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

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

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

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

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

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.

Bunch and e-cloud profiles ( Ip=20)

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

Bunch and e-cloud profiles at 500 turn 9 9

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

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.

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