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

PASJ2015 THP018

SIMULATION STUDY ON BUNCH COMPRESSION AND
DECOMPRESSION FOR GENERATION OF COHERENT THZ RADIATION
AT THE COMPACT ERL *N. Nakamura, M. Shimada, T. Miyajima, K. Harada, O. A. Tanaka, A. Ueda,
High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki, JapanAbstract
We study bunch compression and decompression in theCompact Energy Recovery Linac (cERL) at KEK byusing simulations to achieve an ultra-short bunch forgeneration of the THz coherent radiation planned for thenear future. In this study, off-crest acceleration in themain superconducting linac and non-zero R56 optics in thetwo arc sections are used and sextupole magnets are
introduced into the two arc sections for optimizing T566 of
the arc sections. The results of the simulation study showthat the bunch can be compressed to less than 50 fs andthen almost decompressed to the initial bunch length.

INTRODUCTION
The commissioning of the entire cERL was started inDecember 2013 and the beam recirculation and energy
recovery were achieved in February 2014[1]. In 2015, themaximum average current was recorded at about 80 µA
and laser-Compton scattering X-rays was successfullygenerated[2]. In the next step, generation of THz coherent
radiation is planned for the near future.

an ultra-short bunch. In the bunch compression anddecompression simulation, sextupole magnets were addedin the two arc sections for optimizing T566 of the arc
sections. In this paper, we present the simulation results
and requirements for the sextupole magnets including
their field strengths, number and layout.

LINEAR OPTICS AND SEXTUPOLEMAGNETS OF ARC SECTIONS
Linear Optics
In the bunch compression and decompression schemeof the cERL, the bunch is accelerated off-crest in the mainsuperconducting linac to have a correlation between theenergy and longitudinal position and then the bunch
length is compressed in the 1st arc section with a positive
R56 value. After the bunch compression, the bunch lengthis decompressed through the 2nd arc section with anegative R56 value and then decelerated off-crest tocompress the energy spread to the initial value before thebeam enters the dump line. Figure 2 shows the linear
optics of the arc section with three different R56 values.
The optics with R56=0 is used in the normal operation andthe optics with R56=0.15 m and R56=-0.06 m correspond to
the 1st and 2nd arc sections in the bunch compression anddecompression operation, respectively.

Figure 1: CSR spectra of the 20 MeV cERL for threedifferent bunch lengths of 50, 100 and 200 fs, at thebunch charge of 7.7 pC and the bunch repetition
frequency of 130 kHz.
The coherent synchrotron radiation (CSR) spectra
generated at a bending magnet of the arc sections arecalculated and shown in Fig. 1. An electron bunch lessthan 100 fs is required for providing intense THz-CSR up
to 5 THz to users. We simulate bunch compression anddecompression in the cERL by using a tracking code
ELEGANT [3] to check the feasibility of generating such____________________________________________*norio.nakamura@kek.jp

Figure 2: Horizontal and vertical betatron functions(!x, !y) and dispersion function ("x) of the arc sections
with three different R56 values of 0.0 m (black brokenline), 0.15 m (blue solid line) and -0.06 m (red solid line).
B, Q and SX1-4 indicate the bending, quadrupole andsextupole magnets, respectively.

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

PASJ2015 THP018

Sextupole Magnets
Sextupole magnets must be introduced in the two arc
sections for the second–order correction of the energydependent path length (T566 correction). In each arc
section, all or any of four sextupole magnets from SX1 toSX4 with the length of 10 cm can be inserted for thebunch compression and decompression as shown in Fig. 2.
In order to decide the required number and field strengths
and the optimum layout of the sextupole magnets for the
1st arc section, the bunch compression simulation is firstperformed. Here the beam energies at the entrance andexit of the main linac are 2.9 MeV and 20 MeV. We set
the bunch charge to 7.7 pC and assume the initial bunch
distribution at the entrance of the main linac to be a sixdimensional Gaussian distribution with the bunch lengthof 2 ps, the relative momentum spread of 0.1 % and thehorizontal and vertical normalized emittances of 1
mm·mrad. In this bunch compression simulation, thebunch length is minimized at the exit of the 1st arc section
by optimizing the main-linac RF phase and sextupole
magnet strengths.

Figure 3: Change of time-momentum (t, p) distribution of
the electron bunch from before the main linac to after the
1st arc section in the bunch compression process. The
numbers on the distribution plots mean their temporalorder. (3a) and (3b) correspond to two cases of SX1-4
OFF and SX2&4 ON listed in Table 1. The bunch lengthand momentum spread are also shown on each plot. In thesimulation, the bunch length is minimized at the exit of
the 1st arc section.

Table 1: Simulation Result of Bunch Compression
Sextupolemagnets

σt *[fs]

ε nx/ε ny #[mm·mrad]K2 †[m-2]

SX1-4 OFFSX1-4 ON875
60.6

1.14/1.03
1.13/1.16

SX1 ONSX2 ONSX3 ONSX4 ON
SX1&2 ON
SX1&3 ON
SX1&4 ON
SX2&3 ON
SX2&4 ON
SX3&4 ON

65.7
66.4
74.4
67.4
65.3
61.4
62.6
62.2
60.9
68.5

1.60/1.35
1.59/1.16
1.95/1.20
1.55/1.19
1.50/1.26
1.18/1.25
1.32/1.23
1.27/1.15
1.13/1.15
1.65/1.19-14.9, -33.3-21.0, -22.2-106.4-84.6-112.2-80.2-62.4, -34.7-69.8, -38.8-69.4, -28.2-60.6, -31.5-42.4, -40.1-54.3, -41.0

preserved probably because the betatron phase advance
between the two magnets is the nearest to 90 degrees. In
addition, T166 and T266 of the 1st arc section are also
comparatively small. Therefore we decide to choose thecombination of SX2 and SX4 for the arc sections.

BUNCH COMPRESSION AND
DECOMPRESSION SIMULATION*, # Bunch length and hor./vert. normalized emittances atthe exit of 1st arc † Strengths of sextupole magnets of the
1st arc

Table 1 shows the bunch length and the horizontal andvertical normalized emittances at the exit of the 1st arc
section and the required sextupole magnet strengths
obtained from the bunch compression simulation. Figure
3 shows the change of time-momentum distribution in thebunch compression process for SX2&4 ON and SX1-4
OFF listed in Table 1. The bunch length is effectively
reduced from 875 fs to less than 100 fs by excitation andoptimization of the sextupole magnets. Combination ofSX2 and SX4 (SX2&4 ON) has almost the same
performance in bunch compression as all of SX1-4 (SX14 ON). For this combination, the emittances are wellIn this section, both bunch compression anddecompression are simulated. Similarly we assume theinitial bunch distribution at the entrance of the main linac
to be a six-dimensional Gaussian distribution with thebunch charge of 7.7 pC, the bunch length of 1 or 2 ps, therelative momentum spread of 0.1 % and the horizontal
and vertical normalized emittances of 1 mm·mrad. Thebunch length is minimized at the entrance of the 2nd arc
section, which is very close to the planned THz-CSR port
at the 1st bending magnet of the 2nd arc section. Then thebunch is decompressed through the 2nd arc and themomentum spread is minimized at the entrance of thedump line by optimizing the sextupole magnet strengthsof the 2nd arc and the decelerating RF phase of the main
linac in order to recover the initial bunch state.
The present beam energy of the cERL (20 MeV) issufficiently low so that the momentum or velocity
difference of electrons in the bunch gives the significant
difference of the arrival time or effective difference ofpath length R56eff, which is expressed with the Lorentz
factor γ and the velocity normalized by the speed of light
β as follows:- 969 -Proceedings of the 12th Annual Meeting of Particle Accelerator Society of Japan
August 5-7, 2015, Tsuruga, JapanPASJ2015 THP018

LR56 eff = − 2γ β(1)Here L is the path length. The effective difference of thepath length due to the momentum difference is negative.
Furthermore the bunch passes the three chicanes withnegative R56 values of -0.0101 m, -0.0059 m and -0.0032
m from the exit of the 1st arc to the entrance of the dump
line. Therefore we set the R56 values of the 1st and 2nd arc
sections to 0.15 m and -0.06 m. Their absolute R56 values
are not equal because of effects of the R56eff and thechicanes. The two optics with R56=0.015 m and -0.06 m
are shown by blue and red solid lines in Fig. 2.
Table 2: Simulation Result of Bunch Compression andDecompression
Sextupolemagnets

σt *[fs]

σ p/p #[%]

K2 †
[m-2]

SX2&4 ON(σ t0 ‡ =1 ps)
SX2 ON(σ t0 =1 ps)
SX2&4 ON(σ t0 =2 ps)
SX2 ON(σ t0 =2 ps)

45.2
1195
50.1
1287

0.384
0.115
0.390
0.103

-52.3, -35.0-64.4, -40.8-89.8-109.7

45.3
2387
69.4
2648

0.777
0.114
0.779
0.383

-52.2, -35.1-56.6, -46.3-89.8-116.5

Table 2 shows the simulation result of the bunch
compression and decompression at the cERL. Figure 4
shows change of the time-momentum (t, p) distribution of
the electron bunch along the cERL for the initial bunch
length of 1 ps and SX2&4 ON. When the sextupole
magnets of SX2 and SX4 are used in the both arc sections
for the simulation, the bunch is compressed to about 45 fs
for the two initial bunch lengths of 1 and 2 ps and almost
recovered to the initial bunch state in both bunch lengthand momentum spread. On the other hand, when only
SX2 is used, the bunch decompression fails for the initialbunch length of 2ps.

CONCLUSIONSThe bunch compression and decompression simulations
demonstrate that the bunch can be compressed down toless than 50 fs and then almost decompressed to the initialbunch length. From the simulation results, we select thecombination of two sextupole magnets SX2 and SX4 foreach arc section. Four sextupole magnets are being
fabricated and will be installed in 2015 to produce anultra-short bunch for generating THz coherent radiation.

REFERENCES*, # Bunch length and momentum spread at the entrance of
2nd arc after bunch compression (upper row) and at theentrance of the dump line after bunch decompression(lower row) † Strengths of sextupole magnets of the 1st arc(upper row) and of the 2nd arc (lower row) ‡ Initial bunch
length at the entrance of the main linac[1] N. Nakamura et al., Proc. of IPAC’14, Dresden,
Germany, p.353 (2014).
[2] R. Takai et al., FROM03, in these proceedings.
[3] http://www.aps.anl.gov/Accelerator_Systems_Division/Accelerator_Operations_Physics/manuals/elegant_latest/elegant.pdf

Figure 4: Change of time-momentum (t, p) distribution of the electron bunch along the cERL when SX2 and SX4 areused. The numbers on the distribution plots mean their temporal order. The bunch length and momentum spread arealso shown on each plot. In the simulation, the bunch length is minimized at the entrance of the 2nd arc section (4) andthe momentum spread at the entrance of the dump line (6).

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