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Beam-ion Instabilities in SPEAR3
Lanfa Wang, SLAC
KEK accelerator physics Seminar
2/15/2012
1
Outline
Introduction to SPEAR3 Introduction to FII(Fast Ion Instability) Observations in SPEAR3
effect of emittanceEffect vacuum pressureEffect of beam currentEffect of beam filling patternEffect of chromaticityEffect of feedbackEffect Vacuum burst
Summary
Slide 2
KEK Accelerator Physics Seminar L. Wang 02/25/12
SPEAR3 Layout
Slide 3
KEK Accelerator Physics Seminar L. Wang 02/25/12
o 234 m circumference racetracko 7 standard cells per arc (SF, SD)o 4 matching cells (SFM, SDM)
QFCQFQF QD QD
BEND BEND
Arc cell:
SF SFSD SD
Achromat Low emittance“Lower”
emittanceSuperconducting damping wigglers
2004-2007 2007-nowWorking in progress Future
ex0 (nm) 18.0 11.2 7.68 <5.0ex, IDs (nm) 14.6 9.6 6.76 4.9ex,eff (nm) 14.6 10.1 7.24 5.65h, ID (m) 0 0.1 0.1 0.1sE (permil) 0.96 0.98 0.97 1.26nx 14.13 14.13 15.13 15.11
Emittance of SPEAR3, ex
x
x’
Effective emittance, ex,eff includes hx: xxExxxxeffx 22',
KEK Accelerator Physics Seminar L. Wang
Adding nonlinear knobs (simulation)
1. New sextupole magnets Two families On steering magnets
2. Octupole magnets
3. Independent power supply. MOGA (multi-objective Genetic Optimizer) elegant tracking, 6.7 nm lattice, with 21 sextupole families
SHA SHB
SF+OF
SD+OD
KEK Accelerator Physics Seminar L. Wang
start
best results
Main parameters@SPEAR3
Slide 6
KEK Accelerator Physics Seminar L. Wang 02/25/12
Physics Symbol/UnitHorizontal Emittance nm 10Vertical Emittance pm 14Beam Current mA 200 (500)Bunch Number 280Harmonic Number 372Beam Energy GeV 3Circumference m 234Bunch spacing ns 2.1RF frequency MHz 476.315Revolution frequency MHz 1.28038Horizontal tune 14.1Vertical tune 6.177Momentum compaction factor 1.610-3
Energy Spread 9.810-4
Radiation Damping time x /y /z [ms] 4.0/5.3/3.2
Vacuum nTorr 0.1~1
24.7% ion clearing gap0.19s
Introduction to FII(Fast Ion Instability)
Ions generated by beam-gas ionization Ions are trapped along the electron-bunch train; The ions created by the head of the bunch train perturb the bunches
that follow. Occur in rings, linacs or beam transport lines;
Broadband spectrum Normally only in vertical direction due to the small vertical beam size The amplitude saturated at order of beam sigma
7
Characteristic of ion instabilities
Coupled motion
Slide 8
KEK Accelerator Physics Seminar L. Wang 02/25/12
M. Kwon, PRE Vol. 57,1998
Simulation
0 20 40 60 80 1000
5
10
15
20
25
30
35
40
f(MHz)
Am
p(d
b)+
111
Ib=500mA, Bunch Number=280, 1 Bunch Train,03/22/2010
Experimental data @SPEAR3
Broad band Spectrum
Spectrum depends on the beam current, optics(emittance,
betatron function), vacuum
9KEK Accelerator Physics Seminar L. Wang
10 20 30 40 50 60 7010
-4
10-3
10-2
10-1
100
Turns(1/2)
Am
p (
)
Saturation of beam-ion instability
Different from other instabilities, ions induced instability rarely causes beam loss.
Simulation, FII
Electric field vs. amplitude
1
When the bunches’ amplitude is larger (compare with beam size), the nonlinear force automatically slow down the instability!
10KEK Accelerator Physics Seminar L. Wang
FII Theory: Phys. Rev. E52, No. 5, p. 5487 (1995))
...*exp),(~
c
t
l
zzsy
(T.R & F.Z)
Ion species in vacuum
Gas Species
Mass Number
Cross-section
Percentage in Vacuum
H2 2 0.35 48%
CH4 16 2.1 5%
CO 28 2.0 14%
CO2 44 2.92 17%
H2O 18 1.64 16%
Total pressure <0.5 nTorr
H2
CH4 COCO2H2O
Vacuum in SPEAR3 @500mA
beii nNkT
P Here P is the vacuum pressure, i is the ionization cross-section, Ne is the number of electrons per bunch, T is temperature and k is Boltzmann constant
0.1nTorr
0.01ntorr
KEK Accelerator Physics Seminar L. Wang
-0.4 -0.2 0 0.2 0.40
0.2
0.4
0.6
0.8
1
X (mm)
BeamIon(Analytic)Ion (numerical)
beam size
x=0.1mm
y=0.004472mm
-5 -4 -3 -2 -1 0 1 2 3 4 5 0
0.2
0.4
0.6
0.8
1
1.2
x()
e
ion
ion
, Asymptotic form
Ion distribution (steady status)
the distribution at x0 is [1]
)8
log(2
1)(
2
24 2
2
x
x
x
xex x
=0.577215
2
2
04
42
1)(
2
2
x
x
x
xKex x
(P.F. Tavares, CERN PS/92-55 )
12
KEK Accelerator Physics Seminar L. Wang
Space Charge Wake from ion cloud
0 10 20 30 40 50 60 70-8000
-6000
-4000
-2000
0
2000
4000
6000
8000
10000
Z (m)
Wy (
m-2
)
Numerical MethodAnalytical Method
Comparison with analysis
Wake, Q=7.14, =21.1m
The wake is long range, which causes coupled bunch instability
Where Ni is the ion number; N is e-beam
population; Sb is bunch spacing
)2
sin()(
1
3
4)( ,2
22/32/1
0
,
c
zfe
AS
NrNzW yicQ
zf
xyyb
pi
yi
2/1
, )(3
4
2
yyxb
pyi AS
Nrcf
Frequency of the wake
13
KEK Accelerator Physics Seminar L. Wang
What we expect to be observed
Calculated ion frequency along the ring for a beam current of 200mA
When the beam is evenly filled along the ring, the exponential growth rate of the coupled bunch instability for mode is [Alex Chao’s book, for example]
p
ybionebe pnZ
T
crnN))((Re
2
102
0
bnjj ey /2
2/1
, )(3
4
2
yyxb
pyi AS
Nrcf
0 20 40 60 80 100 120
10
20
30
40
50
60
70
80
90
100
S (m)
f ion (
MH
z)
COH
2
H2O
CO2
The frequency of the unstable modes depends on the optics!
14
KEK Accelerator Physics Seminar L. Wang
Observations with high pressure(gas injection)Instability has been observed at many laboratories when vacuum is not good
Artificially increasing the vacuum pressure (ALS, PLS, ATF) At commissioing times or restart after a long shutdown (ESRF, DIAMOND) After installation of new (insertion device) chambers (SPring-8, ESRF)
ALS
y~30m
C. J. Bocchetta, et. al. 1994
ELETTRA
15
KEK Accelerator Physics Seminar L. Wang
(M. Kwon et al., Phys. Rev. E57 (1998) 6016)PF
Observations at Nominal conditionsInstability has been observed at many laboratories when vacuum is not good
Artificially increasing the vacuum pressure (ALS, PLS, ATF) At commissioing times or restart after a long shutdown (ESRF, DIAMOND) After installation of new (insertion device) chambers (SPring-8, ESRF)
The instability also occurs at nominal condition (SOLEIL, SSRF, SPEAR3…) For existing light sources it does not pose a problem. May become a problem
for lower emittance rings
SSRF, B. Jiang, NIMA 614 (2010) 331–334
Vertical amplitude along the bunch trainSSRF, nominal vacuum
16
KEK Accelerator Physics Seminar L. Wang
Observations in SPEAR3
Effect of emittanceEffect of vacuum pressureEffect of beam currentEffect of beam filling patternEffect of chromaticityEffect of feedbackEffect of vacuum burst
17
KEK Accelerator Physics Seminar L. Wang
Ion instability at SPEAR3@200mA
Beam Current: 192mABunch Number: 2801 Bunch Train
Experiment condition:
Vertical low sideband was observed at frequency from 5~26MHz , which agrees with the analysis
0 5 10 15 20 25 30 350
5
10
15
20
25
30
f(MHz)
Am
p(d
b)+
125
Beam Current 192mA, Bunch Number 280,One Bunch Train,02/22/2010
Normal CouplingSkew Quadpole off
The sidebands move to low frequency region when the beam emittance increases, which agree with the theory , and confirms this is FII(fast ion instability)
2/1
,,,, )(
2
2
xyyxyxb
peyxi kAS
rNcf
Vertical sideband
Lower instability rate with a larger emittance
KEK Accelerator Physics Seminar L. Wang
Effects of coupling
0
0.5
1
1.5
2
k=0.12%
0 5 10 15 20 25 300
0.5
1
1.5Am
p( m
)
k=1.3%
f(MHz)
skew quadrupole magnets are on
skew quadrupole magnets are off
0 20 40 60 80 1000
5
10
15
20
25
30
35
40
f(MHz)A
mp
(db
)+11
1
Ib=500mA, Bunch Number=280, 6 Bunch Train,03/22/2010
Normal CouplingSkew Quadpole off
190mA single bunch train 500mA Six bunch trains
19
KEK Accelerator Physics Seminar L. Wang
Bunch oscillation along the bunch train
05
1015
100200
300
0
5
10
15
a) Osc. Envelopes in Time Domain
Am
pli
tud
e ( m
)
010
0200
0
0.5
1
Time (ms)
b) Evolution of Modes
Mode No.
m
Single bunch train@200mA
Vertical bunch oscillation amplitude saturated at the amplitude around 1 sigma (12um)
0 100 200 300 4000
2
4
6
8
10
12
14
Bunch number
RM
S am
plit
ude
(m
)
20KEK Accelerator Physics Seminar L. Wang
Effects of beam current
Observed vertical lower sidebands at different beam currents. The beam has single bunch train with 280 bunches
0
2
4 I=200 mA
0
2
4 I=300 mA
0
2
4 I=400 mA
0 10 20 30 40 50 600
2
4
Am
p( m
)
I=500 mA
f(MHz)
21
KEK Accelerator Physics Seminar L. Wang
Effects of bunch train gap
Single bunch-train, 200mA
100 200 300 400 500 600 700 800 900 1000
100
200
300
400
500
600
700
100 200 300 400 500 600 700 800 900 1000
100
200
300
400
500
600
700
42ns gap
No gap
0
1
2
3 Train Gap=189ns
0
1
2
3 Train Gap=38ns
0 5 10 15 20 25 30 350
10
20
Am
p( m
)
Train Gap= 17ns
f(MHz)
22
KEK Accelerator Physics Seminar L. Wang
Mitigation with multi-bunch train beam filling
Bunch
Missing bunch
23
KEK Accelerator Physics Seminar L. Wang
Effects of beam filling pattern@200mA
0 5 10 15 20 25 30 350
5
10
15
20
25
30
f(MHz)
Am
p(d
b)+
125
One Bunch Train,NB=280, I=200mA, 02/23/2010Filling 1: 1 Bunch Train (3pm)
1 Bunch Train;200 mA280 Bunches
Vertical sideband with 1 bunch train
Sideband found
Filling 3: 2 Bunch Train (4:15pm)
2 Bunch Train;200 mA280 Bunches
No sideband
50 100 150 200 250 300
26.16
26.18
26.2
26.22
26.24
26.26
26.28
Bunch ID
be
am
fill
ba
ttern 0 100 200 300
25
25.5
26
26.5
27
27.5
Bunch ID
be
am
fill
ba
ttern
Growth time about 2.5ms~5ms?24
KEK Accelerator Physics Seminar L. Wang
1
2
3
4
One Bunch Train
1
2
3
4
Four Bunch Train
0 10 20 30 40 50 60
1
2
3
4
Am
p( m
)
Six Bunch Train
f(MHz)
Effects of beam filling pattern@500mA
Beam current 500mA
25
KEK Accelerator Physics Seminar L. Wang
Simulation of ion cloud build-up
0 500 1000 15000
0.5
1
1.5
2
x 1012
Time (ns)
i (m
-3)
One Bunch TrainTwo Bunch TrainFour Bunch TrainSix Bunch Train
Build-up of ions with different beam filling pattern@500mA
0 2 4 6 80.6
0.8
1
1.2
1.4
1.6
1.8
2x 10
12
Number of Bunch Train
i (m
-3)
diffusiongapeNf
traingap /1
11
Ion density reduction due to multi-bunch train
Train gap=30ns =1 wavelength for 33MHz
The required train gap is only about 1 ion oscillation period. A short gap for high intensity beam (PEPX uses more than 100 bunch trains)
26
KEK Accelerator Physics Seminar L. Wang
Effect of chromaticity
123
y=2.0,=10hrs
123
y=3.1,=8.8hrs
123
Am
p (
m)
y=4.2,=8.1hrs
123
y=5.1,=7.0hrs
123
y=6.2,=6.0hrs
0 10 20 30 40 50 600123
f(MHz)
y=7.0,=4.7hrs
@Single bunch train, 500mA
27
KEK Accelerator Physics Seminar L. Wang
Effect of Chromaticity@500mA
1.5 2 2.5 3 3.5 4 4.5 50
5
10
15
20
25
Vertical Chromaticity
Am
p(d
b)+
107
One Bunch-Trains,500mA,05/04/2010
2 2.5 3 3.5 40
5
10
15
20
Vertical Chromaticity
Am
p(d
b)+
107
Four Bunch-Trains,500mA,05/04/2010
2.2 2.4 2.6 2.80
2
4
6
8
10
12
14
16
Vertical Chromaticity
Am
p(d
b)+
107
Six Bunch-Trains,500mA,05/04/2010
With vertical chromaticity 2.6, the sideband disappear.
With vertical chromaticity 3.6, the sideband becomes weak.
Increase chromaticity, lifetime drop from 11hrs to 9.hrsWith vertical chromaticity 4.6, the sideband still appear.
1 bunch train
4 bunch train
6 bunch train
1 bunch train 4 bunch train 6 bunch train
28
KEK Accelerator Physics Seminar L. Wang
Effects of vacuum pressure@300mA Six bunch train
The beam consists of six bunch trains with total bunch number of 280. The beam current is 300 mA. There are no sidebands with the nominal pressure of 0.37nTorr. The vacuum pressure is increased by partially turning off the ion pumps.
0
5
10
15P=0.37nTorr
0
5
10P=0.86nTorr
0
5
10P=1.29nTorr
0 20 40 60 80 1000
5
10
Am
p( m
)
P=1.75nTorr
f(MHz)
29
KEK Accelerator Physics Seminar L. Wang
Preliminary feedback test
0 5 10 15 20 25 30 35-6
-4
-2
0
2
4
6
Time(ms)
y (
m)
Measured beam’s unstable mode 354 when the bunch-by-bunch feedback is on and off,
Almost uniform filling pattern: 448mA, six bunch train, bunch number 366, (only 1 missing bunch in each train gap)
There is no bunch-by-bunch feedback in SPEAR3, we tested once of the feedback from Dimtel, Inc
The oscillation amplitude has been reduced. Some bunches still have residual oscillationsPossible reasons:(1) The bandwidth of the feedback kicker
is not large enough(2) The instability is too fast
010
2030
100200
300
0
10
20
30
Am
pli
tud
e (
m)
0
20
0
200
0
2
4
6
Time (ms)
b) Evolution of Modes
Mode No.
m
(a)
30
KEK Accelerator Physics Seminar L. Wang
Effect of Vacuum burst
In nominal case, the beam ion instability can’t case beam loss due to the saturation mechanism.
However, when there is a vacuum burst, partial beam loss and strong beam ion instability
31
KEK Accelerator Physics Seminar L. Wang
8 bunch train
Comparison with simulation
0 5 10 15 2010
-3
10-2
10-1
100
101
102
Time (ms)
Y (
m)
one bunch-train, =0.38mstwo bunch-trains, =0.93msfour bunch-trains,=1.60mssix bunch-trains, =1.62ms
Simulated beam ion instability for different beam filling patterns
0.5nTorr total pressure is used in the simulation(nominal pressure is order of 0.3ntorr)Simulated growth time with 6 bunch-trains beam is 1.6ms( 2.7 ms for 0.3nTorr pressure)Simulation doesn’t include chromaticity and radiation damping,The vertical radiation damping times is 5.3ms.The real growth time should be <5.3ms
500mA280 bunches0.5nTorr
32
KEK Accelerator Physics Seminar L. Wang
1 bunch train; 1ntorr
Comparison of simulation with analysis (6 bunch train)
0 50 100 150-1
-0.5
0
0.5
1
1.5x 10
4
S (m)
Wak
e (m
-2)
f = 29.6457(MHz), W0= 12931.7128m-2, Q=4.8642 = 0.50547(ms)
DataFitting
0 5 10 15
10-6
10-4
10-2
100
Time (ms)
X,Y
()
=0.73996 ms
xy
six trains, CO only 0.5ntorr
Tau=0.74ms
Tau=0.5ms
CicQ
zs
xyye
iyiring ds
c
zse
sss
s
c
szW
i
0
2
)(
, ))(
sin( ))()()((
1)()(
3
4)( 0
Optics effect is included
Qcr ye
1effi
e
it
L
cW ,
2ˆ
Multi-bunch train Instability
(PRSTAB, e084401)
both nonlinear space-charge effect and optics are included
Beam ion instability at nonlinear region (y>)
KEK Accelerator Physics Seminar L. Wang
34
0 500 1000 1500 2000 2500 300010
-6
10-5
10-4
10-3
10-2
10-1
100
101
Turns
Am
p (
)
Beam-ion instability @500mA
Strong nonlinearity
Slow growth with amplitude beating
experiment
Summary of Mitigations
Better vacuum Clearing electrode (only practicable for small ring, add impedance) Multi-bunch-train (simple, cheap, very effective for high intensity beam) Chromaticity (useful with side-effects: lifetime & injection rate drop) Feedback System (very effective, need more R&D?)
35KEK Accelerator Physics Seminar L. Wang
Summary
The observations in SPEAR3 agree with theory & simulationsThis type of instability can be mitigated by multi-bunch train beam filling SPEAR3@500mA: 6 bunch-trains filling pattern 200mA: 2 bunch trains
Multi-bunch train is very effective for high intensity beam such as ILC, SuperKEKB, PEPX. (up to two orders of magnitude)
Chromaticity can mitigate the instability at the cost of lifetimeBunch-by-bunch feedback is very effective(need more test? FII can be very fast although the amplitude is small )The beam ion instability is not a problem for SPEAR3 although we don’t have feedbackBeam-ion Instability can be important for future small emittance rings, such as ultimate storage ring light source ~pm, especially for collider.
36KEK Accelerator Physics Seminar L. Wang
Acknowledgements
Thanks James Safranek, Jeff Corbett, John Schmerge, Jim Sebek, Dmitry Teytelman, and other SSRL members for the data taking and discussions
37
KEK Accelerator Physics Seminar L. Wang
Thank You!
38
Backup slides
39
Comparison of FII in various electron rings (single bunch train mode is assumed)
RING E (GeV)
Cir(m) nb I (mA) LSP(m) EX/x nmrad/m
EY/Y nmrad/m
i,eff/
PEPII 8.0 2199 1588 1550 1.26 31/660 1.4/144 1.1KEKB 8.0 3016 1387 1200 2.1 24/500 0.49/75 1.0ALS 1.5 196.8 320 400 0.6 6.3/160 0.06/23 1.2APS 7.0 1104 24 100 45.9 3.0/276 0.025/11 0.4PLS 2.0 280 180 360 0.6 12.1/350 0.12/35 0.3ATF 1.3 138 20 64 0.77 1.2/70 0.0045/5 1.6SPEAR3 3.0 234 280 500 0.63 10/200 0.014/10 1.6NSLSII 3.0 792 1040 500 0.6 1.0/122 0.008/11 8.1SUPERKEKBI 3.5 3016 5120 9400 0.6 24/600 0.24/60 18.7SUPERKEKBII 7.0 3016 2500 2600 1.18 5.1/280 0.013/14 23.7ILC 5.0 6000 3K/6K 400 0.5/1 0.8/120 0.002/6 55.3PEPX 4.5 2199 3154 1500 0.6 0.08/18 0.0043/5.7 596
For present day light sources/e-rings, FII does not pose a serious problem. It can be a problem for future low emittance light sources and damping rings.
40
Effect of frequency spread of HOM (BBU)
/=0.5/=0
Constant Wake of ion-cloud
)sin()( 20 c
zeWzW iQc
zi
i
iiQ
QWZ tt
1
)(
Frequency spread model: 10 modes with equal frequency variation
[Yokoya, ? ]
Types of beam ion instability[1] Single bunch train: Fast ion Instability (FII)
zero frequency spread (next page)
With large frequency spread
Uniform beam filling pattern
Multi-bunch train beam filling pattern
)(1
a
Qcr ye
)15.0( a
/a
5.0a0.1a
The maximum exponential growth rate
Is the average ion density seen by all bunches
Is the maximum ion density seen by all the bunches
t
ety )(~ )(3
2,
xyy
ieffi
Q : typically 1~8, can be smaller than 1 42
Quasi-exponential growth Regime I(FII, Zero Frequency spread case)
10 20 30 40 50 60 7010
-4
10-3
10-2
10-1
100
Turns(1/2)
Am
p (
)
Regime I
Regime II
FII , simulation
c
i t
c
l
2
1
( T. Raubenheimer, F. Zimmermann, PRE V51, 5487, 1995)
Region I
),(~4
),(~2
zsyzzsyzs
y
c
yy t
l
zszszIzsy
exp2
exp2
),(~0
c
zcrlW
Nncrieffiyebye
c
,)(ˆ
2
11
Fast instability only when the amplitude is small than the beam size!
43
Theory of FII
( T. Raubenheimer, F. Zimmermann, PRE V51, 5487, 1995)
c
t
l
zzsy
exp),(~
c
zcrlW
Nncrieffiyebye
c
,)(ˆ
2
11
44
Zero frequency spread (w.o optics), Quasi-exponential growth
With frequency spread due to optics, exponential growth
[G. Stupakov, KEK Proceedings 96-6, 243 (1996)]
iixyy
iye
FIIe
cr
/
1
)(23
1
,
Single bunch train instability
Multi-Bunch-train instability
Qcr ye
1
)15.0( a a=1 for an even beam filling pattern; a=0.5 for a single bunch train beam filling pattern
/a
Both Optics effect beam
Comparison of simulation with analysis(1 bunch train)
0 1 2 3 4
10-6
10-4
10-2
100
Time (ms)
X,Y
()
=0.12859 ms
xy
One train, 500mA, 280 bunches, CO only 0.5ntorr
0 50 100 150-4
-3
-2
-1
0
1
2
3
4
5x 10
4
S (m)
Wak
e (m
-2)
f = 29.7159(MHz), W0= 48919.0898m-2, Q=4.9009 = 0.13294(ms)
DataFitting
Calculated wake
Simulation
Tau=0.128ms
Tau=0.132ms
Analysis Using the total wake (Q0=8)
CicQ
zs
xyye
iyiring ds
c
zse
sss
s
c
szW
i
0
2
)(
, ))(
sin( ))()()((
1)()(
3
4)( 0
Optics effect is included
Can a slower feedback suppress the instability?
0 20 40 60 80 1000
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Turn
Y(
)
0 20 40 60 80 10010
-3
10-2
10-1
100
Turn
Y(
)
=3turn
Feedback damping time 10 turn. It is turned on around 50th turn when the instability is already developed. (file:ocs_2767nb3devefdbk_amp)
• A bunch-by-bunch feedback with a damping rate slower than the exponential growth rate may limit the oscillation amplitude in the exponential growth region (0.1~1sigma ) by suppressing the linear oscillation.
46
KEK Accelerator Physics Seminar L. Wang
Slide 47
KEK Accelerator Physics Seminar L. Wang 02/25/12