fast ion effects

1
fast ion effects

• analytical estimates of
• trapping condition
• exponential FBII rise time
• incoherent tune shift at end of train

compare three rings OTW (3.2 km), OCS (6.1 km),
TESLA (17 km) assume partial CO pressure of 0.01
nTorr
use excel file provided by Tor Raubenheimer add
beam sizes from A. Wolski, parameters for OCS
2
parameters TESLA ring w/o (w) coupling bumps
straight wiggler arc
length km 14.5 0.54 2.0
energy GeV 5 5 5
bunches 2820 2820 2820
bunch population 2x1010 2x1010 2x1010
bunch sep. m 5.994 5.994 5.994
gex mm 5 (2.5) 5 5
gey mm 0.014 (2.5) 0.014 0.014
average bx m 139 10.2 11.9
average by m 142 13.5 24.8
ave. sx mm 0.267 (0.19) 0.072 0.357
ave. sy mm 0.014 (0.19) 0.004 0.006
3
parameters OCS (assume single train, and 5 GeV)
straight wiggler arc
length km 3 0.12 3
energy GeV 5 5 5
bunches 2820 2820 2820
bunch population 2x1010 2x1010 2x1010
bunch sep. m 1.844 1.844 1.844
gex mm 5.5 5.5 5.5
gey mm 0.02 0.02 0.02
average bx m 29.3 15.7 26
average by m 39 9.2 32.5
ave. sx mm 0.128 0.094 0.618
ave. sy mm 0.009 0.004 0.008
4
parameters OTW
straight wiggler arc
length km 1.24 0.24 1.74
energy GeV 5 5 5
bunches 2559 2559 2559
bunch population 2.2x1010 2.2x1010 2.2x1010
bunch sep. m 1.259 1.259 1.259
gex mm 4 4 4
gey mm 0.02 0.02 0.02
average bx m 85.9 4.51 12
average by m 90.9 4.94 24.8
ave. sx mm 0.187 0.043 0.374
ave. sy mm 0.014 0.003 0.007
5
results for TESLA damping ring w/o (w) coupling
bumps
straight wiggler arc
critical mass mp 24 (1) 285 44
ty,exp (e-f. time) ms 76 (1364) 67 350
incoh. tune shift DQy 0.173 (0.010) 0.007 0.008
net rise time ty,exp 83 ms (162 ms) total tune
shift DQy0.188 (0.025)
rise-time tune-shift estimate assumes trapping
of CO, 0.01 nTorr CO pressure all around the
ring, and 0.3 relative ion-frequency spread
even if ions not trapped for final conditions,
certainly they are trapped during the damping
process
6
results for OCS damping ring
straight wiggler arc
critical mass mp 24 69 6
ty,exp (e-folding time) ms 127 633 187
incoherent tune shift DQy 0.032 0.006 0.001
net rise time ty,exp 210 ms total tune shift
DQy0.04
rise-time tune-shift estimate assumes trapping
of CO, single train, 0.01 nTorr CO pressure all
around the ring, and 0.3 relative ion-frequency
spread even if ions not trapped for final
conditions, certainly they are trapped during the
damping process
rise time larger tune shift smaller than for
17-km ring
7
results for OTW damping ring
straight wiggler arc
critical mass mp 8 151 8
ty,exp (e-folding time) ms 121 441 120
incoherent tune shift DQy 0.014 0.005 0.003
net rise time ty,exp 199 ms total tune shift
DQy0.022
rise-time tune-shift estimate assumes trapping
of CO, single train, 0.01 nTorr CO pressure all
around the ring, and 0.3 relative ion-frequency
spread even if ions not trapped for final
conditions, certainly they are trapped during the
damping process
rise time similar to tune shift smaller than
for 6.1-km ring
8

• conclusion from comparison
• ions like CO are trapped over most of
• the circumference for all three designs
• the 3.2-km ring (OTW) yields smallest
• tune shifts (0.022)
• smallest growth rates are obtained for both
• 3.2-km (OTW) and 6.1-km ring (OCS)
• exponential rise time is about 200 ms for an
  average CO pressure of 0.01 nTorr
• with coupling bumps the tune shift and rise
  time for the TESLA ring assume comparable
  values, but in this case
• even H ions may be trapped