Simulation study of e-cloud in
KEK-B LER
L. WANG

1) Three dimensional PIC program2) Photoelectron cloud in various magnetic fields
3) Remedies to clear the e-cloud4) Summary
In collaboration with H. Fukuma, K. Ohmi, S. Kurokawa, K. Oide,
F. Zimmermann,...
KEKB REVIEW

L.F. Wang, KEK, Feb10-11, 2003

Study methods for E-cloudØ Analysis method (E. Perevedentsev, S. Heifets, E. Metral,…)Ø Numerical Method

Photoelectron cloud build-up, distribution, heat loading ……
(M.A. Furman, Mauro Pivi, K. Ohmi, F. Zimmermann and G.
Rumolo, L. Wang … )Transverse single bunch instability simulation (Gaussian/UniformCloud) (K.Ohmi, F. Zimmermann, G. Rumolo,Y. Cai, …)
Extracting wakefield from simulation program, then analysis thetransverse mode coupling, get the electron cloud thresholddensity (F. zimmermann, K. Ohmi, L. Wang…)

Coupled bunch
instability(S. S.Win)Ø Experimentalmethod(CERN-SPS
and PS, KEK-KEKB, SLAC-PEPII,

LANL-PSR, LBNL-APS, BNL-AGS and RHIC, IHEP-BEPC,ALS,CESR,…)KEKB REVIEW

L.F. Wang, KEK, Feb10-11, 2003

3D PIC Program--- CLOUDLAND
LProgram modelwThree dimension
PIC methods

Magnetic fieldzyp+x2h2aeλSolenoid &magnets

wGeneral 3-dimensional magnetic fields.
wFields can also be import from other program

Beam potentialw
w

Gaussian bunch in round chamber ( image charge is included)
PIC method for general geometry

Secondary emission and reflective electron are included
Irregular mesh & high order element are applied
KEKB REVIEW

L.F. Wang, KEK, Feb10-11, 2003

Field free region
Preliminary eProton/Positron bunch

Electron trapping near beam

photoLive Cloud Distribution inTransverse Plane(a)(b)

Orbit of tapped electron with larger amplitude.

ØLarge central density due to the confinement of positron beamØMulti-pacting and heating-load effect are important
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L.F. Wang, KEK, Feb10-11, 2003

Normal Dipole

MP

EnergySecondary mission yield
Live Cloud Distribution

Multipacting mechanism

Central density +local multipacting+local heating
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L.F. Wang, KEK, Feb10-11, 2003

Normal Quadrupole & Sextupole

quadrupole

sextupole

Weak multipacting+low central density+weak heating+trapping
KEKB REVIEW

L.F. Wang, KEK, Feb10-11, 2003

Trapping phenomenonØIt happens in quadrupoleand sextupole magnets

Ø The photoelectron can betrapped in quadrupole andsextupole magnets for very
long time until it
longitudinally drift out of
the magnets.(vz~0.004mm/ns)

Ø The trapping phenomenon
is strongly beamdependent. T h e r e i s n osuch kind of trapping when
the positron beam force is
not included
KEKB REVIEW

Average cloud density evolution
in different magnetic fields

L.F. Wang, KEK, Feb10-11, 2003Trapping phenomenon---in quadrupole magnet

3D orbit2D orbit

Orbit of a trapped photoelectron in normal quadrupolemagnet during the train gap (field gradient=0.5T/m)

KEKB REVIEW

Field lines

L.F. Wang, KEK, Feb10-11, 2003

Trapping phenomenon---in sextupole magnet

Orbit of a trapped photoelectron in normal sextupole magnet
during the train gap

KEKB REVIEW

L.F. Wang, KEK, Feb10-11, 2003

Trapping mechanism – Mirror field trap
Invariation value of motion
Positron bunch

2m 2 m || m ⊥2
W==+= cons tan t2221m ||2 +2m

B = const

Reflective Points:

Beam E-fieldυ =0||Trapping condition
Γtrap > 12FBmax⊥0Γtrap == 22FB+⊥0|| 0 B0
if no other force (except B force) disturbs
the electron,Trap factor is constant andsmaller than 1.0, no trapping
KEKB REVIEW

Turning points

mirror field trappingΓtrap =2
⊥02
⊥0+2||0 at the emission
po int= cons tan t ≤ 1

L.F. Wang, KEK, Feb10-11, 2003

Trapping mechanism ---Beam potential effect on Fυ & Γtrap
Trap requirement for positron bunch
Bunch length should be shorter than period of gyration
motion2 cm 1l<eBl(mm) < 10.7 / B (T )Non-adiabatic region(a) 4mm(b) 4cmParticle
motion in
non-adiabaticregion

Beampotential

Trapped photoelectron distribution in quadrupole
magnet with field gradient 10.3 T/m during thetrain gap for different bunch length
KEKB REVIEW

L.F. Wang, KEK, Feb10-11, 2003

Orbit of the Guiding Center(Contd.)

Longitudinal Velocity of the Guiding Center (Beam direction)•Magnetic gradient driftm ⊥2õ grad =B × ∇B With normal gradient −B n/RB
32eB

•Centrifugal force drift

Example: one electron in Quadrupole:m ||2 R B m ||2Fc ==nRB2RB

Simulation: 236 ns and 0.0066 mm/ns
Analysis: 228 ns and 0.0063 mm/ns

õF =F×Bn
B=×eB 2BΩ s RBnB
õ gz =×BΩ s RB=∫dl||KEKB REVIEW( +2||gz =12⊥∫

Magnets length=0.4m2||/2gz||)

Very slow drift velocity vgz(1.5~3.5 10-3 mm/ns )Long trapping time(~105 ns)

dlCoupled-bunch effects!!
L.F. Wang, KEK, Feb10-11, 2003

III Cures of e-cloud
Weak Solenoid (work well in drift region, but not in magnets)
Chamber surface preparation (Vacuum chamber coatings, ribbedstructures, Beam scrubbing)
BPM serve as clearing electrode?

KEKB REVIEW

L.F. Wang, KEK, Feb10-11, 2003

Uniform Solenoid effect in drift region
50

50
40
30

40

30

39

20

20

38

10100400

Bz=10Gauss-10-1037

Bz=20Gauss

36
35-20-2034-30-30

33-40-40

32

-50

-50
-50 -40 -30 -20 -1050

0102030400102030405031-385040-36-34-32-30

4030

30

20Clearing mechanism

20100-40 -30 -20 -1050

10Bz=30Gauss

0-10Bz=40Gauss-10-20-20-30-30-40-40-50-40 -30 -20 -10010KEKB REVIEW

20304050-50-50 -40 -30 -20 -100102030

40

50

L.F. Wang, KEK, Feb10-11, 2003

Solenoid

Solenoid

KEKB REVIEW

L.F. Wang, KEK, Feb10-11, 2003

Periodic Solenoid
LEqual polarity
configuration2aλ2hB0=50 Gauss, h=0.4 m, a=70 mm,=1 m∞∑ sin nhk K1(nka) I1(nkr ) sin nkz

Br = B0 2h 2ka ∞B z = B0 +sin nhk K1 (nka) I 0 (nkr ) cos nkz n =1

B z = B0

Br = B02ka

n =1

∑

4ka

4ka∞

∑ sin nhk K1 (nka) I1 (nkr ) sin nkz

n =1,3,5∞∑ sin nhk K1 (nka) I 0 (nkr ) cos nkz

n =1,3,5

By E. Perevedentsev
KEKB REVIEW

L.F. Wang, KEK, Feb10-11, 2003

BPM serves as clearing system?
505040403030-q-V+V+V202010100-Vθ-q-q0-10-10-20-20-q-30-30-40-40-50-50 -40 -30 -20 -1001020304050-50-50 -40 -30 -20 -1001020304050

Stripline-type BPM

Button-type BPM(wire-type)(ion clearing system type)

Replace the electrodes with wires to reduce the impedance!
KEKB REVIEW

L.F. Wang, KEK, Feb10-11, 2003

Clearing effects for Drift region
505040403030

2020101000-10-10-20-20-30-30-40-40-50-50 -40 -30 -20 -1001020304050-50-50 -40 -30 -20 -10-100V

01020304050-150V
414040303920Requirement:

381037036-1035-203433-3032-200V for 4 electrodes system-400 V for 2 electrodes system
KEKB REVIEW-40-50-50 -40 -30 -20 -10

3101020304050-38-36-34-32-30-200V 4 electrodes
L.F. Wang, KEK, Feb10-11, 2003

Clearing electrodes for Dipole Magnet
Inside the strong dipole magnets, crossed-field and gradient drifts couldn’t eliminate theelectrons. Therefore, the electric field must be along the magnetic field line in order toeffectively repel the electron. This conclusion holds for other strong magnetic fields
The wire electrodes must have negative potential relative to the grounded chamber!!!
The field is perfect!!! (very weak field at chamber center, strong vertical field aroundboth the top and bottom of the chamber, where multipacting could happen.
5040302010Wires position

0-10-20-30-40-50-50

KEKB REVIEW

050

L.F. Wang, KEK, Feb10-11, 2003

Clearing effects in dipole magnet-300V-200V-200~400V ok50

37.2

40373036.82036.6

100-400V

36.4-1036.2-2036-33.8-33.82-33.84-33.86-33.88-33.9-30-40-50-50 -40 -30 -20 -10

KEKB REVIEW

01020304050

246.18246.16246.14246.12246.1

246.08L.F. Wang, KEK, Feb10-11, 2003

Cloud Density in Different Fields

No saturation

Central density

Average density

Electron volume density as a function of time for a train with200 bunches spaced by 7.86 ns and followed by a gap
KEKB REVIEW

L.F. Wang, KEK, Feb10-11, 2003

Summary: e-Cloud in various fields
q Drift region
Ø Large central density
Ø Multipacting & heating
Ø Trapping by beam fieldq Dipole magnet
Ø Strong local multipacting &heating
Ø Important central density
Ø Multipacting mechanism

q Quadrupole andsextupole magnets
Ø Low central density
Ø Low heating load
Ø Deep trap

KEKB REVIEWq SolenoidØ Uniform solenoid is preferredØ Solenoid work well (No multipacting,no heating-load problem)q Multi-wire clearing system
Ø Work in both drift region andmagnet
Ø Small impedanceØ Easy mechanical design,…..
Ø Realistic study?

q BPM & ion clearing systemØ Stripline-type works well but
impedance…
Ø Button-type doesn’t apply
Ø Ion-clearing system work, but its
effect is not perfect, long bunch…
L.F. Wang, KEK, Feb10-11, 2003

Thanks!!

KEKB REVIEW

L.F. Wang, KEK, Feb10-11, 2003