Compact buncher cavity for muons accelerated by a radio-frequency quadrupole
M. Otani, Y. Sue, K. Futatsukawa, T. Iijima, H. Iinuma, N. Kawamura, R. Kitamura, Y. Kondo, T. Morishita, Y. Nakazawa, H. Yasuda, M. Yotsuzuka, N. Saito, T. Yamazaki
CCompact buncher cavity for muons accelerated by a radio-frequency quadrupole
M. Otani, ∗ Y. Sue, † K. Futatsukawa, T. Iijima, H. Iinuma, N. Kawamura, R. Kitamura, Y.Kondo, T. Morishita, Y. Nakazawa, H. Yasuda, M. Yotsuzuka, N. Saito, and T. Yamazaki High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan Nagoya University, Nagoya, Aichi 464-8602, Japan Ibaraki University, Mito, Ibaraki 310-8512, Japan Japan Atomic Energy Agency (JAEA), Tokai, Naka, Ibaraki 319-1195, Japan University of Tokyo, Hongo, Tokyo 171-8501, Japan J-PARC Center, Tokai, Naka, Ibaraki 319-1195, Japan
A buncher cavity has been developed for the muons accelerated by a radio-frequency quadrupolelinac (RFQ). The buncher cavity is designed for β = v/c = 0 .
04 at an operational frequency of324 MHz. It employs a double-gap structure operated in the TEM mode for the required effectivevoltage with compact dimensions, in order to account for the limited space of the experiment.The measured resonant frequency and unloaded quality factor are 323.95 MHz and 3 . × ,respectively. The buncher cavity was successfully operated for longitudinal bunch size measurementof the muons accelerated by the RFQ. I. INTRODUCTION
Muon linacs have been studied for their potential ad-vantages in various branches of science. After the muonsare cooled to thermal energy [1, 2], the muons are accel-erated to the specific energy required by an applications.One of the applications of accelerated muon beams is thetransmission muon microscope [3], which is used in mate-rials and life sciences. If the muons are accelerated up to10 MeV, it enables three-dimensional imaging of livingcells, which is impossible with the use of transmissionelectron microscope. Another application of the muonlinac is the precise measurement of the muon anomalousmagnetic moment ( g µ −
2) and electric dipole momentat the Japan Proton Accelerator Research Complex (J-PARC E34) [4]. In the J-PARC E34 experiment, themuons are accelerated to 212 MeV by a series of accelera-tion cavities [5–9]. Recently muon acceleration to 89 keVusing a radio-frequency quadrupole linac (RFQ) [10] wasdemonstrated [11]. In order to reach the specific energyrequired for various applications, it is necessary to per-form additional acceleration with successive RF cavities.Beam matching between the RF cavities is extremely im-portant, as is the case with the linac for proton or ions, inorder to avoid substantial emittance growth. Especiallyin the muon linac for the J-PARC E34 experiment, thelongitudinal beam matching after the RFQ using bunchercavities is extremely important because a cavity followedby the RFQ adopts an alternative phase focusing (APF)scheme [12, 13]; there is a strong correlation betweenthe longitudinal and transverse directions in the APFscheme, and the longitudinal mismatch results in emit-tance growth in both the transverse and longitudinal di-rections.A buncher cavity has been developed for the muon ac- ∗ [email protected] † [email protected] celerated by the RFQ. The designed particle velocity β is0.04, and the operational frequency is 324 MHz, which isthe same as that of the RFQ. From among the differenttypes of room temperature cavities, a quater-wave res-onator with a double-gap is employed to account for thelimited space of the experiment. The buncher cavity forthe accelerated muons presented here has a unique fea-ture; it has a compact structure compared to the bunchercavities developed for protons or heavy ions [14–17]. Theresults presented in this paper are first demonstration ofthe buncher cavity dedicated for muons, which is essen-tial step to realize a new-generation muon beam discussedfor several applications [18–20]. The buncher cavity pre-sented here is an exotic one by reason of its compactness.It will stimulate new opportunities in the field.In this paper, we describe the design and results ofthe buncher cavity. In Sec. II, the designs and fabrica-tions are described. Section III is devoted to the resultsobtained in the RF measurements and operation. Theconclusions are presented in Sec. IV II. DESIGN AND FABRICATION
The buncher cavity is designed for measuring the lon-gitudinal bunch size after acceleration with the RFQ.The experiment was conducted at the J-PARC muonscience facility (MUSE) [21]. The J-PARC MUSE pro-vides a pulsed muon ( µ + ) beam with a 25-Hz repetitionrate. The muons are decelerated by an aluminum de-grader, and some portions form negative muonium (Mu − , µ + e − e − ). The Mu − ’s are extracted and accelerated to5.6 keV by an electrostatic lens [22]. They are then in-jected into the RFQ and accelerated to 89 keV. Then,the accelerated Mu − ’s are transported to a detector viaa diagnostic beamline.Figure 1 shows the layout of the diagnostic beamline.In previous experiments for the demonstration of muonacceleration [11] and profile measurement [23], the diag-nostic beamline consisted of a pair of quadrupole mag- a r X i v : . [ phy s i c s . acc - ph ] J u l nets (QM1 and QM2) and a bending magnet (BM). Inthis experiment for longitudinal bunch size measurement,a buncher cavity is added between the quadrupole mag-net and the bending magnet. A single-anode (SA) mi-crochannel plate (MCP, Hamamatsu photonics F9892-21 [24]) and multi-anode (MA) MCP detectors are placedat the downstream end of the straight line and 45 ◦ line,respectively. The SA-MCP detector measures the pene-trating µ + [11] for the beamline tuning. The MA-MCPdetector is used for the longitudinal bunch size measure-ment [25]. In order to focus the beam longitudinally, andmeasure the longitudinal beam properties, it is neces-sary to have a buncher cavity. Because there is a beam-dump just after the detectors, the available space for thebuncher cavity is approximately 150 mm. Mu - (89 keV)QM1 QM2 Buncher BM MA- MCP
SA-
MCP beam- dumpRFQ end
FIG. 1. Layout of the diagnostic beamline for the muon ac-celeration experiment using the RFQ.
The function of the buncher cavity is to provide suffi-ciently large effective voltage for the longitudinal bunchsize measurement with the available space. In order toestimate the required effective voltage, a series of simu-lations are performed. The muon beamline is simulatedusing g4beamline [26]. The conversion from µ + to Mu − is implemented using the data from a separate experi-ment [27]. The simulation of the electrostatic lens wasconducted using GEANT4 [28] in order to estimate notonly Mu − but also positrons generated from decay ofmuon stopped in the electrostatic lens. In the simula-tion, the electric field of the electrostatic lens was cal-culated using OPERA [29]. PARMTEQM [30] was em-ployed for the RFQ simulation because it can reproducedata well from the experience at the J-PARC linac. Forthe end cell section, PIC simulation with GPT [31], inwhich the electric field calculated with CST MW Stu-dio [32] was implemented, was employed to estimate theeffects due to the unequal spacing of the vanes at theend. TRACE3D [33] was used to design the beam op-tics and PARMILA [34] was employed to obtain particledistribution for the diagnostic beamline simulation.Figure 2 shows the simulated phase-space distributions at the MA-MCP detector location. The longitudinalbunch width is estimated to be 600 psec in rms, whichis sufficiently small compared to the detector sensitiv-ity [25]. On the basis of the simulaton, the required ef-fective voltage for the buncher is estimated to be 5.3 kV. (A) (B)(C) (D) RMS X 5.24RMS X’ 11.33 RMS Y 6.27RMS Y’ 17.31RMS T 0.59RMS ΔT 2.37
RMS X 5.24
RMS Y 6.27
FIG. 2. Calculated phase space distributions at the MA-MCPdetector location. (A) the horizontal divergence angle x (cid:48) vs x , (B) the vertical divergence angle y (cid:48) vs y, (C) ∆ W vs ∆ t ,and (D) y vs x. The red dotted circle in (D) represents theeffective area of the MA-MCP detector. The buncher cavity is designed using CST MW Stu-dio. Figure 3 shows the cutaway of the three-dimensionalmodel. The inner radius of the drift tube ( R b ) is deter-mined from the transverse beam size obtained from thesimulations. The fillet radius of the drift tube ( R fillet )is adjusted to make the surface field lower and then theouter radius of the drift tube ( R a ) is decided. The lengthsof the cavity, drift-tube, and gap ( L cav. , L dtl , and L gap )are designed with the particle velocity to account for thelimited space of the experiment. The stem dimensions( R stem , R stem , L stem ) are determined on the basis ofmechanical strength. The cavity radius ( R cav. ) is tunedso that the operational frequency is 324 MHz. The cavitydimensions are summarized in Table I.The RF parameters obtained using CST MW Studioare summarized in Table II. The power needed to supplythe required voltage is 0.21 kW, which is sufficiently smalland satisfies the requirement.In a QWR structure, a dipole field exists in the ac-celeration gaps [35]. The dipole field effect on the beamdynamics is investigated by using GPT. The dipole fieldeffect is negligible and the result is consistent to thatobtained from PARMILA. Because the effect is negligi-ble, conventional correction methods such as shifting theinner drift tube was not implemented. L cav. R cav. R b R a R fillet R1 stem R2 stem L stem L gap L dtl FIG. 3. Cutaway view of the three dimensional model of thebuncher cavity. TABLE I. Cavity dimensions
Dimensions Values [mm] R b R a R fillet L cav L dtl L gap R stem φ −
20 (ellipse) R stem φ L stem R cav TABLE II. RF parameters.
Parameters ValuesFrequency [MHz] 324.01Effective voltage [kV] 5.3 Q . × E pk [MV/m] 2.8Power dissipation [kW] 0.21 R sh [MΩ] 0.13of the cavity is oxygen-free copper (OFC, JIS C1020).The ISO KF40 duct and the side plate are attached byvacuum brazing. The transverse length of the bunchercavity is 450 mm, and the longitudinal length includingthe NW40 duct is 142 mm.Figure 5 shows the fabricated center plate. Three-dimensional measurement after fabrication showed thatthe fabrication had an accuracy of approximately0.05 mm. This fabrication error corresponds to 30 kHz. Side plate Center plateRF contactor rubbergasketNW40 duct
FIG. 4. Mechanical structure of the buncher cavity.FIG. 5. Center plate connected to a side plate.
III. RF MEASUREMENTS AND RESULTS
Measurements of the resonant frequency f and the un-loaded quality factor Q were performed using a VectorNetwork Analyzer (VNA). Table III shows the measuredand simulated values of f and Q . The measured reso-nant frequency is in good agreement with the simulatedone. The discrepancy of 0.02% between the measuredand simulated frequencies is considered to be due to theeffect of the loop-type of the RF pickup. The measured Q is about 99% of the simulated one. TABLE III. Resonant frequency and quality factor of thebuncher cavity.
Parameters simulation measurementResonant frequency (MHz) 324.01 323.95Quality factor 3 . × . × Figure 6 shows a bead pull measurement setup [36].A 3 mm diameter spherical metal bead on a fishingline is advanced by a motor driven pully. The value ofS21 is measured with the VNA while the metal beadis moving. The result of the phase shift measurementis shown in Fig. 7. The phase shift is proportional to ε E − µ H / ε is the permittivity, E isthe electric field, µ is the magnetic permeability, and H is the magnetic field. Two phase-shifting cycles are ob-served due to the double-gap. The measured phase shiftalong the z-direction is in excellent agreement with thesimulated one. Especially around the gap, the differenceis less than 4%, which is within the uncertainties of mea-surement due to the fishing line alignment and accuracyof the phase shift. VNA DAQ PCMotor driven pully pullyBuncher cavity bead Fishing line
FIG. 6. Bead pull measurement setup
The longitudinal bunch size measurement was per-formed for six days in November 2018. A loop-typeRF coupler was inserted into the side plate. TheRF pulse was generated by a Tektronix signal gener- ator TSG4104 [38], and then amplified by a 324-MHz5 kW solid-state amplifier unit, R&K CA324BW0.4-6767R(P) [39]. The RF power was transmitted via 50-Ωcoaxial cables. The RF pulse width was 100 µ s, and therepetition rate was 25 Hz; these were the same as thatof the muon beam. The relative phase of the RFQ wastuned by a trombone phase shifter with an accuracy ofless than 1 degree. The RF power and phase were moni-tored using a loop pickup monitor that was inserted intothe cavity.During measurement, the buncher cavity was success-fully operated. The relative phase shift between thebuncher cavity and the RFQ was stable within 1 degree.The pick-up power was stable within a few percent duringthe experiment. IV. CONCLUSION
A buncher cavity has been developed for the bunchsize measurement after muon acceleration by the RFQ.It is designed for β = 0 .
04 with a frequency of 324 MHz.It employs a double-gap structure operated in the TEMmode to account for the limited space of the experiment.The buncher cavity was designed using CST WMStudio. The cavity inner radius and total length are -20 0 20 ( d e g r ee ) fD datasim. z (mm)-20 0 20 d a t a - s i m . ( % ) -10-505 FIG. 7. Phase shift by the bead pull measurement. (Top)measured (green solid line) and simulated (black dotted line)phase shift. The red dotted line shows the gap region. (Bot-tom) difference between measurement and simulation. Q was about 99% of the simulated one.The buncher cavity was successfully operated for thelongitudinal bunch size measurement of muons acceler-ated by the RFQ. ACKNOWLEDGMENTS
We express our appreciation to TOTAL INTEGRA-TOR MACHINERY&ENGINEERING Co., who fab-ricated the buncher cavity. This work is supportedby JSPS KAKENHI Grant Numbers JP16H03987,18H05226, and JP18H03707. The experiment at theMaterials and Life Science Experimental Facility of J-PARC was performed under user programs (Proposal No.2018A0222). [1] P. Bakule et al., Design and RF test of MEBT bunchercavities for C-ADS Injector II at IMP, Nucl. Instru. Meth.B266, 335, 2008.[2] G.A. Beer et al., Enhancement of muonium emission ratefrom silica aerogel with a laser-ablated surface, Prog.Theor. Exp. Phys. 091, C01, 2014.[3] http://slowmuon.kek.jp/MuonMicroscopy_e.html [4] http://g-2.kek.jp/portal/index.html [5] Y. Kondo et al ., High-power test and thermal character-istics of a new radio-frequency quadrupole cavity for theJapan Proton Accelerator Research Complex linac, Phys.Rev. ST Accel. Beams 16, 040102, 2013.[6] Y. Kondo et al ., Simulation study of muon accelerationusing RFQ for a new muon g-2 experiment at J-PARC,Proc. of IPAC2015, 2015, THPF045, 2015[7] M. Otani et al ., Interdigital H-mode drift-tube linac de-sign with alternative phase focusing for muon linac, Phys.Rev. Accel. Beams, , 040101 (2016).[8] M. Otani et al ., Development of muon linac for themuon g-2/EDM experiment at J-PARC, in Proceedingsof IPAC2016 (Busan, Korea, 2016) pp. 1543 - 1546.[9] Y. Kondo et al ., Beam dynamics design of the muon linachigh-beta section, Journal of Physics: Conference Series , 012054 (2017)[10] Y. Kondo, K. Hasegawa, and A. Ueno, Fabrication andLow-Power Measurement of the J-PARC 50-mA RFQPrototype, in
Proceedings of LINAC2006 (Knoxville,Tennessee USA, 2006) pp. 749 – 751.[11] S. Bae et al. , First muon acceleration using a radio fre-quency accelerator, Phys. Rev. Accel. Beams , 050101,2018.[12] Good, M.L., Phase-reversal focusing in linear accelera-tors, Phys. Rev. 92, 538, 1953.[13] S. Minaev and U. Ratzinger, APF or KONUS drift tubestructure for medical synchrotron injectors – a compari-son, in Proceedings of 1999 PAC Conf pp. 3555.[14] Ki R. Shin et al , Double-gap rebuncher cavity design ofSNS MEBT, in
Proceedings of IPAC2012 (New Orleans,Louisiana, USA, 2006) pp. 3898 – 3900.[15] Ki R. Shin et al ., Feasibility of Folded and Double DipoleRadio Frequency Quadrupole (RFQ) Cavities for Parti-cle Accelerators, IEEE Transactions on Nuclear Sciences, , 2 (2014).[16] S. Huang et al ., Design and RF test of MEBT bunchercavities for C-ADS Injector II at IMP, Nucl. Instru. Meth.A799, 44, 2015.[17] Y. Yamazaki, “Technical Design Report of J-PARC”(KEK Report 2002-13); JAERI-Tech 2003-44 [18] H.M. Miyadere, A. J. Jason, K. Nagamine, Design ofMuon Accelerators for an Advanced Muon Facility, in Proceedings of PAC 07 (Albuquerque, New Mexico, USA,2007) pp. 3032-3034. [19] J. S. Berg et al ., Cost-effective design for a neutrino fac-tory, Phys. Rev. Accel. Beams 9, 011001, 2006.[20] M. Yoshida, et al ., Re-acceleration of Ultra Cold Muonin J-PARC MLF, in
Proceedings of IPAC 15 (Richmond,VA, USA, 2015) pp. 2532-2534 .[21] W. Higemoto, R. Kadono, N. Kawamura, A. Koda, K.M.Kojima, S. Makimura, S. Matoba, Y. Miyake, K. Shi-momura and P. Strasser, Materials and Life Science Ex-perimental Facility at the Japan Proton Accelerator Re-search Complex IV: The Muon Facility, Quantum BeamSci. , 1(1), 11.[22] K. F. Canter et al. , in “Positron studies of solids, surfacesand atom” (World Scientific, Singapore, 1986) p. 199.[23] M. Otani et al ., Muon Profile Measurement After Ac-celeration With a Radio-Frequency Quadrupole linac, J.Phys. :Conf. Ser. , 052018 (2018).[24] Hamamatsu Photonics K. K., [25] Y. Sue et al ., Development of the good time resolutionmonitor to measure the longitudinal structure of low-ratemuon bunch for J-PARC E34 Experiment, in
Proceedingsof PASJ2018 (Nagaoka, Japan, 2018) pp. 1051 - 1054.[26] G4beamline, http://public.muonsinc.com/Projects/G4beamline.aspx [27] R. Kitamura et al ., First trial of the muon acceleration forJ-PARC muon g-2/EDM experiment, Journal of Physics:Conference Series , 012055 (2017).[28] Geant4, http://geant4.cern.ch/ [29] OPERA3D, Vector Fields Limited, Oxford, England., https://operafea.com/ [30] K. R. Crandall et al. , “RFQ Design Codes,” LA-UR-96-1836 (1996).[31] General Particle Tracer, Pulsar Physics. [ ][32] CST Studio Suite, Computer Simulation Technology(CST). [ ][33] K.R. Crandall and D.P. Rustoi, “TRACE 3D Documen-tation”, Los Alamos Report, No. LA-UR-97-886, 1997.[34] Los Alamos Accelerator Code Group (LAACG), LANL,Los Alamos, [ ].[35] P.N. Ostroumov, K.W. Shepard, Correction of beam-steering effects in low-velocity superconducting quarter-wave cavities, Phys. Rev. Accel. Beams Cavities at Daresbury.[37] Klein, H., CERN Accelerator School on RF Engineeringfor Particle Accelerators, CERN 92-03, Vol. 1, 1992, p.115. [38] Tektronix Inc., [39] R & K Co. Ltd.,[39] R & K Co. Ltd.,