L. Xiao, LARP-CM12, April 9, 2009 1 RF Heating in the SLAC Rotatable Collimator Design Liling Xiao Advanced Computations Department SLAC National Accelerator Laboratory
Jan 09, 2016
L. Xiao, LARP-CM12, April 9, 2009
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RF Heating in the SLAC Rotatable Collimator Design
Liling Xiao
Advanced Computations Department
SLAC National Accelerator Laboratory
L. Xiao, LARP-CM12, April 9, 2009
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Outline
Simulation Model Rectangular vacuum tank, Circular vacuum tank
Longitudinal Trapped Modes (loss factor, Q0)
Beam energy loss, Power dissipation
Transverse Trapped Modes (kick factor, Q0)
Beam instability, Power dissipation
Ferrite-Loaded Collimator
Damped trapped modes in circular vacuum collimator
Summary
L. Xiao, LARP-CM12, April 9, 2009
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Omega3P calculates the trapped modes below 2GHz and provides HOM parameters for beam heating and coupled-bunch stability studies
F(Hz)
Beam Frequency Spectrum
L. Xiao, LARP-CM12, April 9, 2009
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Rectangular Vacuum Tank Design Circular Vacuum Tank Design
The collimator jaw will move in and out with a 2mm to 42mm gap.
Easier for fabrication
Beampipe R = 42mm, Fc(TE11) = 2.1GHz, Fc(TM01) = 2.7GHz
Rotatable Collimator
L. Xiao, LARP-CM12, April 9, 2009
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Simulation Model
Rectangular Design Circular Design
y
x
z
¼ Omega3PModel
L. Xiao, LARP-CM12, April 9, 2009
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Finite Element Mesh Tetrahedras with 2nd order curved surface
Denser mesh along beam path plus 3rd order basis functions for better accuracy
L. Xiao, LARP-CM12, April 9, 2009
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Trapped Mode Excitation
Longitudinal Modes
With magnetic boundary conditions on x and y symmetric planes, modes with Ez component on z beam axis are excited resulting in energy loss and collimator power dissipation.
Transverse Modes
With magnetic/electric boundaries on y/x symmetry planes, modes with Ey component between the two jaws are excited when the beam crosses the collimator at an y-offset generating a transverse kick in the y-direction as well as beam energy loss. Due to the small gap of the jaws, this Ey is very strong over the full length of the collimator.
L. Xiao, LARP-CM12, April 9, 2009
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Loss factor for a Gaussian bunch with sigma=7.6cm
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
1.E+08
5.0E+07 2.5E+08 4.5E+08 6.5E+08 8.5E+08
F (Hz)
Klo
ss (V
/c)
open gap=42mm
closed gap=2mm
Loss factor for a Gaussian bunch with sigma=7.6cm
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
1.E+08
5.0E+07 2.5E+08 4.5E+08 6.5E+08 8.5E+08
F (Hz)
Klo
ss (
V/c
)
open gap=42mm
close gap=2mm
Loss Parameters vs. Jaw’s Opening
Rectangular Tank Circular Tank
When the two jaws move out, more and more EM fields will be generated along the beam path. The loss factors are getting the largest for fully retracted jaws with gap=42mm.
Longitudinal Trapped Modes
L. Xiao, LARP-CM12, April 9, 2009
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Quality Factor
100
1100
2100
3100
4100
5100
6100
7100
8100
9100
5.0E+07 5.5E+08 1.1E+09 1.6E+09
F (Hz)
Q0
round tank for open gap=42mm
rectangular tank for open gap=42mm
RF Parameters for fully retracted jaws, gap=42mm
Vacuum tank is made of stainless steel, σ=0.116e7s/m. Two jaws are made of copper, σ=5.8e7s/m
Shunt Impedance for a Gaussian bunch with sigma=7.6cm
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
5.0E+07 5.5E+08 1.1E+09 1.6E+09 2.1E+09
F (Hz)
R (o
hm)
round tank for open gap=42mm
rectangular tank for open gap=42mm
Longitudinal Trapped Modes
R
Q0
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Cir. Tank: f1=93MHz, Q=1662The trapped mode spreads around the jaws. Q is higher.
E-field
B-field
Rec. Tank: f1=82MHz, Q=279The trapped mode locates between the jaw and chamber wall. Q is lower.
E-field
B-field
Longitudinal Trapped Modes
Lowest Trapped Mode Field Pattern
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Transient Heating Effects
Transient beam energy losses is total energy left by the passage of the bunch train through the collimator.
WrecPJerecE
WcirPJecirE
nsTnCqN
TNEPkNqE
b
bi
7.0.)(,55.)(
7.)(,45.)(
25,4.18,2808
)*/(,2
The transient heating power normally causes no problem for structures with good thermal conduction.
Longitudinal Trapped Modes
L. Xiao, LARP-CM12, April 9, 2009
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Resonant Heating Effects
Resonant power losses are due to the excitation of these trapped modes. Assuming all bunches are in phase with them and mode decay is lower from bunch to bunch (Td>>Tb):
WrecP
WcirP
ATqI
QeQ
RIP
b
ic
ii
15.)(
515.)(
582.0/
,*)(222 2/2
The trapped mode frequencies should be shifted away from 40MHz beam harmonic thus reducing the resonant heating power.
Longitudinal Trapped Modes
L. Xiao, LARP-CM12, April 9, 2009
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Kick Factor
1.E+07
1.E+08
1.E+09
1.E+10
1.E+11
1.E+12
1.E+13
1.E+14
1.E+15
5.00E+07 4.50E+08 8.50E+08 1.25E+09 1.65E+09 2.05E+09
F (GHz)
Kick
Fac
tor (
V/C/
M)
Round tank for closed gap=2mm
Rectangular tank for closed gap=2mm
RF Parameters for fully inserted jaws, gap=2mmQuality Factor
100
1100
2100
3100
4100
5100
6100
7100
8100
9100
5.00E+07 4.50E+08 8.50E+08 1.25E+09 1.65E+09 2.05E+09
F (GHz)
Qual
ity F
acto
r
Round tank for closed gap=2mm
Rectangular tank for closed gap=2mm
When the two jaws are fully inserted with gap=2mm, the kick factors are highest due to the strongest Ey between the two jaws.
Transverse Trapped Modes
Kick
Q0
L. Xiao, LARP-CM12, April 9, 2009
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Lowest Trapped Mode Field Patterns
Transverse Trapped Modes
Rec. Tank: f1=79MHz, Q=382The trapped mode is between the two jaws and the jaw and chamber wall. Q is lower.
Cir. Tank: f1=85MHz, Q=1344The trapped mode is between the two jaws. Q is higher.
E-field
B-field
E-field
B-field
L. Xiao, LARP-CM12, April 9, 2009
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Loss ParametersLoss Factor for rectangular tank with gap=2mm, Gaussian
bunch=7.6cm
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
5.00E+07 4.50E+08 8.50E+08 1.25E+09 1.65E+09 2.05E+09
F (GHz)
Loss
Fac
tor (
V/C)
at o
ffset
y
offset y=0.05mmoffset y=0.075mmoffset y=0.1mm
Loss Factor for round tank with gap=2mm, Gaussian bunch=7.6cm
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
5.00E+07 4.50E+08 8.50E+08 1.25E+09 1.65E+09 2.05E+09
F (GHz)
Loss
Fac
tor (
V/C)
at o
ffset
yoffset y=0.05mmoffset y=0.075mmoffset y=0.1mm
Rectangular Tank Circular Tank
Loss factors of transverse modes depend on the beam offset.
Transverse Trapped Modes
L. Xiao, LARP-CM12, April 9, 2009
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Max. Power dissipation on wall
Beam offset at y-direction
0.075mm
(Max.)
0.050mm
Rectangular Vacuum Tank
Transverse Modes (<2GHz) gap=2mm
6W 3W
Longitudinal Modes (<2GHz) gap=42mm
15W
Circular Vacuum Tank
Transverse Modes (<2GHz) gap=2mm
15W 7W
Longitudinal Modes (<2GHz) gap=42mm
515W
To be safe, beam heating due to the longitudinal trapped modes in the circular vacuum design needs to be reduced.
Trapped Mode Heating
L. Xiao, LARP-CM12, April 9, 2009
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Ferrite-Loaded Collimator
Chosen Lossy Material
“First Studies for a Low Temperature Higher-Order-Mode Absorber For the Cornell ERL Prototype”, M. Liepe, et al.
At room temperature and 100K
“Measurements of ε and μ of Lossy Materials for the Low Temperature HOM LOAD”, V. Shemelin, et al.
Re. ε Im.ε
Re. μ Im. μ
F=0~2GHz, ε~10-j0.2, μ~2-j10 at 297k
L. Xiao, LARP-CM12, April 9, 2009
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Ferrite-Loaded Collimator
TT2-111R Ferrite Tile t=2mm
Attaching ferrite tiles on vacuum wall above the top and bottom of the jaws can strongly damp the longitudinal trapped modes.
Jaw fully retracted gap=42mm
Damping Longitudinal Trapped Modes w/ Ferrites
t
ε=10-j0.2, μ=2-j10
Longitudinal trapped mode in round tank design
1
10
100
1000
10000
0.0E+00 2.0E+08 4.0E+08 6.0E+08 8.0E+08 1.0E+09 1.2E+09 1.4E+09
F (Hz)
Q-v
alu
e
w ithout ferrites
w ith ferrites at 297k
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Lowest Trapped Mode Field Patterns
After adding ferrite tiles, the trapped mode is absorbed in the lossy material.
E-field
B-field
Without Ferrite Tiles With Ferrite Tiles
Cir. Tank without ferrite tiles: f1=93MHz, Q=1662
E-field
B-fieldCir. Tank with ferrite tiles: f1=86MHz, Q=10
Ferrite-Loaded Collimator
L. Xiao, LARP-CM12, April 9, 2009
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Summary
All trapped modes below 2GHz in the SLAC design are calculated using Omega3P, and their RF heating effects are evaluated.
The longitudinal trapped modes in the circular vacuum chamber design have higher Q-value. In the worst case, the total power heating can reach 500W if they all interact with the beam in resonance.
The heating due to the transverse trapped modes are negligible but the transverse kick on the beam needs to be evaluated.
Adding ferrite tiles in the circular vacuum chamber collimator can strongly damp the trapped modes. Need effort on design and analysis of the tiles that include ferrite’s thermal/mechanical effects.
Using the amplitude ratio of longitudinal and transverse modes to determine the position of the beam is underway.
Special thanks to Fritz Caspers for his helpful discussions and advice.