PROGRESS OF THE NOVEL SPIRAL INJECTION TEST EXPERIMENT∗M. A. Rehman† , SOKENDAI (The Graduate University for Advanced Studies),
Kanagawa 240-0193, Japan
H. Iinuma, Ibaraki University, Mito, Ibaraki, Japan
S. Ohsawa, H. Nakayama, H. Hisamatsu, K. Furukawa, T. Mibe, High Energy Accelerator ResearchOrganization, 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan
Abstract
A new muon g – 2/EDM experiment at J-PARC (E34)
is under preparation in order to resolve a 3 σ discrepancyof muon anomalous magnetic dipole moment between themeasurement and the standard model prediction. The E34
experiment will employ a unique three-dimensional spiralinjection scheme in order to store the muon beam into a small
storage orbit. In order to demonstrate the feasibility of thisnovel injection scheme, the Spiral Injection Test Experiment(SITE) with the electron beam is under construction at KEK
Tsukuba campus. The goals of the SITE are divided into twophases. In the ﬁrst phase of the SITE, 80 keV DC electron
beam was injected and detected as a ﬂuorescent light due tothe de-excitation of the nitrogen gas into solenoidal storage
magnet. In the second phase of the SITE, the pulsed electron
beam, and a pulsed magnetic kicker are developed in order tokeep the pulsed beam on the very midplane of the solenoidal
storage magnet. This paper describes the achievements of
the ﬁrst phase of the SITE and progress towards the secondphase.

INTRODUCTION
The muon’s anomalous magnetic moment is one of mostimportant measurement in elementary particle physics. The
recent measurement of muon g – 2 results a 3 σ [1] discrepancy with the equally precise standard model prediction.
The new J-PARC muon g – 2/EDM (E34) is under preparation to resolve current discrepancy. The E34 experiment isaiming to measure muon’s g – 2 to the precision of 0.1 ppm
and EDM down to the sensitivity of 10−21 e.cm [2].
The key idea to measure muon g – 2 is to store polarized
muon beam in a magnetic ﬁeld and measure the evolutionof spin precession vector with respect to time. In E34 a low
emittance muon beam of momentum 300 MeV/c from muon
accelerator will be injected into a 3-T Magnetic ResonanceImaging(MRI)-type solenoid magnet in order to store themuon beam in 0.66-m diameter orbit. In order to enhance
injection eﬃciency and overcome technical challenges related to small storage orbit, a new three-dimensional spiralinjection scheme is under development to inject the muon
beam into MRI type storage magnet. Figure 1 shows thebasic concept of a three-dimensional spiral injection scheme.
The details and recent updates of three-dimensional spiralinjection scheme can be found in [3–5].
∗ Work supported by “Grant in Aid” for Scientiﬁc Research, JSPS (KAK-ENHI#26287055)† rehman@post.kek.jp

The three-dimensional spiral injection scheme is an unproven idea, therefore, a demonstration experiment to prove
the feasibility of this unique scheme is inevitable. A scale
down Spiral Injection Test Experiment (SITE) by the useof electron beam is under development at KEK Tsukuba
campus. This paper will describe the development of thespiral injection scheme test experiment (SITE).

Figure 1: Layout of three-dimensional spiral injection
scheme.

SPIRAL INJECTION TEST EXPERIMENT(SITE)
The SITE setup contains a 2 m long straight beamline, asolenoid storage magnet to store the electron beam and forty
degrees bend section to guide the electron beam towards thestorage magnet. A triode type thermionic electron gun with
LaB6 cathode is used to generate the DC electron beam of
80 keV with current in the range of few μA.
After the electron gun, a magnetic lens is placed to focus
the low energy beam. A pair of steering coils also has beenplaced to control the transverse position of the beam. An
electric chopper system has been placed after the electron
gun to produce the pulsed beam. Details of the electricchopper can be found in [6]. A collimator of diameter 3
mm and depth 5 mm is placed after the electric chopper.
The collimator is served as the beam dump for the chopper
system and also used to create the diﬀerential vacuum system
for the gas monitor in the storage magnet.
A bending magnet (BM1) is placed on the straight beamline to deﬂect the beam at forty degrees towards the storage
magnet. A second bending magnet (BM2) is also placednear the injection point in order to control the injection angleslightly. Air core quadruple magnets have been placed ona bend section to create required beam phase space for thespiral injection.
A pulsed magnetic kicker is also under development inorder to keep the beam to the very center of the storage

Air core quadrupole magnets have been mounted on thebend section in order to create required beam phase space.
The details calculation of TWISS and coupling parameters
can be found in [3].

Figure 2: (a) A diagram showing the 3D schematic of spiralinjection test experiment. (b) The schematic of the storagemagnet with monitors and reference trajectory.

magnet. The kicker system for the SITE will be discussed in
the forthcoming sections. The details about each device on
the straight beamline of SITE can be found in [7]. The layoutof the SITE experimental setup is shown in Fig. 2 (a). The
schematic of the storage magnet with a reference trajectoryand monitors are shown in Fig. 2 (b). A comparison ofparameters between SITE and E34 is given in Table 1.
Table 1: Comparison of Parameters between E34 and SITE.
Parameters
Magnetic ﬁeld strength
Momentum
Cyclotron Period
Storage orbit diameter

E343T
300 MeV/c
7.4 ns0.66 m

SITE
0.0082 T
0.296 keV/c
5 ns
0.24 m

In the ﬁrst phase of the SITE, DC electron beam wasdetected as ﬂuorescent light. In the SITE nitrogen gas monitor was used to detect the DC electron beam spiral track inthe storage magnet’s vacuum chamber. In the gas monitor,
diﬀerential vacuum pumping has been employed to detect
electron beam as a ﬂuorescent light due to the nitrogen gas
de-excitation along the beam path. The details of beam
detection in the storage magnet can be found in [7].

BEAM PHASE SPACE FOR SPIRALINJECTION
The radial fringe of the solenoid storage magnet requiresa strongly XY-coupled beam. In Fig. 3 above four plots
are showing the beam phase space at the matching point
Z = −500 mm from the center of the storage magnet. The
matching point lies outside of the storage magnet. Blackpoints show the uncoupled beam (ideal parallel beam) andred points show the required coupled beam phase space. Thebottom two plots in Fig. 3 shows the beam injection without(black) and with coupled (red) beam. In the Fig. 3 bottom
left the beam start diverging vertically after Z = −100 mm
in the case of non-coupled beam whereas in the case of
appropriate coupled beam injection beam do not diverge
completely at Z = −100 mm.

Figure 3: The above four plots are the required phase spaceat the matching point (Z = −500 mm). The black points
show the beam phase space without coupling and red points
show with coupling. Bottom two plots are showing the beam
injection with and without coupled beam.

PULSED MAGNETIC KICKER
The pitch angle of the beam will be reduced to 0.018 raddue to the radial ﬁeld of storage magnet at Z = −100 mm.
At the Z = −100 mm, the vertical magnetic kicker will apply
the kick to guide the beam to the very center of the storage
magnet. The kicker ﬁeld can be deﬁned as follows

2π
Bkick = Bpeak SintTkick

(1)where Tkick is the duration of the kick and Bpeak represent
the peak kicker ﬁeld. The half sine shape has been considered for the kick, therefore, Tkick = T2 and T is total time
period.
After the kick, the beam will be stored under the weakfocusing ﬁeld. In the weak focusing ﬁeld the beam motion
will be oscillatory in the storage volume. The weak focusing
magnetic ﬁeld can be deﬁned as follows



z2



Δr+n 2r2rz
Br = − n B0r

Bz = B0 1 − n(2)(3)

where B0 (= 82.5 Gauss) is the main solenoidal ﬁeld atr = 12 cm, z =0 cm and Δr = r − r0 . Here n is ﬁeld indexz
n = − Br00 ∂B∂r . The radial and vertical focusing can beachieved if n < 1 and n > 0 respectively. Figure 4 is showing
the magnetic ﬁeld proﬁle of the SITE storage magnet withthe ﬁeld index value of n = 1 × 10−3 .

Figure 4: Left: Axial ﬁeld proﬁle of the storage magnet.
Right: Radial ﬁeld proﬁle of the storage magnet with weakfocusing index n = 10−3 .
Figure 5 (a) shows two kicker coil design for 2π and π/6cases. In the 2π conﬁguration of the kicker, the current inupper and lower coils are opposite to each other and they
produced cylindrical symmetric radial ﬁeld. The π/6 kicker
design can be realized by the rectangular dipole coil. In thecase of 2π kick shape the required kicker duration is Tkick =95/2 and Bkick = 70 mG. In the case of π/6 kick shape therequired kicker duration is Tkick = 95/2 and Bkick  1 G.

shows the reduction of the pitch angle due to the kicker ﬁeld(c) and storage of the beam in midplane (d).
The π/6 kicker coil shape has been optimized to reducethe inductance of coils. The optimization results in thecoils of height 175 mm, width 62 mm and the gap between
coils was 35 mm. The total inductance of optimized coils
in series has been estimated at 0.8 μH by using CST [8].
Figure 6 left shows the optimized π/6 coil shape and rightshows the magnetic ﬁeld map in radial and vertical directions.
The kicker coil excitation current was set to 10 A for thesimulation. The details of the pulsed magnetic kicker canbe found in [9].

Figure 6: Left:Optimized π/6 kicker model. Right: Magnetic ﬁeld map in radial and vertical directions. The exciting
current of the coil was set to 10 A.
The pulsed current power supply for the magnetic kickeris also under development. The schematic of an electronic
circuit for the current power supply is shown in Fig. 7.
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Figure 7: Top: The schematic electronic circuit for thepulsed magnetic kicker. Bottom: The pulsed current throughkicker coil.
Figure 5: (a) Two models of the magnetic kicker. (b) Magnetic ﬁeld proﬁle for the 2π and π/6 kicker model. The
required magnitude of magnetic ﬁeld increase in the caseof π/6 kicker model due to a limited region. (c) The pitch
angle starting from the injection point to the storage region
as a function of the vertical position (Z). (d) Pitch angle in
the kicker and storage region.
Both types of kicker will be tested in SITE in order to ﬁnd
the best shape for the kicker. The bottom two plots in Fig. 5CONCLUSION
A new three-dimensional spiral injection is under development by using the electron beam in order to realize new
J-PARC’s muon g – 2/EDM experiment. An electron beamline and storage magnet has been constructed for the SITE.
The electron beam in the storage magnet was conﬁrmed
as ﬂuorescent light due to the de-excitation of nitrogen gas
in the storage magnet. The required beam phase space forthe spiral injection has been calculated. A pulsed magnetic

kicker and the power supply is under development to guidethe pulsed beam at the midplane of the storage magnet. Particle tracking studies have been carried out with the diﬀerent
shapes of the kicker in the kicker and weak focusing ﬁeld inorder to ﬁnd the appropriate magnetic ﬁeld and time period
for a kicker.

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Dipole moment at J-PARC (2011)”[5] H. Iinuma et al., “Development of three-dimensional spiralbeam injection scheme with X–Y coupling beam for MRI sizedcompact storage ring” in Proc. of PASJ2018, paper WEOM07.
[6] M.A. Rehman et al., “Development of the three-dimensional
injection spiral injection by using electron beam for muon g –2 experiment” in Proc. of the 14th Annual Meeting of Particle
Accelerator Society of Japan (PSAJ’17), Sapporo, Japan, Aug.
2017, paper WEOM01.
[7] M.A. Rehman et al., “Test experiment of 3-D spiral injection
scheme using electron beam for new g – 2/edm experimentat j-parc” in Proc. of the 13th Annual Meeting of Particle
Accelerator Society of Japan (PSAJ’16), Chiba, Japan, Aug.
2016, paper TUP056, pp. 1004–1007.

[3] H. Iinuma et al., “Three-dimensional spiral injection scheme
for the g – 2/EDM experiment at J-PARC” Nucl. Instr. Meth.,Vol. A832, pp. 51-62, 2016.

[8] http://www.cst.com[4] H. Iinuma et al., “Three-dimensional spiral injection for acompact storage ring” in Proceedings of IPAC2018, Vancouver,BC, paper TUPML060.

[9] M.A. Rehman et al., “Development of the pulsed magnetic
kicker for the spiral injection test experiment” in Proc. ofPASJ2018, paper THP006.