Beam instabilities at the SuperKEKB
KEKB accelerator review committee 17/Feb./04
H. Fukuma, K. Ohmi (KEK), L. F. Wang (BNL)
1. Resistive wall instability
2. Closed orbit instability
3. Electron cloud instability
4. Ion instability

1. Resistive wall instability
Growth rate
(cI
g=Re Z(( pM + µ + N $ )% 0 + &# $ ))4 "# $ E p='(Re Z = sign(" ) #!

Z0 # R# $, " =3b2c
Z0# $Z0=377Ω, δ:skin depth, b:chamber radius
M:number of bunches, µ:mode no.

!

!

N " ,#$ " :integer and fractional part of tune!

UsingM=5120 (uniform fill),
b=25mm(HER),45mm(LER),
I=4.1A(HER), 9.4A (LER),
Growth rate
HER(horizontal/vertical)
LER(horizontal/vertical)

959/1096 (s-1)
843/ 919 (s-1)

Damping time of a bunch by bunch feedback system 5000 s-1

Instability will be suppressed by the bunch by bunch feedback system.

2. Closed orbit instability
Recently V. Danilov et al. pointed out that the closed orbit
may experience an unstable drift due to a long-range wakefield such as a resistive wall wake.

Closed orbit distortion

Accumulation of wake

Unstable drift of closed orbit

Dispersion equation of closed orbit y(s)iNr0y(s) =ds' Z˜ & (s',') % (s)% (s') cos[#$ ( ) (s,s')] + y(s')*
2"Tsin#$ %Z˜ " (s',#) : linear density of impedance

N:the number of particles, T:revolution time!
!

If " (s) and Z˜ " (s',#) are uniform,
2Nrc"n 2# 2 + # $2 = i 0 Z & (')%C!

C: ring circumference!

At threshold, Ω=0, n=integer part of νβ!
!

N thResistive wall impedance(A. Chao, S. Heifets and B. Zotter, Phys. Rev. ST-AB, 5, 111001 (2002),
Y. Shobuda and K. Yokoya, Phys. Rev. E, 66, 056501 (2002),
A. Burov and V. Levedev , EPAC2002, 1452)

Skin depth" = c / 2#$% >> wall thickness doutsidebModel by A. Burov and V. Levedev

Z01
˜!Z " (#) = $i %b 2 2 + & ' tanh(&d)
Z1Z˜ " (#) = $i 02%b 1+ & ' tanh(&d)!

!

!

Vacuum outside
Ideal magnetic material outside

Z 0 = 377" , b: chamber radius (b>>d) , " = (1# i) /$Z 0 g%
" >> dZ˜ " (#)=!
2$b # + i%
g=1/2 : Vacuum outside,!
!

1! %i#( Z˜ " (#) =$" << d )g=1 : Ideal magnetic material outside!

dThreshold intensity of the instability
2" 2b 2#$ % &$ %N th =r0Cg"# $ : fractional part of tune

Nth: the number of particles at
the threshold of instability1) SuperKEKB LER!
!

C=3016m, ν =43.55, γ =7000, b=45x10-3m, g=1
Nth=7.7 x 1014 > design 5.9 x 1014
2) SuperKEKB HER
C=3016m, ν =41.57, γ =16000, b=36.5x10-3m(ave.), g=1
Nth=5.0 x 1014 > design 2.6 x 1014

3. Electron cloud instability
Estimation for HER
Cloud buildup
Simulation by CLOUDLAND (developed by L.F.Wang)
3D PIC code to calculate electron cloud formation

Assumption
Ante-chamber will be installed.
Shape of chamber : round
Uniform production of electrons on chamber wall.
Primary electrons
Primary electron yield of 0.01 is artificially usedin order to take into account of the reduction ofelectron yield by the ante-chamber.

Parameters used in a simulation of electron cloud buildup
Beam energy(GeV)
Bunch spacing(ns)Number of particles in a bunch
Chamber radius(mm)Maximum secondary emission yield
Energy of maximum secondary yield
Number of bunches
Number of train
Primary electron yieldrms bunch length(mm)Horizontal emittance(m)Vertical emittance(m)Average horizontal beta function (m)Average vertical beta function (m)82
5.2 1010
37
1.5
250eV
200
10.01
32.4 10-8
4.8 10-101010

Distribution of electron cloud1) Drift space

Very high central density of electrons.

2) Quadrupole magnet
No saturation
Trapping

At the end of bunch train

Trapped electrons

At a bunch gap (40ns after the last bunch in the train)

Trapping of electrons.

3) Dipole magnet

Very strong multipacting.

4) Uniform solenoid field of 60G

Trapping

60 G is enough to suppress the electron cloud near the beam.

Average electron volume density and electron volume
density at a pipe center in various magnetic fields

Drift space
DipoleQuadrupole
Solenoid

Field strength0.25(T)
10.3(T/m)
60(G)average (1012m-3)
1.0
20.0
8.4
0.61

at pipe center (1012m-3)
100.6
0.46
0.0

Solenoid field of 60G is very effective.
Electron cloud remains inside bendingand quadrupole magnets.

Threshold of strong head-tail instability(K. Ohmi and F. Zimmermann)
Instability occurs if

2%& s$ " # ds > 'r (0 y!

0.6 x 1015m-2

ρ:density of electrons, s:orbit length
βy:beta function, νs:synchrotron tune

4.5 x 1015m-2(by using ρ from simulation)

Solenoid system
Solenoid will be installed on ante-chambers.

LER
Field strength(G)Current(A)Diameter of wire(mm)Layers of winding
Total length of solenoid(m)Total turns of winding(104)Resistance of wire(kΩ)
Dissipated power(kW)

HER
60
3.8
1.6
2

2470
309
13.1
189

1850
231
9.1
131

Main parameters of solenoid system

Simulation shows
1) Solenoid field of 60G is very effective to reduce the electron density
at the center of a chamber.
2) Substantial electron cloud stays inside bending and quadrupole
magnets.
3) Simulated electron density is below the threshold of the strong
head-tail instability.
We need further experimental and simulation study to obtain morereliable estimation.
Refinement of input parameters for simulations,the number and distribution of primary electrons
in the ante-chamber,secondary emission coefficient etc..
Understanding of behavior of electrons inside magnets.

4. Ion instability
In SuperKEKB the electron beam is stored in LER after
LINAC upgrade.
Comparing with KEKB,
beam energy : 8

3.5 GeVbeam current :1.1

9.4A

Ion instability would be strong enough to degrade theluminosity.

Simulation (by Ohmi’s code)
2 dimensional model
Beam : rigid Gaussian, ions : macro particles
Beam-ion force by Basetti-Erskine formula
One ionization point in a ring

Parameters used in a simulation of ion instability
Beam energy(GeV)(LER/HER)
3.5/8
Bunch spacing(ns)2
Number of particles in a bunch(LER/HER) 11.7 1010/5.1 1010
Number of bunches
5000
Number of train
1
Vacuum pressure(Pa)
1 10-7rms bunch length(mm)3Horizontal emittance(m)2.4 10-8
Vertical emittance(m)4.8 10-10
IonCO+
5 times smaller than design value

(vertical emittance)1/2

The amplitude grows rapidly up to about verticalbeam size then almost saturates.
growth time at 10-7 Pa < 10 turns (rapid growth region)
560 turns (saturated region)
damping time of the bunch-by-bunch feedback: 20 turns

The ion instability may not cause a beam loss. Bunch bybunch feedback will suppress the beam oscillation insaturated region.
However, it may cause a dipole oscillation whose
amplitude is order of the beam size and may lead to a lossof luminosity.
The ion instability would be an issue of SuperKEKB.
Unknowns which may mitigate the instabilityFeedback system and noiseBeam-beam force...
Simulation and experimental study is needed.

If the electron beam is stored in the HER,
the growth time is 50 turns in the rapid growth region in 1x10-7Pa.
Electron storage in the HER is preferable to that in the LER
from the view point of the ion instability.

Summary
Resistive wall instability
will be cured by the bunch by bunch feedback system.
Closed orbit instability
Threshold is above the design intensity both in LER and HER.
In LER, threshold is near the design intensity. Detailed analysis may benecessary.

Electron cloud instability
In the present stage of the simulation , threshold of strong head-tailinstability will not be reached in HER.
In the simulation, strong multipacting in a dipole magnet and trapping ofelectrons in a quadrupole were found.
To understand the behavior of electrons inside magnets may be
important to estimate the electron cloud instability more accurately.
Ion instability
Simulation assuming the vacuum of 1x 10-7Pa shows thatgrowth time is shorter than the damping time of the bunch by bunch
feedback system τg(F.B.) in case of electron storage in LER,growth time is longer than τg(F.B.) in case of electron storage in HER.
Electron storage in HER is preferable from the view point of theion instability.
(For the design pressure of 5x10-7Pa, the growth time will be larger than τg(F.B.) even in HER.)

BackupEffect of beam energy on electron cloud instability (SuperKEKB)Electron cloud density in drift space(K. Ohmi, PAC03)
Simulation by code PEI

preliminary
m-3

averagem-3

HER

near beam
HERLER
LER

secondSimlation by code CLOUDLAND

secondElectron density
HER : LER" 2 to 3 :1

EnergyHER : LER!

Growth rate

" 2.3 : 1

" electron density / energy

In drift space, effect of electron density and energy
tend to cancel each other. HER and LER havecomparable growth rates.

!

Inside magnets, solenoid ??

!

LER Blowup in 2003
1) Change of connection of solenoid
1 train, 1284 bunches, 3.77 spacing
5!

Bz

3.77 (before connection-change)
3.77 (before connection-change)
3.77 (after connection-change)
3.77 (after connection-change)

4"#$%&#'(!

afterBeam size@IP(micron)

before321"#$%&#'(0400

600

800

1000

1200

1400

Beam current(mA)

Almost no improvement was observed.

1600

1800

2) Solenoids in long four straight sections have an effecton the blowup.
4
3.5

Beam size@IP(micron)3
2.5

Oho off
Fuji off

2All on
1.5
1
0.5
00

100

200

300

400

Beam current(mA)

500

600

700

Putting more solenoids inFuji straight section isunderway.

3) Field strength vs. Threshold bunch current of blowup

4 spacing Jun. 2003
1.5

Thereshold bunch current (mA)

4 spacing Mar. 2003
1.0
3 spacing Jun. 2003

0.52 spacing Jun. 2003

4 spacing Oct. 2000

0.0020406080

Solenoid Current [%] (100%<->4.5 A)

100120Stronger field will be helpful
for raising the threshold if
bunch spacing is larger than
3 buckets.

4) Attempt to detect head-tail motion by streak camera(preliminary)
Solenoid off

1000 bunches, 4 bucket spacing

Train headLongitudinal

Vertical

Tail

893mA

900mA

Vertical beam size starts to increase at 3 or 4th bunch.

Clear tilt of bunch is not observed.

Plan in 2004
1) More solenoids
Fuji straight sections :about 40m2) Study electron cloud in magnets