BUNCH COMPRESSOR SYSTEM FOR JLC
T. Okugi, K. Kubo and M. Kuriki, KEK, Tsukuba, Ibaraki, Japan
Abstract

221 INTRODUCTION
JLC bunch compressor system is located between thedamping ring and the main linac. The main purpose of thebunch compressor system is to compress the bunch length
to an acceptable length for the main linac acceleration,
keeping the small horizontal and vertical emittance. For
the X-band main linac, the requirement of the final bunch
length is 90-150 µm and the bunch length have to bechanged flexibly [1].
At first, the bunch compressor system was designed tobe “single-stage”. The single stage bunch compressor,
however, is not adopted because of the limitation of thebunch length compression by the higher order component.
Furthermore, the chromatic emittance growth is anotherdisadvantage of the single-stage bunch compressor. If weused the single stage bunch compressor, the final energy
spread is increased up to 5%. For these reasons, we use a“two-stage” bunch compressor. The first stage compressor(BC1) compresses the bunch length from 5 mm to a few
hundred µm. After the beam acceleration to 10 GeV (prelinac), the bunch length is compressed to the target bunch
length of 90-150 µm (BC2).
If a longitudinal position at the exit of the bunch
compressor system is shifted by 18 µm (10-20% of finalσz), the beam energy at the interaction point will beshifted by 0.1%. The longitudinal position stability isimportant for the bunch compressor system.

2 EMITTANCE DILUTION SOURCE
The main source of the horizontal emittance dilution isan aberration by coherent synchrotron radiation (CSR) for
low energy bending system. Longitudinal electric field of
the CSR induces an energy variation along the bunch like

Bunch Distribution

Bunch Distribution [a.u.]

The JLC bunch compressor system is required to compress the rms bunch length from 5 mm to 90-150 µm,keeping the small horizontal and vertical emittance.
The main source of the horizontal emittance dilutionis
an aberration by synchrotron radiation and coherent
synchrotron radiation on dispersive position. Verticalemittance dilution is generated by the wake eldin
accelerating structures. The emittance dilution wascalculated with a 6 dimensional tracking code. A bunchcompressor system is designed to change thenal bunch
length to 90-150 µm exibly with almost 10% of theemittance dilution for horizontal plane in the bunch
compressor system.

F (x)110-1-1-20bunch
tailbunchhead-2-4-2024

Figure 1: The potential of coherent radiation, neglecting
the shielding effects of vacuum chamber.
a longitudinal wake field, but the field travels faster thanthe bunch and acts on leading particles. The CSR
potential, neglecting the shielding effects of vacuumchamber, is expressed asVCSR (s) = 0 pp2N e2 3 32 z4F (s=z ) ;(1)

where F(x) is shown in Figure 1[2]. Since Eq. (1) does notdepend upon the beam energy, the effect will be neglected
for high energy beam. On the other hand, the amount of
the horizontal emittance growth by the synchrotron
radiation is written as

1"x = 2:0 2 10011E 5[GeV]I5 ;(2)

I5 = ∫ dsHx / |ρ |3.
where I5 is the radiation integral
Since the emittance growth is increased as ∝ E5, thesynchrotron radiation is the main source of horizontal
emittance growth for the high energy beam in the bending
system.

3 DESIGN OF BC1
Since the energy jitter is smaller than the longitudinal
position jitter at the exit of damping ring, BC1 is designedwith 90° longitudinal phase space rotation. Bunch
compression ratio in BC1 is limited by the effect of thehigher order effect of rf cavities and chicanes in BC1,
such as R566 for chicanes or R655 in rf cavities. The
longitudinal position at the end of BC1 is expressed as afunction of the longitudinal injection position shift,z1i22) 0g1 256 f (1+20i2( 0 )23+ 566( 0( +)28 )1 i3 + (1 i4) (3)1 f  10 0kR56 V C
Ek RVCEk RESVSVC EEzV SVSVSzzoz;

Type R56[m] V[MeV] [ ] z [m] 1"x="xA 0.40 167 14.0 400 5.25%
B 0.50 133 11.3 500 3.64%
C 0.60 110 9.5 600 2.68%
(a) m = 4.0100
Type A
Type B
Type C8060
4020000.05

0.1

0.15

0.2

Bunch Lenght by Nonlinear Term [ µm]Bunch Lenght by Nonlinear Term [ µm]Table 1: The parameter of BC1. We assume an initial
beam of σz = 5mm, σp /p = 0.1%, and L-band structure.

(b) m = 5.0
100Type A
Type B80

Type C

60
40
20000.05

R 56 [m]0.2

4 DESIGN OF BC2-0.1

R56∆ε / ε6x

5-0.3

4-0.4

3-0.5

2

1-0.6
60
80
100 120140 160
Phase Advance per 1 FODO Cell [deg.]∆ε x / ε x [%]R 56[m]x-0.2∆ε x /εx [%]BC2 is designed with 180° longitudinal phase spacerotation, because energy stabilities at the exit of pre-linac
will not be small enough for our longitudinal position
jitter requirement. If it is 90° rotation, we must stabilize arf amplitude of pre-linac to be less than 0.05%.
Furthermore, since a bunch length contribution from
nonlinear term is not sensitive to a rf phase of cavities for
BC2, the contribution can not be canceled by adjusting
the rf cavity phase. Thereby, the phase of rf cavity is set to0° to make a cavity length minimum. The higher ordercontribution is shown in Figure 3 as a function of R56. The
factor m in Figure 3 is the bunch compress ratio in BC2,type A and m = 5 is the parameter, which compress abunch length to 80 µm by linear optics. Thereby, R56 ofBC2 chicane should be less than 0.1 m to compress actual
bunch length to be less than 90 µm.
The horizontal emittance dilutions are evaluated forboth of the arc and the chicane section as a function of R56,
where the bunch compress ratio m is expressed by theratio of R56’s as R56; arc = −mR56, chicane. The arc section
consists of 68 FODO cells and the R56 is varied bychanging phase advance of FODO cells. The chicanesection consists of 10 individual chicanes, and the R56 foreach chicane is 0.0094 m. The simulated result is shownin Figure 4. It is found that the higher R56 makes thelarger emittance dilution. The main dilution source for(a) Emittance Growth and R56 in BC2 Arc
07

Figure 2: BC1 optics for type C. For type B, the firstchicane is not used and first two chicanes are not used fortype A.

0.15

Figure 3: Bunch length contribution from nonlinear term
as a function of R56 of BC2 chicane.

∆ε x /εx [%]where k = 2π f/c, S = sinδ, C = cosδ. The first and second
order aberration can be set to be 0, by adjusting theamplitude and phase of cavities. Since the third ordercomponent, however, can not be canceled, the performance of bunch compression is limited by the thirdorder aberration. R56 should be greater than 0.68m for Sband BC1 accelerating structure, and R56>0.25m for Lband structure (σp,i/p = 0.1%, σz,i = 5mm). If we want tocompress the bunch length to be less than 680 µm, wecould not use the S-band accelerating structures. Thereby,
the L-band cavities are selected for BC1.
As discussed above, the dominant horizontal emittance
dilution source is CSR in BC1. We developed a 6
dimensional tracking code with synchrotron radiation,
CSR and wake functions. The emittance dilution for theBC1 chicane is simulated with this code. We designed 3
type of BC1. Optics of BC1 is shown in Figure 2 (type C),
the bending section consists of 6 chicanes with R56 = 0.1m,
and the parameters are listed in Table 1. For type A setting,last 4 chicanes are used, last 5 for type B and all chicanes
are used for type C. In order to apply the shielding
condition of vacuum chamber[3], the aperture at the exitof last chicane should be 20 mm full height and 30mm
full width. The simulated emittance dilutions, neglecting
the CSR are also listed in Table 1.

0.1

R 56 [m]543210543210(b) Emittance Dilution in BC2 Chicane
Type A of BC1
Type B of BC1
Type C of BC1(m=4)(m = 5)

Type A of BC1
Type B of BC1
Type C of BC1

0.04

0.06
0.08
R56 [m]Figure 4: Emittance dilution as a function of R56.

0.1

Table 4: Summary of the simulation

Table 2: The parameter of BC2.

m R56(arc) R56(chicane) V[MeV] 1"x ="x4.0 -0.376 m 0.094 m 1305 6.92{7.30%
5.0 -0.470 m 0.094 m 1392 8.06{8.50%BC2 arc is synchrotron radiation and both of synchrotron
radiation and CSR affect the emittance in BC2 chicane.
However, the R56 dependence is not so strong. The
difference of the emittance dilution R56 = −0.23 m and R56= −0.47 m is only 3% for BC2 arc and only 1% for BC2chicane. On the other hand, the amplitude of the rf
voltage in BC2 cavity is determined to bec(m 0 1)EV =2fmR56;chicane:(4)

If the R56 is increased by factor two, we can reduce thecavity length by factor two. Thereby, we chose the R56 =0.094 m, which is almost the limit of nonlinear bunch
length enhancement. The final BC2 parameters are listed
in Table 2.

5 EMITT ANCE DILUTION IN
ACCELERATING STRUCTURE

y;

(5)

y;

(6)

y;

(7)

These alignment tolerances are not so tight comparing
with another sections in JLC. The multi-bunch emittance
dilution, however, strongly depends upon the design ofaccelerating structures and the alignment tolerance may
Table 3: The parameter of accelerating structure in bunch
compressor system. (S,L) shows rf frequency.
E[GeV]

L[m] g[MeV/m]

m5
45
454

z [m] 80
100
100
125
120150;l[m] 1" ="88.6 13.75
104.6 12.55
106.3 11.94
126.1 10.79
123.5 10.74
150.9 9.60z;sxx

be very tight. The multi-bunch emittance dilution in the
pre-linac is expressed as
2 l 2a a i
h1 "i  q mc2 g

p 0p  N 2fp i b W
2i;

(8)

where βi the initial beta function, γi, γf the initial and final
Lorentz factor, g the accelerating gradient, la thealignment unit length, σa the alignment accuracy, q thebunch charge and Nb the bunch number. σW is, roughly,
the magnitude of the wake function. On the other hand,
the multi-bunch emittance dilution for the BC1 or BC2
cavities is
2 l 2 L N 2b W
a ah1 "i  q mc
2 2E
2:

(9)

The tolerance of the wake function for 3% emittance
dilutions are calculated as

Many kinds of vertical emittance dilutions exist in theJLC bunch compressor system. Most of the emittance
dilution depend upon the alignment accuracy, such as themisalignment of accelerating structures, rotation error ofquadrupole and bending magnets and vertical position
offset of quadrupole magnets, and so on. However, thealignment tolerance of the quadrupole magnet andaccelerating structures are from 50 µm to a few hundredµm for position offset and a few hundred µrad for rotation
error (3% vertical emittance dilution). For example, thealignment tolerances for accelerating structures in theBC1, the pre-linac and the BC2 are BC1 = 500m PL = 1000150m BC2 = 1600200m :TypeABCz [m]BC1 (L)

1.98

20

15.8

5000

Pre-linac (S)1.98-10270

30.0

400{600

BC2 (S)

10-9.769

25.0

900-1200

W;BC1 < 1:4 2 1014 V=Cm2
W;PL < (5:8 0 3:9) 2 1013 V=Cm2
W;BC2 < (6:4 0 4:6) 2 1013 V=Cm2 ;

(10)
(11)
(12)

where Nb = 100, σa = 50µm (a half of single bunchtolerance) are assumed. The requirement of long-range
wake for pre-linac is tightest in this bunch compressor
system and this value is about 1/50 of the maximum wake
function of S-band structure.

6 DISCUSSION AND SUMMARY
Some parameters for bunch compressor system ischanged from old design[3] by using the 6 dimensional
tracking code with emittance dilution by synchrotron
radiation and CSR. The final result of bunch lengths andemittance dilutions are listed in Table 4 for the newdesign. The horizontal emittance dilution is almost 10%
for all 90-150µm final bunch length. On the other hand, it
was found that if we require the vertical emittance
dilution due to long range wake field to be less than 3%,
assuming 50 µm alignment error, we need an accelerating
structure with W⊥<4 × 1013 [V/Cm2].

7 REFERENCES[1] “International Study Group Progress Report”, KEKReport 2000-7, SLAC R-559 (2000).
[2] Y. S. Derbenev et al., TESLA-FEL 95-05(1995).
[3] “LC Design Study”, KEK Report 97-1 (1997).