CSR in Damping Ring

2012/2/21
The 17th KEKB Accelerator Review Committee
H.IkedaDamping Ring of SuperKEKB
Damping Ring 

primary e-

3.5GeVe+

The SuperKEKB DR is now under construction. DR is necessary to inject thelow emittance positron beam to the LER, which has very small acceptance inboth of transverse and longitudinal planes. Beam instability is important todesign the DR since the bunch current is relatively high. Since it was found thatthe instability due to CSR severely damages the beam performance for shorterbunch-length and lower momentum compaction, we tried to found the good shapeof beam pipe for suppression of the instability.

DR Parameter
Parameter
EnergyNo. of bunch trains/ bunches per trainMaximum bunch charge
CircumferenceMaximum stored current*
Energy loss per turnHorizontal damping time
Injected-beam emittanceEquilibrium emittance(h/v)
Coupling
Emittance at extraction(h/v)
Energy band-width of injected beam
Energy spreadBunch lengthSynchrotron tune
Momentum compaction factor
Number of normal cellsCavity voltage for 1.5 % bucket-heightRF frequency

1.12/2
8
135.5
70.8
0.091
10.9
1700
41.4/2.07
5
42.5/3.15
1.5
0.055
6.53
.02569
0.0141
32
1.4
509

unit
GeV
nC
m
mA
MV
ms
nm
nm
%
nm
%
%
mm

MV
MHz

Wakepotential•Longitudinal wake potential per turn has been estimated for eachvacuum component, RF cavity and resistive-wall with 0.5mm bunch
length (< 1/10 of the natural bunch length). •The CSR wake is 100 times higher than the other components inthis case. CSR
Vacuum Component
RF Cavity
BellowsFlange
SR Mask
Resistive wall
BPM
Strip line

# of component
288
176
176
135.5[m]821(T.Abe, K.Shibata, M.Tobiyama)

Calculation of CSR and Tracking

The cross section of DR beam pipe is decided based on the CSRinstability. The wake potential by CSR is calculated by two independent codes
and the results agree for rectangular cross section chambers.
Following results are using numerical calculation by Oideʼs code
which is implemented to SAD.
The tracking simulation was made for Gaussian beam and thetracking used up to 5,000,000 macro particles to confirm theconvergence in the number of particles. BendLength[m]Bending angle# of elements

B1.74248.2767932B2.28654.0968738

B3.39208.124606B4.47935.152182

Parameters of dipole magnets

Calculation of CSR due to Chamber shape
The wake potentials by CSR are calculated for 7 types crosssection. 1523647

Calculation of CSR and Tracking [1]Antechamber 34 φ

Antechamber 24 mmCalculation of CSR and Tracking [2]Antechamber 34 mm rectangularAntechamber 24 mm rectangularCalculation of CSR and Tracking [3]Normal chamber 34 φ

34 mm rectangular

24 mm rectangularCalculation of CSR and Tracking [summary]
Cross section of beam pipe

σΔ/σΔ0σz/σz0

4nC

8nC

4nC

8nC

(1) Antechamber 34 φ

39%

65%

40%

66%

(2) Antechamber 24 mm

15%

43%

15%

43%

(3) Antechamber 34 mm
rectangular

63%

98%

63%

98%

(4) Antechamber 24 mm
rectangular

20%

44%

20%

44%

(5) Normal chamber 34 φ

45%

77%

45%

78%

(6) 34 mm rectangular

39%

115%

39%

115%

(7) 24 mm rectangular

14%

39%

14%

40%

• We chose a design with antechamber for the DR beam pipe to reducethe instability caused by the wake field of vacuum components.
• The antechamber with smaller pipe height shows better situation.

Design of beam pipe
• We designed the actual cross section of the beam pipe,
considering the easiness of the production and the tracking
simulation was made.

(K.Shibata)

Calculation of CSR and Tracking:Change the mesh size

•Change the mesh size in order to check the calculation are converged.

Maxmesh=hac/2

Maxmesh=hac/3

Calculation of CSR and Tracking:Change the mesh size
Maxmesh=hac/3.5

Maxmesh=hac/4

Calculation of CSR and Tracking:Change the mesh size
Maxmesh=hac/5

Maxmesh=hac/6

Calculation of CSR and Tracking:Add other components wake
Maxmesh=hac/5
CSR only

Maxmesh=hac/5
CSR+otherIn the case of the wake potentials by other vacuum components areadded, the peak position is changed. Calculation of CSR and Tracking:Linac beam. We also checked the tracking result by using the beam fromlinac before damping instead of damped Gaussian beam. (Kamitani, N.Iida)Calculation of CSR and Tracking:Gaussian and Linac beam

Maxmesh=hac/5
The beam from linac damps to somewhat different statecompared to the case starting from the damped beam. Maxmesh=hac/6

Maxmesh=hac/7

An instability with high frequency mode causes the oscillation of bunch lengthand energy spread. The emittance fluctuates greatly at the same time. The
cycle of emittance change is 10 times of the synchrotron oscillation. This isthought a sort of saw tooth instability. Summary• We calculated the longitudinal microwave instability effectfor SuperKEKB DR. • The longitudinal wake is dominated by the CSR wake field
and the effect is tolerance level except some peak of energy
spread and bunch length. • The hexangular antechamber has been proposed as beam
pipe based on the calculation result. • The mechanism of the instability at some bunch current isunder consideration. • We already started the R&D of prototype, including monitor
chamber. Fabrication of chambers is scheduled in the JFY
2012.