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## PowerPoint Slideshow about ' Smaller (vertical) beta function Long bunch spacing' - quentin-branch

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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

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)

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

Radiation damping time 30ms

Close to the experiment

Tune shift is very small

- 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=1.1681010
- Nbunch=180
- rad=16ms

ILC P=5nTorr

- Energy 5.0GeV
- Lsep=4~20ns
- x=0.5nm
- y=0.002nm
- N=21010
- Nbunch=2820

>100s

scaling>21s

Calculation (don’t know the optics)

0.9 ms for 100% CO+

5ms for 100% H+

B-factories

KEKB(P=1nTorr)

- Energy 8.0GeV
- Lsep=2.4m
- x=24nm
- y=0.4nm
- N=5.61010
- Nbunch=1389
- feedback=0.5ms

PEPII(P=1nTorr)

- Energy 8.0GeV
- Lsep=1.26m
- x=50nm
- y=1nm
- N=4.61010
- Nbunch=1732
- cal=0.23ms
- Qcal=0.008

scaling_ILC>1s

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

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

TESLA

OCS

Damping ring is different from B-factories & Light source

The required gap varies with time!

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.

- 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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