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Wi =Length_element/ Length_section Wi=0 if ion is unstable. Both growth rate and tune-shift are small if there is a. Smaller (vertical) beta function Long bunch spacing. Peak growth rate of FII for CO+. Pwiggler= 2.0nTorr ; Plong_straight = 0.1nTorr P_arc= 0.5nTorr.

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Wi =Length_element/ Length_section

Wi=0 if ion is unstable

Both growth rate and tune-shift are small if there is a

  • Smaller (vertical) beta function

  • Long bunch spacing


Peak growth rate of FII for CO+

Pwiggler=2.0nTorr;

Plong_straight=0.1nTorr

P_arc=0.5nTorr

Growth time is less than 1 turn!

Peak growth rate of FII for H+

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

Shorter average growth time

  • TESLA; DAS; MCH; OTW; OCS; BRU;PPA


Tune-shift

H+

CO+

The Tune shift caused by CO+ is 30~100 times larger than H+!!


Ion yield
Ion yield

Aluminium

Copper

H+ is dominant component!


Incoherent vertical tune shift-strongly optics dependent

Larger tune shift

  • OTW; DAS; TESLA; MCH; PPA; BRU; OCS

  • 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)



ATF

Nbunch=20, P=10nTorr, 20% is CO+

Radiation damping time 30ms

Close to the experiment

Tune shift is very small


PLS

  • Ions are not trapped at some location with the equilibrium emittance, especially in Wiggler

  • Long straight section

PLS(P=5nTorr)

  • Energy 2.0GeV

  • Lsep=2ns

  • x=12.1nm

  • y=0.12nm

  • N=1.1681010

  • Nbunch=180

  • rad=16ms

ILC P=5nTorr

  • Energy 5.0GeV

  • Lsep=4~20ns

  • x=0.5nm

  • y=0.002nm

  • N=21010

  • Nbunch=2820

>100s

scaling>21s

Calculation (don’t know the optics)

0.9 ms for 100% CO+

5ms for 100% H+


B factories
B-factories

KEKB(P=1nTorr)

  • Energy 8.0GeV

  • Lsep=2.4m

  • x=24nm

  • y=0.4nm

  • N=5.61010

  • Nbunch=1389

  • feedback=0.5ms

PEPII(P=1nTorr)

  • Energy 8.0GeV

  • Lsep=1.26m

  • x=50nm

  • y=1nm

  • N=4.61010

  • Nbunch=1732

  • cal=0.23ms

  • Qcal=0.008

scaling_ILC>1s

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


Gaps

T

Stable Zone with gap (linear model)

tgap

  • Long term motion of ions are likely unstable; (multi-turn trapping is difficult)

Trapping time(0.1MHz for 6km ring)


Decay of ion cloud during the train gap
Decay of ion-cloud during the train-gap

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.

Gap in KEKB HER: 69.38m(230ns)

Gap in PEPII HER: 40m(130ns)

(Tco+=110ns; TH+=30ns)


Co oscillation period
Co+ oscillation period

TESLA

OCS

Damping ring is different from B-factories & Light source

The required gap varies with time!


Gap effect on stable zone ocs
Gap effect on stable zone (OCS)

Gap=8 bunch spacing=49.2ns

Trapping location varies with time


Summary
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.


Conclusion

  • 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

Peak growth rate of FII and tune shift with CO+


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