1. 10/18/2005 FII in damping ring L Wang1  Smaller (vertical) beta function  Long bunch spacing Both growth rate and tune-shift are small if there is a Wi =Length_element/ Length_section Wi=0 if ion is unstable

2. 10/18/2005 FII in damping ring L Wang2 Peak growth rate of FII for CO+  TESLA; DAS; MCH; OTW; OCS; BRU;PPA Shorter average growth time RingPPAOTWOCSBRUMCHDASTESL A  wiggler (  s) 0.60.8 0.71.752.672.4  arc (  s) 254.23.63.569.4312.713.5  straight (  s) 58919248821929844  ring (  s) 2.68.84.43.220.840.544.3 RingPPAOTWOCSBRUMCHDASTESL A  wiggler (  s) 558767631482423  arc (  s) 23533327933086811541360  straight (  s) 377115203430492057275413  ring (  s) 231961339281170534094027 Peak growth rate of FII for H+ Pwiggler=2.0nTorr; Plong_straight =0.1nTorr P_arc=0.5nTorr The growth time is 100 times longer than CO+!! (H+ has small cross section and it is likely unstable after several damping time) 17km ring has a longer growth time Growth time is less than 1 turn!

3. 10/18/2005 FII in damping ring L Wang3 Tune-shift CO+ H+ The Tune shift caused by CO+ is 30~100 times larger than H+!!

4. 10/18/2005 FII in damping ring L Wang4 Ion yield H+ is dominant component! AluminiumCopper

5. 10/18/2005 FII in damping ring L Wang5 Incoherent vertical tune shift-strongly optics dependent Larger tune shift  OTW; DAS; TESLA; MCH; PPA; BRU; OCS RingPPAOTWOCSBRUMCHDASTESLA Wiggler 127 225350824721592609 ARC 2697 89847223180345530522015 Long straight 0 210110402329117591337014376  OCS has the longest ARC  OTW has the shortest ARC and small beta at ARC!  DAS, MCH and TESLA has a long bunch spacing!! (ion is Not easy to be trapped)

6. 10/18/2005 FII in damping ring L Wang6 OTW OCS A smaller beta function help in two aspects!

7. 10/18/2005 FII in damping ring L Wang7 Nbunch=20, P=10nTorr, 20% is CO+ ATF Close to the experiment Tune shift is very small Bunch intensity Growth time (ms) Tune shift 0.16E10276.8648e-006 0.37E10121.5875e-005 0.63E106.72.7030e-005 Radiation damping time 30ms

8. 10/18/2005 FII in damping ring L Wang8 PLS( P=5nTorr)  Energy 2.0GeV  Lsep=2ns   x=12.1nm   y=0.12nm  N=1.168  10 10  Nbunch=180   rad =16ms ILC P=5nTorr  Energy 5.0GeV  Lsep=4~20ns   x=0.5nm   y=0.002nm  N=2  10 10  Nbunch=2820  scaling >21  s  Ions are not trapped at some location with the equilibrium emittance, especially in Wiggler  Long straight section  >100  s PLS Calculation (don’t know the optics) 0.9 ms for 100% CO+ 5ms for 100% H+

9. 10/18/2005 FII in damping ring L Wang9 B-factories KEKB( P=1nTorr)  Energy 8.0GeV  Lsep=2.4m   x=24nm   y=0.4nm  N=5.6  10 10  Nbunch=1389   feedback =0.5ms  scaling_ILC >1  s PEPII( P=1nTorr)  Energy 8.0GeV  Lsep=1.26m   x=50nm   y=1nm  N=4.6  10 10  Nbunch=1732   cal =0.23ms   Q cal =0.008 There is no FII observed in usual operation of B-factories except at the beginning of the operation after long shutdown (suppressed by Feedback?) ILC has a faster FII than B-factories

10. 10/18/2005 FII in damping ring L Wang10 Gaps  Long term motion of ions are likely unstable; (multi-turn trapping is difficult) Stable Zone with gap (linear model) Trapping time(0.1MHz for 6km ring) t gap T

11. 10/18/2005 FII in damping ring L Wang11 Decay of ion-cloud during the train-gap Gap in KEKB HER: 69.38m(230ns) Gap in PEPII HER: 40m(130ns) (T co+ =110ns; T H+ =30ns) The decay time of ion-cloud is about 1 times of the ion oscillation period: Wiggler section need a short gap Light ion need a short gap.

12. 10/18/2005 FII in damping ring L Wang12 Co+ oscillation period OCS TESLA Damping ring is different from B-factories & Light source The required gap varies with time!

13. 10/18/2005 FII in damping ring L Wang13 Gap effect on stable zone (OCS) Gap=8 bunch spacing=49.2ns Trapping location varies with time

14. 10/18/2005 FII in damping ring L Wang14 Summary  The instability/tune shift is dominated by CO+ if it is more than 10% in the vacuum  17km rings has longer growth time (factor 5~10 better than 6km and 3km rings)  Scaling with the present machines is NOT easy! The shorter growth time is around 100  s (scale with PLS)  Feedback is certainly necessary  Necessary gap is around 1.2 times of ion oscillation period (PEPII). It varies with the time (emittance) and Optics. We need to define the necessary gap for a certain time.

15. 10/18/2005 FII in damping ring L Wang15 RingPPAOTWOCSBRUMCHDASTESLA  wiggler (  s) 0.60.8 0.71.752.672.4  arc (  s) 254.23.63.569.4312.713.5  straight (  s) 58919248821929844  ring (  s) 2.68.84.43.220.840.544.3 Tune shift 0.660.282.110.440.240.34 Peak growth rate of FII and tune shift with CO+  Both DAS and TESLA have longer growth time and small tune shift  Feedback is necessary  Necessary gap is about 1 period of ion oscillation period. 17km ring need a longer train gap Conclusion