Beam-ion Instabilities in SPEAR3 Lanfa Wang, SLAC KEK accelerator physics Seminar 2/15/2012 1.

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


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


start

best results

Main parameters@SPEAR3

Slide 6


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


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!


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


-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


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


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


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


(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


Observations in SPEAR3

Effect of emittanceEffect of vacuum pressureEffect of beam currentEffect of beam filling patternEffect of chromaticityEffect of feedbackEffect of vacuum burst

17


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


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


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

)


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


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


Mitigation with multi-bunch train beam filling

Bunch

Missing bunch

23


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


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


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


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


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


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


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


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


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


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


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


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>)


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?)


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.


Acknowledgements

Thanks James Safranek, Jeff Corbett, John Schmerge, Jim Sebek, Dmitry Teytelman, and other SSRL members for the data taking and discussions

37


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


Beam-ion Instabilities in SPEAR3 Lanfa Wang, SLAC KEK accelerator physics Seminar 2/15/2012 1.

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Transcript of Beam-ion Instabilities in SPEAR3 Lanfa Wang, SLAC KEK accelerator physics Seminar 2/15/2012 1.