Proceedings of the 10th Annual Meeting of Particle Accelerator Society of Japan (August 3-5, 2013, Nagoya, Japan)

Simulation studies of low-emittance muon re-acceleration for muon
microscopy application
S. Artikova, F. Naito, M. Yoshida (KEK), N. Hayashizaki (Titech)
KEK, Ibaraki, Japan
Abstract
While conventional muon beam can be used to investigate rather small samples, there is a strong requirement
for still lower energy ultra-slow muons that can be stopped
near sample surfaces, in thin films and near multi-layerinterfaces. A number of muon cooling techniques havebeen suggested to produce ultra-slow muons, such as twophoton laser resonant ionization of muonium atoms and energy moderation of muons in a thin foil-degrader. In thiswork, in close collaboration with the Muon Science Establishment (MUSE) at Material and Life science experimental Facility (MLF) of the Japan Proton Accelerator Research Complex (J-PARC), we provide a brief overview ofthe primary muon production target, where two of the four
associated secondary beam transport lines which are dedicated to experiments employing the ultra-slow muons. Inparticular, we present the simulation results of the ultraslow muon production with tunable energies in the range
of energies between 5.65 and 30 keV based on the simple energy moderation of transported muon beam in thinfoil-degrader. In addition, we discuss accelerator optics
design and beam acceleration simulation results provide a
microbeam for muon microscopy.

INTRODUCTION
The spin polarized muon beam application in experimental methods that can probe deep inside a material isenhanced by its exquisite sensitivity to magnetism and its
unique time window (µs order) for dynamical processes.
Lower energy muons are available only from ordinary twobody pion decay. Most positive muon beams are generated from pions stopped at inner surface layer of the primary production target and decaying at rest, hence the common name, surface muons. The muon is emitted isotropically from the pion with momentum 29.8 MeV/c and kinetic energy of 4.119 MeV (in the rest frame of the pion).
The intensity of surface muon beam can be estimated fromthe number of pions stopped near to the surface. Whileconventional muon beam can be used to investigate rather
small samples, there is a strong requirement for still lower
energy ultra slow muons that can be stopped near sample surfaces, in thin films and near multi-layer interfaces
which are important for future technologies. The MUSE
group at the Institute of Materials Structure Science, KEK,
succeeded in extracting the worlds strongest pulsed muon
beam, 2,500,000 muons per pulse (proton beam intensityof 212 kW and pulse repetition rate of 25 Hz) to the ultraslow muon beam experimental area at MLF of J-PARC [1].

Fig. 1 shows sketch of muon science facility of J-PARC
consisting of surface muon production target in the proton
beam transport line tunnel which runs through the centerof MLF building and associated four secondary beam lines.
One of these secondary beam lines extracted at the angle of
60 degrees to the proton beam line backward, is designed
for the ultra-slow muon microscopy experiments [2]. Another beam line extracted at the angle of 135 degrees to theproton beam line forward, will be followed by linear accelerator for new measurements of muon g-2 and electric
dipole moment employing ultra-slow muon beam [3].

ULTRA-SLOW MUON BEAM
GENERATION
Since surface muon beam is produced at 4.1 MeV kinetic energy and beam size of a few cm2 to 10 cm2 , anumber of cooling techniques are developed to create ultra low energy slow muons. Another attribute is, the surface muons are 100% spin polarized opposite to the direction of motion appears from the spin of pion which iszero and a definite helicity of the muon neutrino. The technique for generation of ultra-slow muons is based on producing muonium that is a pure leptonic system formed byelectron capture of µ+ near the surface of the hot tungsten
foil. Transported muon beam will be focused on tungsten
target to produce muonium. Thermal emission of muonium into a vacuum at target temperature of 2000 K proceeded with intense laser irradiation. The electrons arethen stripped from the muonium atoms using two highpower new laser systems. One at wavelength of the muonium Lyman-α photo-excites the muonium from groundto 2P state, and then the other at wavelength of 355 nm
ionizes the excited muonium. The ultra-cold muons produced this way will be fully polarized, with small transverse momentum. The thermalization process is the keypoint to cool down the muon beam. The basis of the technique has been described in detail previously [4, 5]. Analternative technique for generation of ultra-slow muons,originally has been developed using a continuous muonsource at the Paul Scherrer Institute (PSI) in Switzerland.
This method is based on energy moderation in a thin foildegrader. Particularly suitable as moderators are van derWaals bound solids, such as solid argon, neon and nitrogen [6]. One drawback of the moderation method is thatthe intensity of the ultra-low energy muon beam emerging
from the downstream side of the moderator is reduced several orders of magnitude below that of the incident surface
muon beam. In addition, moderated muons still has larger- 544 -

Proceedings of the 10th Annual Meeting of Particle Accelerator Society of Japan (August 3-5, 2013, Nagoya, Japan)

Figure 1: Top view of the muon production target and associated four beam transport lines (J-PARC MLF). Two of thesebeam lines are extracted at the angle of 60 degrees to the proton beam line (backward), and the others are at 135 degrees(forward).
beam size and large divergence. Research for studying
implantation-depth-dependent properties of thin samples,
nanomaterials, multilayered thin films or superconductors
prefers ultra-slow muons with optimized beam parameterssuch as suitable energy range and small beam spot size.
It is experimentally shown that, moderated positive muon
beams with tunable energies in the range of 0 to 30 keV
are possible. This energy range corresponds to implantation depths in solids of less than a nanometer to several
hundred nanometers. The implantation depth can be easily
controlled on a scale ranging from several nanometers tohundreds of nanometers by re-accelerating muons from eVenergies to tens of keV or MeV.

met3 material [8]. A key point about this multistage induction accelerator module, the beam senses a large net accelerating field. The charged particles, in effect, do the integration of the axial electric field in the vacuum beam pipe toachieve a final energy equal to the sum of all the individual
module voltage. Working principle of induction accelerator
can be explained schematically from fig. 4 in which four individual modules are placed in series. A pulsed transformer
provides power to energize the induction module.

MUON RE-ACCELERATIONThe ultra-slow muon microscope will be the first experimental instrumentation in the world with the following
two excellent capabilities, which are essential for materials
and life science experimental research: (1) utra-slow muonfor depth profiling with nanometer depth resolution, and(2) high-density micro-beam for three-dimensional imaging inside materials with micrometer spatial resolution [7].
To produce micrometer size beam at the designed energyof 300 keV, muons are to be re-accelerated by the electricfields associated with changing magnetic flux. RF acceleration is not applicable due to experimental requirements
such as variable implantation-depth (variable energy), scalable energy up to 1 MeV and considering into account large
initial beam size. An induction accelerator as shown infig. 2, will generally contain a number of individual accelerator modules that each add a given increment of energy
to the charged particles that pass through it. Each module as shown in fig. 3 is comprised of a pulse transformer-insulated gate bipolar transistor (IGBT) that powers an induction cell containing an induction core made from Fin-Figure 2: Induction accelerator modules.

Figure 3: IGBT and an induction core.

- 545 -

Proceedings of the 10th Annual Meeting of Particle Accelerator Society of Japan (August 3-5, 2013, Nagoya, Japan)

to produce ultra-slow muons by means of tungten target or
degrader-foil. Fig. 5 shows the simulation of muon beamenergy moderation (from 4.5 MeV to 0) passing throughlithium fluoride (LiF, 2.635 g/cm3 ) foil. From this estimation we define the foil thickness as 788 µm corresponding to 30 keV. Fig. 6 shows the simulation of muon beamenergy moderation in terms of reference particle momentum passing through lithium fluoride foil. Momentum decreases (starting from 30 MeV/c to 0) as a function of foil
thickness, the corresponding values are consistent with previous result.

IBU30Figure 4: Induction accelerator composed of four individual modules placed in series.

25The electric acceleration field is confined primarily to theaxis of the system by the conducting walls surrounding theinduction core. Each core has one turn as the primary andtransformer has four turns for secondary. The accelerating voltage is associated with a changing magnetic field by
U = −dΦ/dt, where Φ is the magnetic flux in the core.
To produce a high accelerating voltage the magnetic flux
has to be changed very fast. Transistors are used for therapid change of the current. Accelerating voltage of 15 kV
per module is possible, to produce 300 KeV muon beam 20
induction modules are combined.

p HMeVcL20
15
10
500.1

0.2

0.3

0.4

0.5

0.6

0.7

s HmmL

Figure 6: Energy moderation of muons in terms of momentum as a function of degrader thickness.

CONCLUSION AND OUTLOOKSIMULATION RESULTS
The secondary beam lines extracted from primary target in the proton beam line and transport surface muons tothe experimental area. Transport beam line in which muon
acceleration linac for g-2 measurements will be installed,
is the sequence of radiation shield from graphite targetzone, superconducting solenoid, bending magnet, a coupleof kicker magnets, separator, a couple of beam transportsolenoids and quadrupole triplet for final beam focusing onto the tungsten or degrader foil. Ultra-slow muon beam line
is composed of radiation shield from graphite target zone,
large angle paramagnetic solenoid, curved superconducting solenoid and superconducting axial focusing magnet.
Final focusing part of the beam transport line is a section

In this paper we present a brief overview of experimental
muon science facility employing ultra-slow muons and preliminary results of the ultra-slow muon production simulations with tunable energies in the range of between 5.65 and
30 keV. In addition, we discuss muon beam re-acceleration
method to provide a microbeam for muon microscopy applications.

REFERENCES[1] http://legacy.kek.jp/intra-e/press/2012/112714/[2] Y. Miyake et al., Hyperfine Interact (2013) 216, p.79-83, DOI
10.1007/s10751-012-0759-4[3] Conceptual design report for the measurement of the muon
anomalous magnetic moment g-2 and electric dipole moment
at J-PARC, December 13, 2011.
[4] Y. Miyake et al., J. Nucl. Sci. Technol. 39 (2002) p.287

4[5] P. Bakule et al., Contemp. Phys. 45 (2004) p.203
E HMeVL

3[6] T. Prokscha et al., Applied Surface Science 172 (2001) p.235[7] http://slowmuon.jp/english/summary.html

2[8] http://lcdev.kek.jp/Conf/LAM30/21P074.pdf
100200400600800x HΜmLFigure 5: Energy moderation of muons as a function ofdegrader thickness.

- 546 -