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Electron cloud in the wigglers of ILC Damping Rings
L. Wang
SLAC
ILC Damping Rings R&D Workshop - ILCDR06 September 26-28, 2006
Cornell University
ILC Damping Rings R&D Workshop, Cornell, Sep. 27
Outline• Introduction• Simulation• Aperture effect• Trapping effect• Bunch train effect • Groove surface• Clearing Electrode • Comparison with dipole field• Summary
ILC Damping Rings R&D Workshop, Cornell, Sep. 27
Ecloud in DAFNE wiggler?
• Fast Horizontal instability (larger Horizontal tune shift, 0.01 at 600mA) was found after modification of the wiggler
• No Vertical instability…
• KEKB, CESR DAFNE: C. Vaccarezza,etc. ecloud04
ILC Damping Rings R&D Workshop, Cornell, Sep. 27
CLOUDLAND 3D PIC code for e-cloud (PRST-AB 124402)
Simulation Key parameters(beam,ring,SEY,electrode, …) Mesh Generator
Magnetic and electric fields input
Space charge solverCharge meshUpdate particle positions
Advance particle positions using the new beam and e-cloud space charge fields
Preliminary electron generator when beam passing
Secondary electron generator
Preliminary electron generator
Wake field Instability code
Future plan --Parallelize for consistent instability study
ILC Damping Rings R&D Workshop, Cornell, Sep. 27
Space charge potential solver -FEM
Mesh of chamber
Three dimensional irregular mesh to better represent the general chamber geometry
handle accuracy with high order elements.
0QNQ ii 1i
iN
20 node element
Adaptive mesh for beam/ecloud.
ILC Damping Rings R&D Workshop, Cornell, Sep. 27
Sample II: Electron cloud with two beams Two beams
Whole section (12m), without magnets, bunch length 10nsModel :
Copper ion N=1109; bunchspacing=1 RFbucket, Copper ion N=6109;
bunchspacing=6 RFbucket,
Z
RHIC
ILC Damping Rings R&D Workshop, Cornell, Sep. 27
Optics of New 6km ring
0 500 1000 1500 2000 2500 3000 3500 4000-20
0
20
40
60
80
100
S (m)
x
y (
m)
x
y
Dx*100
ILC Damping Rings R&D Workshop, Cornell, Sep. 27
CESR-c wiggler
ILC Damping Rings R&D Workshop, Cornell, Sep. 27
Wiggler Field in simulation
kzykxkBk
kB
kzykxkBB
kzykxkBk
kB
yxy
z
yxy
yxy
xx
sinsin)cosh(
,coscosh)cosh(
cossinh)sinh(
0
0
0
0 20 40 60 80 100-1.5
-1
-0.5
0
0.5
1
1.5
Z
Bz
Br
2222 2
kkk yx
),,,,,(,...,3,1
, , zyxnkkkfBBNn
nxnxnn
B0=1.68Tesla
Period =0.4m
Kx=0
ILC Damping Rings R&D Workshop, Cornell, Sep. 27
Simulation in wiggler 3D program is required in wiggler (3D field)
Some electrons can effectively move in longitudinal direction (beam direction) and the electron cloud is not uniform in longitudinal direction (different from dipole magnet). the modeling of beam kick, electron motion and space charge field should consider the 3D effects.
ILC Damping Rings R&D Workshop, Cornell, Sep. 27
Parameters
• 2767 Bunches: 6 ns bunch spacing with a gap about 43ns, Bunch intensity 2E10, 22 bunches/train
• 5782 Bunches; 3 ns bunch spacing with a train gap about 38ns; bunch intensity 1E10; 49bunches/train
• Peak SEY1.75 at 330eV
• Pipe aperture 44mm
ILC Damping Rings R&D Workshop, Cornell, Sep. 27
Train gap effect (2767bunches)
-200 -100 0 100 20010
8
109
1010
1011
1012
1013
Z (mm)
(
m-3
)
Bunch Train gaps reduce the electron cloud density by a factor of 10
0 20 40 60 80 100 12010
9
1010
1011
1012
Bunch ID
e (
m-3
)
average densitycentral density
0 20 40 60 80 100 12010
9
1010
1011
1012
1013
1014
Bunch ID
e (
m-3
)
One train
Short train
ILC Damping Rings R&D Workshop, Cornell, Sep. 27
Effect of pipe aperture, 2767bunches
0 20 40 60 80 100 12010
9
1010
1011
1012
Bunch ID
e (
m-3
)
average densitycentral density
0 50 100 150 200 250 30010
8
109
1010
1011
1012
1013
1014
Bunch ID
e (
m-3
)
R=22mm R=8mm
-10 -5 0 5 100
0.5
1
1.5
2
2.5
3x 10
13
X (mm)
(m-3
)
-10 -5 0 5 100
0.5
1
1.5
2
2.5
3x 10
13
X (mm)
Ecloud density increases by a factor of 10 when I.D. reduce from 44mm to 16mm
ILC Damping Rings R&D Workshop, Cornell, Sep. 27
Mirror field trapping
kzykxkBk
kB
kzykxkBB
kzykxkBk
kB
yxy
z
yxy
yxy
xx
sinsin)cosh(
,coscosh)cosh(
cossinh)sinh(
0
0
0
No mirror field trapping was found
0 20 40 60 80 100 12010
9
1010
1011
1012
Bunch ID
e (
m-3
)
average densitycentral density
Mirror field
ILC Damping Rings R&D Workshop, Cornell, Sep. 27
Beam filling pattern effect
0 20 40 60 80 100 12010
9
1010
1011
1012
Bunch ID
e (
m-3
)
average density, 2767 bunchescentral density, 2767 bunchesaverage density, 5782 bunchescentral density, 5782bunches
Low Q beam pattern(5782bunches) has lower electron cloud density (I.D.=22mm)
ILC Damping Rings R&D Workshop, Cornell, Sep. 27
Comparison with dipole
0 20 40 60 80 10010
9
1010
1011
1012
1013
1014
Bunch ID
e (
m-3
)
average densitycentral density
0 20 40 60 80 100 12010
9
1010
1011
1012
Bunch ID
e (
m-3
)
average densitycentral density
Dipole, B=0.194TWiggler
There is a lower electron density in Wigglers (one order)! (assuming the same initial electrons rate )
ILC Damping Rings R&D Workshop, Cornell, Sep. 27
Comparison with dipole
-30 -20 -10 0 10 20 300
1
2
3
4
5
6x 10
13
X (mm)
(m-3
)-10 -5 0 5 100
0.5
1
1.5
2
2.5
3x 10
13
X (mm)
Wiggler Dipole, B=0.194T
The multipacting strips of electron cloud in the wigglers is more close to the beam
ILC Damping Rings R&D Workshop, Cornell, Sep. 27
Clearing Electrode
0 20 40 60 80 100 12010
9
1010
1011
1012
1013
1014
Bunch ID
e (
m-3
)
average density, long traincentral density, long trainaverage density, bunch train, -100Vcentral density, bunch train, -100Vaverage density, bunch train, 200Vcentral density, bunch train, 200V
stripline position
Strip-line typeWire type
Strip-line type Wire type
Calculation of the impedance ( Cho, Lanfa)
Design & test of impedance is under the way, test in PEPII Dipole & CESR Wiggler
Submitted to PRSTAB
Suetsugu’s talk
ILC Damping Rings R&D Workshop, Cornell, Sep. 27
Geometry of Grooved surface
(a) Triangular surface
(b) Sawtooth surface
(c) Overhanging surface
ILC Damping Rings R&D Workshop, Cornell, Sep. 27
Collection of the stripped electron at injection (SNS)
Foil center(40,23,307)
Magnetic field at foil center=( -3.6, 2504,-547.9) Gauss; =210mrad
Energy of stripped electrons =522keV, =11.98mm, T=0.289ns, v=2.6e8m/s, =0.866
Catcher shape: =25, =65Z
Y
0.34% Carbon9.2 % Copper
L. Wang,et al. PRSTAB 094201(2005)
ILC Damping Rings R&D Workshop, Cornell, Sep. 27
Triangular grooved surface in wiggler
Effective SEY of an isosceles triangular surface with rounded tip. max=1.74, max=330eV, B0=0.2Tesla, Rtip=0.2mm, W=4.52mm.
)
W
0 100 200 300 400 500 600 7000
0.2
0.4
0.6
0.8
1
1.2
1.4
Energy (eV)
SE
Y
=65o, =50o
=70o, =40o
=75o, =30o
=80o, =20o
Effective SEY from an isosceles triangular surface in a dipole magnetic field. max=1.74, max=330eV, B0=1.6Tesla and W=1.89mm
0 100 200 300 400 500 600 700
0.2
0.4
0.6
0.8
1
1.2
Energy (eV)
SE
Y
=70o
=75o
=80o
To reduce the impedance
The effective SEY of triangular grooved surface has very weak dependence on the size W and magnetic field.
L wang, T. Raubenheimer, G. Stupakov, (slac-pub-12001)
Experiment in PEPII Dipole & CESR Wiggler
ILC Damping Rings R&D Workshop, Cornell, Sep. 27
Impedance of triangular groove
-20 -10 0 10 20
-20
-15
-10
-5
0
5
10
15
20
X (
mm
)
Y (mm)
Magnetic field lines penetrating in a groove (a half a period of a groove is shown).
The enhancement factor as a function of angle.
Gennady
Calculation of impedance with rounded tips is under the way
(Gennady, Karl and Lanfa)
Machining and extrusion
Copper-coated
Impedance increases 15%(alfa=70), it will be lower when round tips are used
ILC Damping Rings R&D Workshop, Cornell, Sep. 27
Summary Bunch train can effectively reduce the build-up of ecloud in
wiggler ( a factor of 10!)
Low Q beam pattern has lower ecloud density
No mirror field trapping was found
Ecloud in wiggler also has two strips, but it is more closer to the beam comparing ecloud in the dipole magnet.
Electron cloud density in wiggler is lower than that in dipole.
Electrodes works in wiggler. (Heat & impedance is the main concerns, Exp. in PEPII and CESR )
Triangular Grooved surface likely works in wiggler, but it would be important to check with realistic field. (Impedance optimization, manufacture) (exp. At SLAC and CESR)
ILC Damping Rings R&D Workshop, Cornell, Sep. 27
Acknowledgement
Thanks to all colleagues in the damping ring study, especially thanks to K.L.F. Bane, Y. Cai, T. Raubenheimer, G. Stupakov, A.Wolski, J. Gao, S. Guiducci, M. Zisman, M. Palmer, M. Pivi, F. Zimmermann, H. Fukuma, K. Ohmi, E. Kirby, Y. Suetsugu, S. Mark, R. Schlueter, D. Plate, …….
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