Fast Ion Instability Studies in ILC Damping Ring Guoxing Xia DESY ILCDR07 meeting, Frascati, Mar. 5~7, 2007

Fast Ion Instability Studies in ILC Damping Ring

Guoxing Xia

DESY

ILCDR07 meeting, Frascati, Mar. 5~7, 2007

Outlines

• Ions-related instabilities

• Fast ion instability (FII)

• Simulation of FII

• Future R&D for FII

• Summary


Ions related instabilities (1)

• The ions come from collision ionization process of residual gas in the vacuum chamber by beam particles, or via residual gas ionization and desorption by synchrotron radiation or via beam losses

• These ions in the beam result in beam emittance growth, beam size blow-up, additional tune shifts and beam lifetime reduction etc.

• Ion instabilities include conventional ion trapping instability and fast ion instability


Ions related instabilities (2)

• At conventional storage rings, ion trapping instabilities can be cured by filling the ring partially, e.g, leaving an ion clearing gap of a few us in length

• In low emittance and high intensity rings, such as ILC damping ring (DR), the effects of ions created during the passage of a single bunch train become important.

• The so called fast ion instability is one of the most important issues in R&D of ILCDR


Fast ion instability (1)

The residual gas in the vacuum chambers can be ionized by the single passage of a bunch trainThe interaction of an electron beam with residual gas ions results in mutually driven transverse oscillationsIons can be trapped by the beam potential or can be cleared out after the passage of the beamFor ILC damping ring, the growth rate of this instability is high


Linear theory of FII (Tor, Frank, Stupakov, etc)This instability has been confirmed experimentally in many facilities such as ALS, TRISTAN AR, PLS, Spring-8, ESRF, KEKB HER, ATF DR etc.

Characteristics of FII


• Linear theory of FIICritical mass

Incoherent tune shift

The exponential vertical

instability rise time

yxy

psepbcrit

rLNA

2

Tk

pCrnNQ

B

ion

yx

ebbion

i

iB

ionyebb

yxFII f

f

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8

# ofbunches

bunchspacing

bunchintensity

critical mass

incoh. tuneshift at trainend

exponentialrise timeat train end

2625 6 ns 2.0E10 5.4 0.0037 0.005 s

5534 3 ns 1.0E10 1.4 0.0039 0.004 s

Partial pressure of CO is 0.15nTorr; one long bunch train and 30% relative ion frequency spread are assumed here

Estimation of FII in OCS6 DR



• Traditional methods to clear ions from electron beam include electrostatic electrodes, beam shaking and gaps in the bunch trains

• Clearing electrodes may increase the chamber impedance

• Beam shaking requires dedicated device to drive the ions and beam and may cause coherent transverse instabilities

• Multi-train fill pattern with regular gaps is an efficient and simple way to remedy of FII

• Bunch by bunch feedback system?



• Ion line density is

• If mini-train is introduced in the fill pattern, the diffusion of the ions during the gaps causes a larger size of ion cloud and a lower ion density. In order to evaluate the effects of gaps, an Ion-density Reduction Factor is defined as

here, is the diffusion time of ion cloud. IRF is the ratio of the ion density with gaps and without gaps.

• So the fill pattern can be optimized in terms of obtain the smallest possible IRF (this work is ongoing)

TknpN Bbbionion /

iongaptrainNIRF

/exp1

11


ion

Simulation results on effect of train gaps for ILC DR

( Wang, et al. EPAC06)

0 50 100 150 200

10

20

30

40

50

60

70

Bunch ID

beam fill battern )/exp(1

11IRF

ionsgaptrainN

Beam fill pattern

38ns

118 trains

0 500 1000 1500 20000

0.5

1

1.5

2x 10

7

No. Bunches

average

(m-3)

0

0.5

1

1.5

2

2.5

3

x 1012

center

(m-3)

Average densityCenter density

Bunch ID

ρav

erag

e [

m-3]

Central iondensity isreduced by afactor 60compared to a fillconsisting of asingle long train.

Build-up of CO+ ion cloud at extraction (with equilibrium emittance). The total number of bunches is 5782, P=1 nTorr. IRF=0.017 in this case!

with equilibrium emittanceεx = 0.5 nm εy = 2 pm



Simulation of FII (1)

• Weak-strong approximation• Electron beam is a rigid gaussian• Ions are regarded as Marco-particles• The interaction between them is

based on Bassetti-Erskine formula• Six collision points in the ring

Circumference [m] 6695.057

Energy [GeV] 5.0

Harmonic number 14516

Arc cell type TME

Transverse damping time [ms] 25.7

Natural emittance [nm] 0.515

Norm. natural emittance [μm] 5.04

Horizontal initial emittance [nm] 4.599

Vertical initial emittance [nm] 4.599

Horizontal equilibrium emittance [nm] 0.8176

Vertical equilibrium emittance [pm] 2.044

Natural bunch length [mm] 6.00

Natural energy spread [10−3] 1.28

Average current [mA] 402

Mean horizontal beta function [m] 13.1

Mean vertical beta function [m] 12.5

Bunches per train 2820

Particles per bunch 2 x 1010

Bunch spacing [m] 1.8


Simulation of FII (2)• Kicks between electrons and ions (based on Bassetti-Erskine formula)

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exp)(2)(2

),(222

2

2

2

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y

x

x

y

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iyx

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),(2,, ieiei

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xiy ),(2

''

)]erf(1)[exp()( 2 izzzw


c

Lvyy

c

Lvxx sep

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x 00 ;

• The ions drift in the space between adjacent bunches linearly


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1cos

sin)sin(cos

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1

22

1

12

21

12

21

1211

2

2

2

yxz

z

z

z

z

• Beam motion between ionization points can be linked via linear optics

• For the flat beam, we mainly care about the vertical direction (y direction)



0 1000 2000 3000 4000-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

y (u

nits

of

y)Turns

Partial pressure of CO: 0.1nTorr


Vertical position of bunch centroid in units of σy as a function of number of turns

0 1000 2000 3000 4000

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15 Bunch 5 Bunch 50 Bunch 100 Bunch 150 Bunch 282

y (u

nits

of y

)

Turns

Partial pressure of CO: 1nTorr

222

)'('21

yyyyJ y

0 1000 2000 3000 40001E-14

1E-13

1E-12

1E-11

1E-10

1E-9

1E-8

1E-7

1E-6

1E-5

1E-4

1E-3

0.01

0.1

J y (uni

ts o

f y

)

Turns


The vertical action of the bunch centroid

0 1000 2000 3000 40001E-17

1E-16

1E-15

1E-14

1E-13

1E-12

1E-11

1E-10

1E-9

1E-8

1E-7

1E-6

1E-5

1E-4

1E-3

0.01

0.1

J y (un

its o

fy)

Turns

Partial pressure of CO: 0.1nTorr



Vertical centroid action in units of εy as a function of number of turns

Vertical oscillation


0 1000 2000 3000 40001E-7

1E-6

1E-5

1E-4

1E-3

0.01

0.1

sqrt

(2J y

y) (u

nits

of

y)

Turns


0 1000 2000 3000 40001E-7

1E-6

1E-5

1E-4

1E-3

0.01

0.1

sqrt

(2J y

y) (u

nits

of

y)

Turns

Partial pressure of CO: 0,1nTorr

Oscillation amplitude in units of σy as a function of number of turns


Future R&D for FII (1)

A proposal has been submitted to TB of ATF international collaboration meeting A plan on experimental studies of FII in ATF DR is ongoing (see Junji’s presentation)

Goals of FII experiment: Distinguish the two ion effects: beam size blow-up and dipole instability. Quantify the beam instability growth time, tune shift and vertical emittance

growth. Based on the linear model, the growth rate is proportional to the ion density (the related parameters include vacuum pressure, gas species, average beam line density, emittance, betatron functions and beam fill pattern).

Flatness of beam and its effect on FII growth. Quantify the bunch train gap effect Beam shaking effect Provide enough experimental data to benchmark against simulations results.

Understand of other measurements (e.g. ALS, PLS and KEKB) Check effectiveness of feedback system to suppress the FII


Beam centroid oscillation amplitude with respect to number of turns

One long bunch train is used in simulation !

The 60th bunch is recorded here

Beam energy [GeV] 1.28

Circumference [m] 138.6

Harmonic number 330

Momentum compaction 2.14E-3

Bunch population [×109] 1.6, 3.7 and 6.0

Bunch length [mm] 6

Energy spread 0.06%

Horizontal emittance [mrad] 1.4E-9

Vertical emittance [mrad] 1.5E-11

Vacuum pressure [nTorr] 1 and 5

Parameters of ATF damping ring




0 200 400 600 800 1000

0.0

0.3

0.6

0.9

1.2

1.5

Am

p ()

Number of turns

Ne=1.6E9

Ne=3.7E9

Ne=6.0E9

p=5.0nTorr

number of bunches per train=20

number of bunch trains=3

bunch spacing=2.8ns

Beam centroid oscillation amplitude with respect to number of turns

If we introduce the gaps between the bunch trains, the growth will be greatly reduced


Bunch population 1.6E9 2.0E10

Vacuum pressure [ntorr] 1 5 10 1 5 10

Ion density [m-1] 309 1545 3090 3862 19312 38625

Critical mass 1.28 1.28 1.28 16 16 16

Ion oscillation frequency 2.4E7 2.4E7 2.4E7 8.6E7 8.6E7 8.6E7

FII growth time [s] 6.8E-5 1.4E-5 6.8E-6 1.5E-6 3.1E-7 1.5E-7

FII grow. time (10% ion freq. spread) [s] 4.0E-4 8.1E-5 4.0E-5 3.2E-5 6.5E-6 3.2E-6

Tune shift 1.9E-5 9.5E-5 1.9E-4 2.3E-4 1.2E-3 2.4E-3

Analytical estimation of Ion effects in ATF damping ring



Summary

• Fast ion instability is still one of critical issues for R&D of ILCDR

• Simulation results show that this instability is within control (need further check)

• R&D of FII should be strengthened further and well coordinated around the world

• Bunch by bunch feedback systems, up-to-date vacuum technology etc. are closely related to FII

• There is an excellent opportunity to characterize FII systematically at ATF DR and to compare to simulation results


ThanksThanks forfor youryour attentionattention !!

Linear theory

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2/12/122/3

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The growth time of FII is closely related to the beam sizes, the larger the value σy

3/2(σx+σy)3/2, the larger the characteristic FII growth time. It is possible to use the up-to-date feedback system (~0.1ms) to damp the FII growth.

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Critical mass, ion density, FII growth time, ion oscillation frequency, ion angular frequency, FII growth time in presence of ion angular frequency variation, and the coherent tune shift due to ions


Documents

Fast Ion Instability Studies in ILC Damping Ring Guoxing Xia DESY ILCDR07 meeting, Frascati, Mar. 5~7, 2007