DEVELOPMENT OF THE PULSED MAGNETIC KICKER FOR THE
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 Research
Organization, 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 sigma discrepancy of muon anomalous magnetic dipole moment between the measurement and the standard model prediction.
The E34 experiment will employ a unique three-dimensional spiral injection scheme in order to store the muon
beam into a small storage orbit. In order to demonstrate thefeasibility of novel injection scheme, the Spiral Injection
Test Experiment (SITE) with the electron beam is underconstruction at KEK Tsukuba campus. In SITE, 80 keV DC
electron beam was injected at forty degree into the storage
magnet, and detected as a fluorescent light due to the deexcitation of the nitrogen gas. The pulsed electron beam,
and a pulsed magnetic kicker are developed in order tokeep the pulsed beam to the very centre of the storage magnet. The magnetic kicker mainly produced the radial field
to reduce the pitch angle of the injected beam to keep thebeam at storage region. In this paper, the development ofmagnetic kicker, tracking studies in kicker field and two
designs for the SITE’s kicker is presented.

INTRODUCTION
The muon's anomalous magnetic moment is one of biggest discrepancies in elementary particle physics and extremely sensitive to the new physics. The most recent
measurement of muon g - 2 results in 3 σ [1] discrepancy
between measured and standard model prediction. The JPARC new muon g – 2 / EDM (E34) experiment is aiming
to measure muon g – 2 to the precision of 0.1 ppm and
EDM down to the sensitivity of 10-21 e.cm [2].
In the E34 experiment the polarized muon beam will be
stored in the magnetic field and the evolution of spin precession vector will be measured with respect to time. In
E34 a low emittance ultracold muon beam of 300 MeV/cfrom muon accelerator will be injected into a 3-T MRI(Magnetic Resonance Imaging) type solenoid magnet inorder to store the muon beam in 0.66 m diameter orbit. In
order to enhance injection efficiency and overcome technical challenges related to small storage orbit a three-dimensional spiral injection scheme is under development toinject the muon beam into a MRI type storage magnet. The
details and recent updates of three-dimensional spiral injection scheme can be found in [3, 6 and 7].
___________________________________________*Work supported by the “Grant in Aid” for Scientific Research, JSPS (KAKENHI#26287055)†rehman@post.kek.jp

The three-dimensional spiral injection scheme is an
unproven idea, therefore, a demonstration experiment toprove the feasibility of this unique scheme is inevitable.
A scale down Spiral Injection Test Experiment (SITE)
by the use of electron beam is under development at KEK
Tsukuba campus (see Figure 1 (a) and b). SITE is consistof a DC electron electron gun and a 2 m long straight beam.
The electron beam from the straight beamline was bent by
the bending magnet I towards storage magnet at 40
degrees. At the injection pipe region near to the injection
duct of the storage magnet a bending magnet II is also
installed. The purpose of this addiational bending is toincrease the acceptance of the injection angle into thestorage magnt. The details of this will be described in next
sections. In Figure 1 (b) the region outside the storage
magnet is highlted in yellow color and injection region andand storage regions are highleted as blue and green clolors
respectively. In the SITE a DC electron beam spiral track
has been confirmed in the storage chamber as a fluorescentlight from the nitrogen gas de-excitation along the electron
beam path (Figure 2). In Figure 2 bright yellow lines show
the electron beam as a fluorescent light. The number ofturns in the storage magnet depends upon injection angle,
in Figure 2 the beam was injected into the storage magnet
at around 40 degrees. The distance between two turns of
the spiral trajectory was 190 mm. The final goal of the
SITE is to store the pulsed electron beam [4, and 5] in the
median plane of the storage magnet for the order of few
milliseconds. In order to store the pulsed electron beam in
the storage region, a pulsed magnetic kicker is being
developed to reduce the vertical momentum of the beam tonearly zero. This paper will describe our recent progress
towards the development of kicker.
Table 1: Comparison of Parameters between E34 and SITE
Parameters

E34

SITE

Storage magnet
field strength
Momentum
Cyclotron Period
Storage Orbit diameter(a)

3T

0.0083 T

300 [MeV/c]
7.4 nsec
0.66 m0.296 [MeV/c]
5.0 nsec
0.24 mthe injection angle of the beam to some extent. In order tostore the beam at the center of the storage magnet, the pitch
angle of the beam must reduce to the zero as it reaches storage region. A pulsed magnetic kicker is used to decrease
the pitch angle (ψ) of the beam. Figure 3 is illustrating thecharacter of the magnetic kicker. The black trajectory is
showing the motion of the beam inside the storage magnet
without kicker, the injection angle of the beam reduced due
to radial fringe field but do not decrease to zero. Beampassed through the middle region of the storage magnet
without getting stopped. Whereas, when an appropriate

Figure 3: Left: Black trajectory is showing the beam injection into the storage magnet without kick. Pink trajectoryshows the case when a suitable kick is applied to the beamin order to stop the beam at mid plane. Right: Black shows
the pitch angle of the beam with respect to vertical position
kick without kick and pink shows that pitch angle reduced
to zero when kick will applied to the beam.

Figure 1: (a) Photo of SITE setup. (b) Schematic of the storage magnet with reference trajectory.

kick is applied to the beam as shown in the pink trajectory,
the pitch angle reduced to zero. The curved region in Figure 3 right depicts the weak focusing region (next subsection).
The pulsed magnetic kicker have to produce the radial
field which will be perpendicular to the vertical componentof the momentum of the beam. The required radial magnetic field and a stopping volume (region needed to stop
the beam) may calculate as following𝑚𝐵𝑟 = 𝑒 𝜃𝑝𝑖𝑡𝑐ℎ 𝜔
(1)
2𝑞

𝑍0 =

𝑐 𝑇
𝑃
𝛾𝑒 𝑚𝑒 4 𝑧0

(2)

Where Br is the required radial field to kick the beam,
𝑃𝑧0
2𝜋
𝜃𝑝𝑖𝑡𝑐ℎ (= |𝑃|) is the pitch angle of the beam, 𝜔(= ) is the𝑇

Figure 2: The electron beam spiral trajectory as a visible
light due to the de-excitation of the nitrogen gas in thestorage magnet vacuum chamber.

PULSED MAGNETIC KICKER
The electron beam is injected into the storage magnet ata vertical angle, therefore the beam has a component parallel to the axial magnetic field of the storage magnet andstarts spiraling through the storage magnet. The radialfringe field of the solenoidal storage magnet will reduce

angular frequency, 𝑚𝑒 is the mass and q is the charge ofelectron. Z0 gives the region in which beam will stop (stopping volume), T is the time period and Pz0 is a vertical momentum of the beam. In SITE, stopping volume have beenchosen 100 mm due to the good field region (the region inwhich pitch angle remains constant) and the realistic number of required kick field and time period from the point ofview of the electronic circuit of the power supply.

Tracking in the kicker field and weak focusing
field
The tracking of the single particle with the different initial condition in the kicker field has been done by using
the Runge-Kutta 4th order method. The kicker field has
been defined as follows
2𝜋
𝐵𝑘𝑖𝑐𝑘 = 𝐵𝑝𝑒𝑎𝑘 𝑆𝑖𝑛(
𝑡)
(3)
𝑇𝑘𝑖𝑐𝑘

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 = T/2, where T is total duration of the kick. Even after the kick, there will be residual
pitch angle, in order to compensate the effect of the residual pitch angle the weak focusing has been introduced in
the storage volume. In the weak focusing field the beam
motion will be oscillatory in the storage volume. The amplitude of the oscillation depends upon the residual pitch
angle from the kicker field. The weak focusing magnetic
field can be defined as follow
𝐵𝑍 = 𝐵0 (1 − 𝑛

∆𝑟
𝑟

+𝑛
𝑍

𝐵𝑟 = −𝑛 𝐵0
𝑟

𝑍2

2𝑟 2

)

(4)
(5)

An additional bending magnet II is also placed near the
storage magnet injection duct (Z = - 450), in order to enhance the acceptance of the injection angle. The grey line
in Figure 5 shows injection pipe. The injection pipe is narrow in bending magnet I region, if we change the injection
angle to large or small values at this point then beam just
hit injection pipe instead of going into the storage magnet.
In order to increase the acceptance of the injection angle alarge diameter beam is used, after bending magnet I region,and one additional bending magnet II is installed in orderto change the injection angle. In Figure 5 Type (I - V)shows the different injection angle (see Table 2) adjusted
by bending magnet II.

Figure 4: Left: Axial field profile of the storage magnet.
Right: Radial field profile of the storage magnet with weakfocusing index n = 10-3.
𝑟 𝜕𝐵𝑧

Where “n (= − 0

𝐵0 𝜕𝑟)” is the field index. Radial focus-

ing can be achieved if n < 1 and vertical focusing can beattained if we set n > 0. Figure 4 is representing the magnetic field profile of the SITE storage magnet with the fieldindex value of n = 10-3.
Figure 5 explains the strategy of the injection angle into
the storage magnet. The electron beam from the straightbeamline was bent by a bending magnet I at bend at 0.698
rad (~ 40 degree) towards the storage magnet shown as a
black line.

Figure 5: The electron beam from the straight beamline
was bend at 0.698 rad (~ 40 degree) towards the storage
magnet (Black Line) by bending magnet I. At Z= - 450
mm from the center of the storage magnet an additional
bending magnet II is installed in order to enhance the acceptance of the injection angle in the storage magnet.

Figure 6: (a) Different pitch angle (ψ) as a function ofvertical position (Z). The starting point of the kick is Z =-100 mm from the center of the storage magnet (b) Zoom
up of the kicker region. (c) Particles get trapped in the
weak focusing field.
The motion of the single particle in the kicker and weakfocusing field was simulated by the 4th order Runge-Kutta
method in Mathematica [8]. Here we will referred injection
angle as an angle at which beam is injected in the storage
magnet and pitch angle when injection angle reduced tosome extent by the radial fringe field of the storage magnet
at 100 mm form the center of the storage magnet. In SITE,
the pitch angle of the beam is adjustable from the injection
point, therefore, we considered five different pitch anglesof the beam (see Figure 5). Figure 6 (a) is representing thedifferent pitch angles as a function of the vertical position(Z). It can be seen that if we decrease the injection angle
then the pitch angle will also decrease accordingly. The
value of the field index (n) for all tracking studies was set
to 10-3. The starting point of the kick was 100 mm from thecenter of the storage magnet. If a pitch angle of the beamchanges then the required kick field (Bkick) and time period
accordingly change.
Figure 6 (b) shows the zoom up of the particle track in
the kicker and weak focusing region. Figure 6 (c) is representing the particle trapping in the weak focusing field. The
amplitude of oscillation depends upon the residual pitch
angle. For all cases in Figure 4, half sine shape (T = T/2)
was assumed for the magnetic field and spatially kicker

field is symmetric over the circumference of the particle.
Table 2 summarizes the required parameter (Bkick, T (ns),and ψ0 (residual pitch angle)) for the different pitch anglesof the beam. The amplitude of the stored beam in the weakfocusing potential depends upon the residual pitch angle ofthe beam.
A thyratron switch will be used as a switching device inthe magnetic kicker power supply. The thyratron switch
has a time jitter of a few nanoseconds, therefore, it is morefeasible to apply the kick with the long time period.
Table 2: Kicker parameters for the different pitch angle,
residual pitch angle and amplitude of the stored beam.
Type

Injection
angle(Radian)

1
2
3
4
5

0.81
0.71
0.67
0.66
0.64

Pitch angle
ψ(Radian)
at Z = -100
mm
0.19
0.08
0.05
0.035
0.018

Tkick/2(ns)

Bkick(Gauss)

15/2
31/2
48/2
62/2
95/2

2.41
0.6
0.27
0.16
0.07

Therefore, the kick with 62 and 95 nanoseconds is easierto produce. In the case of a longer kick time period, therequired kick magnetic field reduce drastically (Table 2), it
is very difficult to measure such a small field. Therefore,
we are considering alternatives configuration of the kicker.
These alternative configurations of the kicker must have alonger time period with the measurable magnetic field.

Alternative Kicker Configurations
One way to overcome the issue of low magnetic field isto reduce the kick region of the magnetic kicker. The higher
magnetic field will be required to kick the beam due to thelimited area of the kicker field. Therefore, we consideredkicking the beam with π/4, π/6 and π/10 shapes instead of
the uniform 2π kick. Figure 5 represents the tracking withkicker field in case of 2π, π/4, π/6 and π/10 shapes.

Figure 7: Type I shows the kick with 2𝜋 uniform kicker
field. Other types II, III and IV shows the kick with 𝜋/4,
𝜋/6 and 𝜋/10 respectively. The starting point of the kick
was Z = -100 mm from the center of the storage magnet
and the initial pitch angle was 0.018 rad.

For all cases in Figure 7 the initial pitch angle and position of the beam was set to 0.96 degrees and Z = -100 mm
respectively and pulse shape for the kicker field was halfsine. The type I in Figure 7 (a) shows the kick with theuniform kicker field of 2π shape, and it can be seen clearly
that the pitch angle of the beam decreases smoothly.
Whereas type II, III and IV shows the kick with non-uniform kicker shapes i.e. 𝜋/4 , 𝜋/6 and 𝜋/10 respectively.
In the case of 𝜋/4, 𝜋/6 and 𝜋/10 kicker shape the pitch
angle decrease in the steps because the beam sees the
kicker field only in the limited region. For the region where
kicker field is absent the pitch angle remains constant andwhen it comes to the kicker field region it starts decreasing
again and this pattern keep repeating until the pitch angle
decrease to zero.
The types II, II and IV overlap each. Although the areaof the kicker reduce in different types but the reduction in
the area of the kicker is balanced by the high magnetic field
Table 3: Kicker parameters for the different kicker shapes
for the fix pitch angle and time period.
Type

Kicker
Shape

T(ns)

Bkick
(G)
0.079

Pitch angle
ψ (rad)
0.018

95
1
2𝜋
95
0.638
0.018
2
𝜋/4
95
0.948
0.018
3
𝜋/6
95
1.58
0.018
4
𝜋/10
value hence the effect of the kicker will remain same. Table
3 summarize the study of the different kicker configurations. The 𝜋/6 and 𝜋/10 configurations both are goodcandidates for the new kicker shape due to the reasonablevalues of magnetic field.

Kicker Design
Figure 9 shows kicker coil design in CST [8] to produce the 2𝜋 uniform kick. In this configuration of the
kicker the current in upper and lower coils are opposite toeach other and they produced cylindrical symmetric radial
field. Figure 9 left shows the field profile along the axial
direction. The alternative design of the kicker shape can berealised by the rectangular dipole coil. The rectangular dipole coil was design in CST [9]. In the CST simulation coilheight was assumed 300 mm, width is 90 mm (correspondto 𝜋/6) and gap between coils is 35 mm. The kicker coilgeometry is shown in Figure 10 left and right shows thefield profile in X (mm) direction. As mentioned in the previous section localized coil do not produced cylindricalsymmetric field but the produced field only in the region
covered by coils. In the simulation coil excitation current
was set to 30 Ampere. The rectangular kicker coil will produce magnetic field in the radial direction of the storage
magnet, the magnetic field of kicker will be perpendicular
to vertical component of the beam. In terms of the requiredmagnetic field and time period rectangular kicker coils is
better option and it will be realized for the SITE.

to find the required magnetic field and time period for a
kicker. From tracking studies it has been found out that the
localized kicker will fulfil the requirement for the SITE.

REFERENCES

Figure 9: (Left) The model of kicker coils to produce uniform 2𝜋 kick. The direction of the current in upper andlower coils are opposite to each other. These pairs of coils
produced cylindrical symmetric field. Right: Field profileof kicker coil along the axial direction.

Figure 10: (Left) Rectangular dipole kicker coil design in
CST the size (width) of the coil correspond to 𝜋/6 shape.
Right: Field profile of kicker coil in the X (mm) direction.
The rectangular kicker coils will also have smaller inductance as compared to full 2𝜋 kicker, therefore, it willease the kicker power supply construction too.

Future Plan
The feasibility of the pulsed magnetic kicker has beenshown, and now we are preparing for the construction of apulsed power supply for the kicker. We will complete theconstruction of the pulsed kicker power supply and test ourpulsed magnetic kicker with the electron beam within Japanese FY2018.

SUMMARY
A new three-dimensional spiral injection is under development in order to realize the new J-PARC muon g – 2 /EDM experiment. For the establishment of this novel
scheme, the Spiral Injection Test Experiment (SITE) by theuse of the electron beam is underway at KEK Tsukuba
campus. A pulsed magnetic kicker is being under development to guide the pulsed electron beam to the very centerof the storage magnet for the SITE. Single particle tracking
studies have been carried out with the different initial conditions in the kicker field and weak focusing field in order[1] G.W. Bennett et al., “Final Report of the muon E821 anomalous magnetic moment measurement at BNL”, Phy. Rev.
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[2] M. Aoki et al., Conceptual Design Report for The measurement of the Muon Anomalous Moment g – 2 and Electric
Dipole moment at J-PARC (2011).
[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.
[4] M.A. Rehman et al., “Test Experiment of 3-D spiral injection scheme using electron beam for new g - 2/edm experiment at 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.
[5] M.A. Rehman et al., “Development of the three-dimensional
injection spiral injection by using electron beam for muon g2 experiment” in Proc. of the 14th Annual Meeting of Particle Accelerator Society of Japan (PSAJ’17), Sapporo, Japan,
Aug. 2017, paper WEOM01.
[6] H. Iinuma et al., “Three dimensional spiral injection for acompact storage ring” in Proceedings of IPAC2018, Vancouver, BC, paper TUPML060.
[7] H. Iinuma et al., “Development of three-dimensional spiralbeam injection scheme with X-Y coupling beam for MRI
sized compact storage ring” in Proc. of PASJ2018, paper
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[8] http://www.wolfram.com/[9] http://www.cst.com