10/18/2005 FII in damping ring L Wang 1

Smaller (vertical) beta function

Long bunch spacing

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

ii ieff

w11

Wi =Length_element/ Length_section

Wi=0 if ion is unstable

10/18/2005 FII in damping ring L Wang 2

Peak growth rate of FII for CO+

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

Shorter average growth time

Ring PPA OTW OCS BRU MCH DAS TESLA

wiggler (s) 0.6 0.8 0.8 0.7 1.75 2.67 2.4

arc (s) 25 4.2 3.6 3.56 9.43 12.7 13.5

straight (s) 589 19 248 821 929 844

ring (s) 2.6 8.8 4.4 3.2 20.8 40.5 44.3

Ring PPA OTW OCS BRU MCH DAS TESLA

wiggler (s) 55 87 67 63 148 24 23

arc (s) 235 333 279 330 868 1154 1360

straight (s) 3771 1520 3430 4920 5727 5413

ring (s) 231 961 339 281 1705 3409 4027

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!

10/18/2005 FII in damping ring L Wang 3

0 2 4 6 80

0.005

0.01

0.015

0.02

0.025

0.03

Time (damping time)

Tu

ne

shif

t

PPAOTWOCSBRUMCHDASTESLA

0 1 2 3 4 5 6 7 80

0.5

1

1.5

2

2.5

Time (damping time)

Tu

ne

shif

t

PPAOTWOCSBRUMCHDASTESLA

Tune-shift

CO+ H+

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

10/18/2005 FII in damping ring L Wang 4

Ion yield

H+ is dominant component!

Aluminium Copper

10/18/2005 FII in damping ring L Wang 5

Incoherent vertical tune shift-strongly optics dependentLarger tune shift

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

0 1 2 3 4 5 6 7 80

0.5

1

1.5

2

2.5

Time (damping time)

Tu

ne

shif

t

PPAOTWOCSBRUMCHDASTESLA

Ring PPA OTW OCS BRU MCH DAS TESLA

Wiggler 127 225 350 824 721 592 609

ARC 2697 898 4722 3180 3455 3052 2015

Long straight 0

2101 1040 2329 11759 13370 14376

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)

10/18/2005 FII in damping ring L Wang 6

0 2 4 6 80

0.5

1

1.5

2

2.5

Time (damping time)

Tu

ne

shif

t

TotalWigglerARC

0 2 4 6 80

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Time (damping time)

Tu

ne

shif

t

TotalWigglerARC

OTW

OCS

0 2 4 6 80

0.2

0.4

0.6

0.8

1

Time (damping time)

Tra

pp

ing

fra

ctio

n trapping in wiggler

trapping in arctrapping in whole ring

0 2 4 6 80

0.2

0.4

0.6

0.8

1

Time (damping time)

Tra

pp

ing

fra

ctio

n

trapping in wigglertrapping in arctrapping in whole ring

1600 1700 1800 1900 20000

10

20

30

40

50

S (m)

x

y (

m)

x

y

1450 1500 15500

10

20

30

40

50

S (m)

x

y (

m)

x

y

A smaller beta function help in two aspects!

10/18/2005 FII in damping ring L Wang 7

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

Close to the experiment

Tune shift is very small

Bunch intensity

Growth time (ms)

Tune shift

0.16E10 27 6.8648e-006

0.37E10 12 1.5875e-005

0.63E10 6.7 2.7030e-005

Radiation damping time 30ms

10/18/2005 FII in damping ring L Wang 8

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

scaling>21s

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

Long straight section

>100s

0 2 4 6 8

100

102

104

106

Time (damping time)

Gro

wth

tim

e (

s)

ave

wig

arc

str

PLS

Calculation (don’t know the optics)

0.9 ms for 100% CO+

5ms for 100% H+

10/18/2005 FII in damping ring L Wang 9

B-factoriesKEKB(P=1nTorr)

Energy 8.0GeV

Lsep=2.4m

x=24nm

y=0.4nm

N=5.61010

Nbunch=1389

feedback=0.5ms

scaling_ILC>1s

PEPII(P=1nTorr)

Energy 8.0GeV

Lsep=1.26m

x=50nm

y=1nm

N=4.61010

Nbunch=1732

cal=0.23ms

Qcal=0.008There 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

10/18/2005 FII in damping ring L Wang 10

Gaps

gapyx

arctgnn

,

22

x ystable

x y

x y gap

x y gap

arctg

T,

,

,

, ( )

22

)(, gapyx T

/2

)(2teqi e

dt

d

dt

d yx,

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)

tgap

T

10/18/2005 FII in damping ring L Wang 11

Decay of ion-cloud during the train-gap

Gap in KEKB HER: 69.38m(230ns)

Gap in PEPII HER: 40m(130ns)

(Tco+=110ns; TH+=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.

0 200 400 600 8000

0.2

0.4

0.6

0.8

1

t (ns)

ION

-CL

OU

D

f= 10MHz, T=100ns, =82ns

f= 12.47MHz, T=80ns, =72ns

f= 7.51MHz, T=133ns, =115ns

10/18/2005 FII in damping ring L Wang 12

Co+ oscillation period

3 4 5 6 7 80

50

100

150

200

250

300

Time (damping time)

Osc

illat

ion

Per

iod

(n

s)

Twig

Tarc

Tstr

3 4 5 6 7 80

100

200

300

400

500

600

700

800

Time (damping time)

Osc

illat

ion

Per

iod

(n

s)

Twig

Tarc

Tstr

OCSTESLA

Damping ring is different from B-factories & Light source

The required gap varies with time!

10/18/2005 FII in damping ring L Wang 13

Gap effect on stable zone (OCS)

0 2 4 6 80

0.2

0.4

0.6

0.8

1

Time (damping time)

Tra

pp

ing

fra

ctio

n

trapping in wigglertrapping in arctrapping in whole ring

Without gap

With gap

Gap=8 bunch spacing=49.2ns

0 2 4 6 8

100

102

104

106

Time (damping time)

Gro

wth

tim

e (

s)

ave

wig

arc

str

3 4 5 6 7 80

50

100

150

200

250

300

Time (damping time)

Osc

illat

ion

Per

iod

(n

s)

Twig

Tarc

Tstr

Trapping location varies with time

10/18/2005 FII in damping ring L Wang 14

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.

10/18/2005 FII in damping ring L Wang 15

Ring PPA OTW OCS BRU MCH DAS TESLA

wiggler (s) 0.6 0.8 0.8 0.7 1.75 2.67 2.4

arc (s) 25 4.2 3.6 3.56 9.43 12.7 13.5

straight (s) 589 19 248 821 929 844

ring (s) 2.6 8.8 4.4 3.2 20.8 40.5 44.3

Tune shift 0.66 0.28 2.1 1 0.44 0.24 0.34

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