10/18/2005 fii in damping ring l wang1 smaller (vertical) beta function long bunch spacing both...
Post on 18-Dec-2015
213 views
TRANSCRIPT
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