,”
Journal of Low Temperature Physics , 772–779 (Aug. 2016).[13] Hill, C. A., Kusaka, A., Barton, P., Bixler, B., Droster, A. G., Flament, M., Ganjam, S., Jadbabaie,A., Jeong, O., Lee, A. T., Madurowicz, A., Matsuda, F. T., Matsumura, T., Rutkowski, A., Sakurai, Y.,Sponseller, D. R., Suzuki, A., and Tat, R., “A Large-Diameter Cryogenic Rotation Stage for Half-Wave PlatePolarization Modulation on the POLARBEAR-2 Experiment,”
Journal of Low Temperature Physics ,851–859 (Dec. 2018).[14] Hill, C. A., Kusaka, A., Ashton, P., Barton, P., Adkins, T., Arnold, K., Bixler, B., Ganjam, S., Lee,A. T., Matsuda, F., Matsumura, T., Sakurai, Y., Tat, R., and Zhou, Y., “A cryogenic continuously ro-tating half-wave plate for the POLARBEAR-2b cosmic microwave background receiver,” arXiv e-prints ,arXiv:2009.03972 (Sept. 2020).[15] Lamagna, L., Addamo, G., Ade, P. A. R., Baccigalupi, C., Baldini, A. M., Battaglia, P. M., Battistelli, E.,Ba`u, A., Bersanelli, M., Biasotti, M., Boragno, C., Boscaleri, A., Caccianiga, B., Caprioli, S., Cavaliere,F., Cei, F., Cleary, K. A., Columbro, F., Coppi, G., Coppolecchia, A., Corsini, D., Cuttaia, F., D’Alessandro, G., de Bernardis, P., De Gasperis, G., De Petris, M., Torto, F. D., Fafone, V., Farooqui, Z., Farsian,F., Fontanelli, F., Franceschet, C., Gaier, T. C., Gatti, F., Genova-Santos, R., Gervasi, M., Ghigna, T.,Grassi, M., Grosso, D., Incardona, F., Jones, M., Kangaslahti, P., Krachmalnicoff, N., Mainini, R., Maino,D., Mandelli, S., Maris, M., Masi, S., Matarrese, S., May, A., Mena, P., Mennella, A., Molina, R., Molinari,D., Morgante, G., Nati, F., Natoli, P., Pagano, L., Paiella, A., Paonessa, F., Passerini, A., Perez-de-Taoro,M., Peverini, O. A., Pezzotta, F., Piacentini, F., Piccirillo, L., Pisano, G., Polastri, L., Polenta, G., Poletti,D., Presta, G., Realini, S., Reyes, N., Rocchi, A., Rubino-Martin, J. A., Sandri, M., Sartor, S., Schillaci, A.,Signorelli, G., Soria, M., Spinella, F., Tapia, V., Tartari, A., Taylor, A., Terenzi, L., Tomasi, M., Tommasi,E., Tucker, C., Vaccaro, D., Vigano, D. M., Villa, F., Virone, G., Vittorio, N., Volpe, A., Watkins, B.,Zacchei, A., and Zannoni, M., “Progress Report on the Large-Scale Polarization Explorer,”
Journal of LowTemperature Physics , 374–383 (Apr. 2020).[16] Columbro, F., Madonia, P. G., Lamagna, L., Battistelli, E. S., Coppolecchia, A., de Bernardis, P., Gualtieri,R., Masi, S., Paiella, A., Piacentini, F., Presta, G., Biasotti, M., D’Alessandro, G., Gatti, F., Mele, L., andSiri, B., “SWIPE multi-mode pixel assembly design and beam pattern measurements at cryo temperature,”
Journal of Low Temperature Physics (Jan 2020).[17] Sakurai, Y., Matsumura, T., and Collaboration, L., “Breadboard model of the polarization modulatorunit based on a continuous rotating half-wave plate for the low-frequency telescope of the LiteBIRD spacemission,”
Proc. of SPIE (2021).[18] Johnson, B. R., Columbro, F., Araujo, D., Limon, M., Smiley, B., Jones, G., Reichborn-Kjennerud, B.,Miller, A., and Gupta, S., “A large-diameter hollow-shaft cryogenic motor based on a superconductingmagnetic bearing for millimeter-wave polarimetry,”
Review of Scientific Instruments (10), 105102 (2017).[19] The LSPE collaboration, Addamo, G., Ade, P. A. R., Baccigalupi, C., Baldini, A. M., Battaglia, P. M.,Battistelli, E. S., Ba`u, A., de Bernardis, P., Bersanelli, M., Biasotti, M., Boscaleri, A., Caccianiga, B.,Caprioli, S., Cavaliere, F., Cei, F., Cleary, K. A., Columbro, F., Coppi, G., Coppolecchia, A., Cuttaia, F.,D’Alessandro, G., De Gasperis, G., De Petris, M., Fafone, V., Farsian, F., Ferrari Barusso, L., Fontanelli,F., Franceschet, C., Gaier, T. C., Galli, L., Gatti, F., Genova-Santos, R., Gerbino, M., Gervasi, M., Ghigna,T., Grosso, D., Gruppuso, A., Gualtieri, R., Incardona, F., Jones, M. E., Kangaslahti, P., Krachmalnicoff,N., Lamagna, L., Lattanzi, M., Lumia, M., Mainini, R., Maino, D., Mandelli, S., Maris, M., Masi, S.,Matarrese, S., May, A., Mele, L., Mena, P., Mennella, A., Molina, R., Molinari, D., Morgante, G., Natale,U., Nati, F., Natoli, P., Pagano, L., Paiella, A., Panico, F., Paonessa, F., Paradiso, S., Passerini, A., Perez-de-Taoro, M., Peverini, O. A., Piacentini, F., Piccirillo, L., Pisano, G., Poletti, D., Presta, G., Realini, S.,Reyes, N., Rubino-Martin, J. A., Sand ri, M., Sartor, S., Pezzotta, F., Polenta, G., Rocchi, A., Schillaci,A., Signorelli, G., Siri, B., Soria, M., Spinella, F., Tapia, V., Tartari, A., Taylor, A. C., Terenzi, L., Tomasi,M., Tommasi, E., Tucker, C., Vaccaro, D., Vigano, D. M., Villa, F., Virone, G., Vittorio, N., Volpe, A.,15atkins, R. E. J., Zacchei, A., and Zannoni, M., “The large scale polarization explorer (LSPE) for CMBmeasurements: performance forecast,” arXiv e-prints , arXiv:2008.11049 (Aug. 2020).[20] Bean, C. P., “Magnetization of High-Field Superconductors,” Reviews of Modern Physics , 31–38 (Jan1964).[21] Columbro, F., de Bernardis, P., and Masi, S., “A clamp and release system for superconductive magneticbearings,” Review of Scientific Instruments (Dec 2018).[22] de Bernardis, P., Columbro, F., Masi, S., Paiella, A., and Romeo, G., “A simple method to measure thetemperature and levitation height of devices rotating at cryogenic temperatures,” Rev. Sci. Instrum. (4),045118 (2020).[23] Pisano, G., Savini, G., Ade, P. A. R., and Haynes, V., “Metal-mesh achromatic half-wave plate for use atsubmillimeter wavelengths,” Journal of Applied Physics , 6251 (Nov. 2008).[24] Pisano, G., Ng, M., Haynes, V., and Maffei, B., “A broadband metal-mesh half-wave plate for millimetrewave linear polarisation rotation,” in [ Progress In Electromagnetics Research M ], , 101–114 (2012).[25] Pisano, G., Tucker, C., Ade, P. A. R., Moseley, P., and Ng, M. W., “Metal mesh based metamaterials formillimetre wave and thz astronomy applications,” in [ ], 1–4 (2015).[26] Pisano, G., Ritacco, A., Monfardini, A., Tucker, C., Ade, P. A. R., Shitvov, A., Benoit, A., Calvo, M.,Catalano, A., Goupy, J., Leclercq, S., Macias-Perez, J., Andrianasolo, A., and Ponthieu, N., “Developmentand application of metamaterial-based Half-Wave Plates for the NIKA and NIKA2 polarimeters,” arXive-prints , arXiv:2006.12081 (June 2020).[27] Salatino, M., de Bernardis, P., and Masi, S., “A cryogenic waveplate rotator for polarimetry at mm andsubmm wavelengths,” A & A , 1–8 (2011).[28] Columbro, F., “Development of the polarization modulator and multi-mode receivers for the search of CMBpolarization,” Memorie della Sait (2021).[29] Duthil, P., “Material Properties at Low Temperature,” arXiv e-prints , arXiv:1501.07100 (Jan. 2015).[30] Reitz, J. R., “Forces on Moving Magnets due to Eddy Currents,”
Journal of Applied Physics , 2067–2071(Apr. 1970).[31] Davis, L. C., Logothetis, E. M., and Soltis, R. E., “Stability of magnets levitated above superconductors,” Journal of Applied Physics , 4212–4218 (Oct. 1988).[32] Columbro, F., Battistelli, E. S., Coppolecchia, A., D’Alessandro, G., de Bernardis, P., Lamagna, L., Masi, S.,Pagano, L., Paiella, A., Piacentini, F., and Presta, G., “The short wavelength instrument for the polarizationexplorer balloon-borne experiment: Polarization modulation issues,” Astronomische Nachrichten , 83–88(Jan 2019).[33] Essinger-Hileman, T., Kusaka, A., Appel, J. W., Choi, S. K., Crowley, K., Ho, S. P., Jarosik, N., Page,L. A., Parker, L. P., Raghunathan, S., Simon, S. M., Staggs, S. T., and Visnjic, K., “Systematic effectsfrom an ambient-temperature, continuously rotating half-wave plate,”
Review of Scientific Instruments87