Proceedings of the 12th Annual Meeting of Particle Accelerator Society of Japan
August 5-7, 2015, Tsuruga, Japan

PASJ2015 WEOM02

DEMONSTRATION OF MUON ACCELERATION AND CAVITY DESIGNOF THE MUON LINAC FOR J-PARC E34
M. Otani, T. Mibe, M. Yoshida, KEK, Tsukuba, Japan
N. Saito, J-PARC/KEK, Tokai, Japan
R. Kitamura, The University of Tokyo, Tokyo, JapanY. Iwashita, KUICR, Kyoto University, Kyoto, JapanY. Kondo, J-PARC/JAEA, Tokai, Japan
Abstract
We are developing a linac dedicated to the muon acceleration. It enables us to measure the muon anomalous magneticmoment with an accuracy of 0.1 ppm and search for the muon
electric dipole moment with a sensitivity of 10−21 e · cm
to explore beyond Standard Model of elementary particle
physics. As a first step for demonstration of the muon acceleration, we are developing the source of slow muons withwhich RFQ acceleration is conducted. In order to cover themiddle beta ( β ∼ 0.3 − 0.7) section of the muon LINAC,
disk and washer coupled cell LINAC is employed and theDAW cell being designed now. This paper describes statusof these developments.

INTRODUCTIONThough the discovery of Higgs at LHC completed theparticles predicted in Standard Model (SM) of elementary
particle physics, some observations such as dark matter existence indicate new physics beyond SM at some energy scale
or interaction scale. One of the clues for new physics isanomaly of the muon anomalous magnetic moment (g − 2) µ; There is a ∼ 3 σ discrepancy between the SM prediction
and the experimental value measured by E821 with a precision of 0.54 ppm [1]. Measurement with higher precision(0.1 ppm) is necessary to confirm this anomaly.
It should be also noted that measurements up to now relyon the technique of the magic momentum. Because themuon beam generated from the secondary pions in flight haslarge emittance, focusing with the electric field in addition
to the magnetic field is necessary in the storage ring. The
spin precession vector of muon is written by~ η~ e ~1  β~ × E~ B+~ E  (1)~ = − a µ B−ωaµ − 2+ β×mc2c
γ −1where e is the elementary charge, m is the muon mass, a µ is
the anomalous magnetic moment, γ is the Lorentz Factor, βis the ratio of particle velocity to the speed of light c, and η
is the electric dipole moment. The second term dependingon the electric field is eliminated when the muon momentumis 3.094 GeV/c, so called magic momentum. Measurementwith a new method should be surveyed for verification ofthe (g − 2) µ anomaly.
The muon electric dipole moment (EDM) is also sensitive
to new physics because it is strongly suppressed in SM (10−38e·cm), and violates CP symmetry assuming the CPT theorem.

In addition to that, there is a possibility that anomaly of(g − 2) µ can be explained by finite EDM with an order of
10−20 e·cm [2], whereas current direct limit is 1.9 × 10−19e·cm [3].
The E34 experiment [4] aims to measure (g − 2) µ with a
precision of 0.1 ppm and search for EDM with a sensitivity
to 10−21 e·cm by utilizing high intensity proton beam at JPARC and newly developed novel technique of the ultra-coldmuon beam. Figure 1 shows the experimental setup. Theexperiment utilizes the proton beam from the 3 GeV Synchrotron ring to Materials and Life Science facility (MLF).
The proton beam is injected to the graphite target. The
generated surface muons are extracted to one of the muon
beamline of H-line. Surface muons stop in the muonium(µ+ e− , Mu) production target of the silica aerogel and thenform thermal muoniums. The paired electron in the muonium is knocked out by laser and thermal muon (3 keV/c) isgenerated. Then the muon is accelerated up to 300 MeV/c
and injected to the storage ring supplying 3 T. The decay
positron is detected by the silicon strip tracker and the spin
precession frequency is obtained from variation of counting
rate of the decay positron.
Thanks to the ultra-cold beam (σ pT /p = 10−5 ) wherepT is the transverse momentum of the beam particles, theelectric focusing is not necessary anymore. Eq. 1 becomes~ =−ωe ~ η ~ ~ aµ B +β × B)
m2(2)Because the anomalous magnetic moment and EDM are perpendicular each other, these can be measured simultaneously.
One of the milestones for the experiment is verificationof the muon acceleration, which will be the first case in
the world. To suppress muon loss in the acceleration, themuon should be accelerated in a sufficiently short period. Torealize the fast acceleration, a linac dedicated to the muonis being developed [5]. Figure 2 shows conceptual designof the muon LINAC. The slow muons are generated in theelectric potential of 5.6 keV which corresponds to the input
energy of radio-frequency quadruple (RFQ). The spare for
the J-PARC LINAC RFQ, so called RFQ II [6,7], will be used
for the muon LINAC. After RFQ, Interdigital H-type (IH)
DTL will be used to accelerate muon from β = 0.08 to 0.27.
Then disk and washer (DAW) coupled cavity is employed toβ = 0.7 and then disk loaded structure accelerates muons
up to 212 MeV/c.

- 56 -Proceedings of the 12th Annual Meeting of Particle Accelerator Society of Japan
August 5-7, 2015, Tsuruga, Japan

PASJ2015 WEOM02

J-PARC proton beam
Lyman α laser

storage ring

Mu production target
detector
Figure 1: Schematic view of E34.
As a demonstration of the muon acceleration, we are planning to accelerate muons with electro-static field and RFQ II.
Next section describes development of the muon source andRFQ for that test. Following section shows current status of
the following RF cavity design, especially for DAW. Development of the RF cavity for low and high β section can befound elsewhere [8, 9]. Other experimental developments
such as decay positron detector can be found on [10–12].

Surface muon beam
Al for Mu- production

Detectors

Electro-static lensElectric quadrupoles

Electric deflector

E = 5.6 keV
β = 0.01
E static.

0.34 MeV
0.08
RFQLow β: IH

4 MeV
0.27

42 MeV
0.7Middle β: DAW~35m

212 MeV
0.95

High β: Disk loaded

Figure 3: Experimental setup for the Mu− emission measurement at the J-PARC MLF muon beamline.

Injection tostorage ring

Figure 2: Conceptual design of the muon LINAC.

MUON ACCELERATION WITH RFQ
In order to conduct muon acceleration with RFQ, slow
muon source is being developed. One of the promising
candidates is negative muonium (µ+ e− e− , Mu− ) or slow
muon emission by injecting the surface muon beam to a thinmetal foil. Previous experiment observed Mu− and slow
muon emission from an Al foil [13] with average energyof 0.2 ± 0.1 keV and few keV, respectively, which can beinjected to the RFQ II whose injection energy is 5.6 keV.
The measurement of the Mu− or slow muon emission efficiency and its kinematics was proposed and approved inJ-PARC MLF. Figure 3 shows the experimental setup of themeasurement. Surface muons are injected into the Mu− production target. The emitted Mu− is accelerated and focusedby the electro-static lens and transported to the detector
chamber by following electro-static quadrupoles and electrostatic deflector. The Micro-Channel-Plate (MCP) [14, 15] isused for counting and timing measurement of Mu− and surrounding plastic scintillators for the decay-positron detection.

Figure 4 shows expected MCP timing distribution estimated by the GEANT4 simulation. In the simulation, theMu− signals are generated at the Mu− target with kinetic
energy of 0.2 keV and beam related backgrounds are estimated by injecting the beam muons towards the target.
Backgrounds mainly consist of decay-positrons from thebeam muons stopped around the target and the deflector,
which can be reduced effectively by lead shields around thetarget chamber and the collimator located on downstream ofthe deflector. The signal to background ratio is estimated tobe more than ten and clear separation between these can beachieved by observed timing as shown in Fig. 4.
The slow muon beamline has been assembled in J-PARC
MLF. It was originally developed and operated in RIKENRAL port-3 [16]. It successfully demonstrated transportation of the slow muon beam. After shutdown of the beamline,
some of the beamline components were moved to J-PARC
for the Mu− measurement in summer 2014. Assembly andcommissioning of all the equipments were completed byMay 2015 as shown in Fig. 5. Figure 6 shows one of thecommissioning results of the beamline; an Al plate installedat the Mu− target holder location is irradiated by UV lightand then generated photo-electrons are accelerated and trans-- 57 -Proceedings of the 12th Annual Meeting of Particle Accelerator Society of Japan
August 5-7, 2015, Tsuruga, JapanPASJ2015 WEOM02

ported to the MCP detector location. The photo-electron
events are observed successfully with nominal setup of thebeamline components. Though current setup for Mu− suffers background due to the field emission electrons fromthe electro-static lens electrodes, the setup for slow muon
setup can be operated stably. Upgrade such as a magnetic
equipment installation to separate the field emission electronfrom Mu− is being discussed.
In conclusion, all the equipments are ready for slow muon
measurement.

In order to verify the RFQ II operation and measure thebackground from the RF field with MCP, the RFQ offline test
was performed in June 2015 in the J-PARC LINAC building.
Figure 7 shows photo of the RFQ offline test setup. TheMCP detector chamber is connected to the RFQ downstream.
Vacuuming is done with an ion pump and reach 10−6 Pa.
Figure 8 shows the RFQ operation setup. The RFQ is powered on by low RF source and solid state amplifier up to 6
kW and 25 Hz repetition. The forward, reflection waves and
RFQ internal power are monitored by power meters.

events/0.020usec

Expected timing distribution with 1 day10RFQ II(upstream)-Mu Signal(6.7 Hz)5+

decay e from Mu(downstream)

MCPchamber-+

BGx10 (decay e )(0.05±0.01 Hz)

104
RF in

103

0Ion pump

1

23usecFigure 4: Expected timing distribution estimated by theGEANT4 simulation.

Figure 7: Photo of the RFQ offline test at the J-PARC LINAC
building.

RF source

Pulse gen.

Agilent 8662A

STARNFORT
Research DG535

RF switchControl lack

SPST RF SWITCH 324 MHz

Main chamber
EQ pairEB

RF ampGiga-tronics 8542c

Power meter
Power meter

Collimator &EQ pairPower meter
RFQ

MCP chamber

controllerFigure 8: Setup of the RFQ operation.
Figure 5: Mu− beamline assembly.

Figure 6: Result of the beamline commissioning. Horizontal
axis is set voltage of the electro-static bending apparatus
and vertical axis is number of observed events by the MCP
detector. Number of events has maximum at expected value
from accelerated energy.

Figure 9 shows frequency dependence of the forward andreflection power and its ratio. The measured value is wellconsistent with designed value and previous measurement.
Figure 10 shows the forward, reflection and pick-up powerin RFQ with nominal power (5 kW) operation. Rising timeis well consistent with expectation from Q factor. Figure 11
shows result of the MCP background measurement. Because
the slow muon beam intensity in the first stage of the acceleration test is expected to be several counts per second, it
is necessary to measure background level with comparable
accuracy to that. Though it was expected that there might
be background events due to electron or X-ray excited by RF
field, all the measurements are consistent each other within
statistical error of about 0.1 Hz and no background events
are observed.
In conclusion, RFQ is successfully operated and accelerated muons can be measured by MCP without beam related
background.

- 58 -Proceedings of the 12th Annual Meeting of Particle Accelerator Society of Japan
August 5-7, 2015, Tsuruga, JapanW

PASJ2015 WEOM02

1200

0.16

for.

0.14

back.

1000

loss.

0.12

800

0.1

600

0.08
0.06

400

0.04

200323.8

0.02

323.82 323.84 323.86 323.88

323.9

0323.92

MHzFigure 9: Forward and reflection power as a function of input
wave frequency.

ForwardBackward
RFQ intimized by calculating acceleration and coupling mode withSUPERFISH. Variable parameters are disk radius (Td ), disk
thickness (Td ), washer radius (Rw ) and gap between washer(G) as shown in red characters in Fig. 12. Optimization
process is done by the SIMPLEX algorithm and the optimization function is constructed with confluent condition( f a = f b ), higher shunt impedance (ZTT), and uniformity of
the acceleration field. After optimization in two dimensionalmodel three dimensional model with the washer supports
is constructed based on the optimized dimensions with the2-D code, with which resonant modes around operation frequency of 1.3 GHz are calculated in CST MICROWAVESTUDIO. Here the connection radius of the supports is decided to be the zero-electric point to minimize perturbation
to the accelerating mode. In addition, the disk radius withand without the supports are slightly modified to recover theperiodic feature of the acceleration field. The three dimensional model is also optimized by using same optimization
function as two dimensional one. Finally the dispersion
curve is investigated to check whether unfavored mode exists or not around the operation frequency. All the steps arerepeated in several cavity lengths of βλ/4.

Figure 10: Forward, reflection wave and pick-up power in
RFQ with nominal power of 5 kW.

Lc

MCP count rate[Hz]

TdTw

Rc

2RdG
Rn10

no RF

5kW, 20usec,25Hz rep.

6kW, 20usec,25Hz rep.

Rw
θRt

Rb

Figure 12: Two dimensional model of the DAW cavity andnotations of the dimensions. Red characters are variable
parameters in the optimization process.

6kW, 40usec,25Hz rep.

Figure 11: Result of the MCP background measurement. All
the measurements are consistent each other within statisticalerror.

DEVELOPMENT OF THE MIDDLE βSECTION
In the middle beta section ( β = 0.3 ∼ 0.7), the DAWcavity will be employed [17]. It has high effective shunt
impedance and high degree of coupling between adjacent
RF cells. In order to solve the mode overlapping problem, abi-periodic L-support structure is employed [18].
It is necessary to design our DAW cavity because muon
acceleration is the first time in the world and the DAW cavity covering such a wide range of velocity is also the firsttime. In order to achieve higher acceleration gradient, thecavity design is optimized as follows. First, two dimensionalmodel without the washer supports as shown in Fig. 12 is op-Figure 13, Fig. 14 and Tab. 1 show the dispersion curve,
optimized model and optimized parameters, respectively,
with β = 0.3, 0.4, 0.5 and 0.6. Because of bi-periodic structure, some stop bands appear in π/2. Though TM11 mode isnear to the operational frequency, the cavity is tuned in theoptimization process so that the operational frequencies sitin the stop band at π/2. Though the dipole mode passband
TE11 crossed the line where the phase velocity matches thespeed of muons, it is considered to be no problem because
the muon beam current is negligibly small and transverse
kick due to this mode is estimated to be much smaller thanour requirement.
In conclusion, we completed design of the DAW cavity
based on computer calculator. We are planning to fabricate
a cold model made by Al and measure resonant frequencies
and fields to confirm the calculation result.

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Proceedings of the 12th Annual Meeting of Particle Accelerator Society of Japan
August 5-7, 2015, Tsuruga, JapanPASJ2015 WEOM020.6

Figure 13: Dispersion curve with optimized cavity in several β calculated by CST MICROWAVE STDUIO.

β = 0.3

Table 1: Parameters of the Optimized DAW Cavity.

β = 0.4ββ = 0.5

L
Rb [mm]Rn [mm]Tw [mm]θ[deg.]
Rc [mm]Rd [mm]Td [mm]Rw [mm]G[mm]fa [GHz]fc [GHz]ZTT[MΩ/m]

β = 0.6

0.3

155
111.3
16.014105.969
15.975
1.300
1.299
57.8

0.4

0.5

0.6

βλ/4
122.6
3.5
30
157
154
108.352 104.52
14.79010.97
105.63 108.14
11.285 7.8976
1.300
1.299
1.301
1.302
46.3
33.8

151
103.2219.630
110.391
6.148
1.301
1.301
18.0

REFERENCES

Figure 14: Optimized three dimensional models in CSTMICROWAVE STUDIO.

[1] G.W. Bennett et al.: Phys. Rev.D73 (2006) 072003.
[2] J.L. Feng et al.: Nucl. Phys. B613 (2001) 366.
[3] G.W. Bennett et al.: Phys. Rev. D80 (2009) 052008.

SUMMARY[4] J-PARC E34 conceptual design report (2011).

Muon acceleration is required for precision measurementof muon g-2 and EDM with ultra-cold muon beam. We areready for demonstration of muon acceleration with RFQ;
slow muon beamline has been completed and RFQ II isavailable in J-PARC. Design of the DAW cavity has been
completed and cold model measurement is planned. The
E34 collaboration submitted Technical Design Report andaims to start physics data taking in 2019.

ACKNOWLEDGMENT
It is a pleasure to thank MLF Muon Section people forhelping assembly of the slow muon beamline. We would liketo thank J-PARC LINAC group for RFQ offline test. This
work was supported by JSPS KAKENHI Grant Numbers
25800164, 15H03666.

[5] M. Otani et al.: Proc. of IPAC2015, WEPWA023 (2015).
[6] Y. Kondo et al.: Phys. Rev. ST Accel. Beams 16. 040102(2013).
[7] Y. Kondo et al.: Proc. of IPAC2015, THPF045 (2015).
[8] K. Saito, Master Thesis, Tokyo Tech., (2012).
[9] M. Yoshida, Proceedings for IPAC 2015.
[10] M. Otani for the E34 collaboration, Proceedings for the JPARC symposium 2014.
[11] S. Nishimura for the E34 collaboration, Proceedings for theJ-PARC symposium 2014.
[12] G.A. Beer et al.: Prog. Theor. Exp. Phys., 091 (2014) C01.
[13] Phys. Rev. A39. 6109.
[14] http://www.hamamatsu.com/resources/pdf/etd/
MCPassy_TMCP0001E.pdf- 60 -

Proceedings of the 12th Annual Meeting of Particle Accelerator Society of Japan
August 5-7, 2015, Tsuruga, Japan

PASJ2015 WEOM02[15] R. Kitamura, Master Thesis, Tokyo Univ., (2014).
[16] NIM B266 (2008) 335.
[17] M. Otani et al., PASJ 2014 (2014) SAP039.
[18] Hiroyuki Ao et al., Jpn. J. Appl. Phys. Vol. 39 (2000) 651-656.

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