1. E-cloud instability at CESR TA
Hyunchang Jin, Moohyun Yoon, POSTECH
Eun-San Kim, KNU, Kazuhito Ohmi, KEK
Presented at the ILC Damping Rings Mini-workshop, KEK, December 2007

2. Outline CESR TA parameters for simulation by PEHTS Linear Theory
Simulation results
Uniform b model
CESR TA Damping ring lattice model
Summary 2 2

3. Parameters for simulation
Positron energy (GeV) 2
Average bunch population
2.0×1010
Horizontal / Vertical b functions (m)
10 / 10
Rms bunch length (mm)
6.8
Horizontal / Vertical emittances (nm)
2.25/ 0.002
Rms energy spread (se/E)
8.6×10-4
Synchrotron tune
0.098
Ring circumference (m)
768.44
Number of interaction points (Ip)
10/20
Horizontal / Vertical tunes
14.59 / 9.63
Horizontal / Vertical chromaticities
0.0 / 0.0 3 3

4. Linear Theory
The oscillation frequency of electrons under a bunch population ( = 2.0×1010 ) is given by
The number of oscillations ( ) is approximately 10.
The threshold of electron cloud density for a given bunch population is given by
where K=Q=10 4

5. Rms vertical beam sizes for Uniform b model
Vertical beam size grows when the beta functions are uniform.
The burst-like behavior of beam size growth is seen above Ne= 2.0×1012 m-3 .
Therefore the threshold of e-cloud density is roughly 2.0×1012 m-3 for both cases.
The vertical beam size under the threshold becomes smaller as the number of interaction points increases. Therefore it can be an artificial incoherent beam size growth. 5 5

6. Bunch and e-cloud profiles ( Ip=10)
The coherent motions of bunch and e-cloud are seen above the threshold around
the burst-like behavior of vertical beam size growth.

7. Bunch and e-cloud profiles ( Ip=20)

8. Rms vertical beam sizes for CESR TA Lattice
Vertical beam size grows when CESR TA lattice (provided by Mark Palmer) is used
assuming that e-cloud exists only in bending magnets.
The threshold of e-cloud density is roughly 1.0×1012 m-3 ~ 1.5×1012 m-3.
At Ne=1.0×1012 m-3, the growth rate of vertical beam size is about 1.9×10-3. This value is greater than the damping rate (~5.5×10-5) of CESR TA lattice. Therefore the vertical beam size growth below the threshold is serious. 8

9. Bunch and e-cloud profiles at 500 turn9 9

10. Bunch and e-cloud profiles at 500 turn
From Ne=1.5×1012 m-3, coherent motions are seen in these snapshots. 10 10

11. The turn-by-turn motions of vertical bunch
and e-cloud centroids
Ne= 1.0×1012 m-3
Ne= 1.5×1012 m-3
In the case of Ne= 1.5×1012 m-3, the coherent motions of positron bunch and e-cloud are seen clearly. Therefore the threshold of e-cloud density is about 1.5×1012 m-3.

12. Summary
Threshold of e-cloud density predicted based on the linear theory is about 2.8×1012 m-3.
The threshold of e-cloud density is about 2.0×1012 m-3 when uniform b functions are used. The coherent motions of bunch and e-cloud are seen above the threshold.
In the simulation with CESR TA lattice, the threshold is about 1.5×1012 m-3. The threshold becomes smaller than the uniform b model. Dispersion can affect (lower) the threshold value. Coherent motions of bunch and e-cloud are seen above the threshold. And the incoherent effect under the threshold may be serious. 12 12