Zenghai LiAdvanced Computations Dept., SLAC
Presented at ICFA Crab-cavity Workshop, Shanghai, April 23-25, 2008
Modeling Wakefield Damping forthe ILC and LHC Crab Cavities
* Work supported by U.S. DOE ASCR, BES & HEP Divisions under contract DE-AC02-76SF00515
HPC Accelerator Simulation In ACD @SLAC
A. CandelA. KabelK. KoZ. LiC. Ng L. Xiao V. AkcelikS. ChenL. GeL. LeeG. SchussmanR. Uplenchwar
Advanced Computations Department (ACD)
Outline
• Parallel electromagnetic tools for cavity design and simulation
• ILC crab cavity LOM/HOM coupler design
• LHC crab cavity RF parameter & coupler studies – preliminary
• Multi-physics analysis for cavity design
SLAC Parallel EM CodesFrequency Domain:
Omega3P – eigensolver for mode damping S3P – S-parameter
Time Domain:
T3P – transients & wakefieldsPic3P – self-consistent particle-in-cell
Particle Tracking:Track3P – dark current and multipactingGun3P – space-charge beam optics
Multi-physics:TEM3P – EM-thermal-mechanical
Graphics:V3D – visualization of meshes, fields and particles
1.2985
1.29875
1.299
1.29925
1.2995
1.29975
1.3
0 100000 200000 300000 400000 500000 600000 700000 800000mesh element
F(G
Hz)
67000 quad elementsError ~ 20 kHz (1.3GHz)(<1 min on 16 CPU,6 GB)
Key Strength of SLAC’s EM Codes
Tetrahedral Conformal Meshw/ quadratic surface
Higher-order Finite Elementsbasis order p = 1- 6
Parallel Computinglarge memory & speedup
dense
Example:LL end cell with Input Coupler Only
Convergence vs FE basis-order Convergence vs N_elements
ILC Crab Cavity LOM/HOM Couplers
• Cockcroft, FNAL, SLAC Collaboration• ILC crab cavity based on FNAL 3.9GHz
deflecting mode cavity• SLAC work involved in
– Optimizing the LOM/HOM couplers for wakefielddamping
– Multipacting analysis of the cavity and the LOM/HOM couplers
ILC Crab Cavity HOM/LOM Coupler Notch Filter
-120
-100
-80
-60
-40
-20
03.6E+09 3.7E+09 3.8E+09 3.9E+09 4.0E+09 4.1E+09 4.2E+09
F (Hz)
S12
(dB
)
notch gap=0.6mm
notch gap=0.64mm
HOM: df/dgap=1.6MHz/μm
LOM filter for crab-cavity-120
-100
-80
-60
-40
-20
02.7E+09 2.9E+09 3.1E+09 3.3E+09 3.5E+09 3.7E+09 3.9E+09 4.1E+09 4.3E+09 4.5E+09 4.7E+09
F (Hz)
S12
(dB
)gap=0.5mml
gap=0.475mm,l_bend+2.4mm
LOM: df/dgap=2.2MHz/μm
Original HOM/LOM Couplers
(TESLA: 0.13MHz/μm)
New HOM design improved the notch sensitivity by one order of magnitudedf/dgap= 0.1MHz/μm
LOM/HOM Damping And Mode Mixing
LOM in Crab-cavity
1.E+04
1.E+05
1.E+06
1.E+07
1.E+08
2.78E+09 2.80E+09 2.82E+09 2.84E+09 2.86E+09F (Hz)
Qex
t
Qext in the original designQext in the new design
Horizontal 7π/9 mode
Vertically aligned SOM
x-y coupled modes
Improved LOM/HOM damping
Simplified LOM coupler geometry
Improved mode separation through cell shape modification
Eliminated V-H mode mixing
SOM
Omega3P calculations
MP Simulation Benchmark With ICHIRO Cavity Measurement
• Multipacting found in the end beam pipe step of ICHIRO cavity• Simulation agree well with measurement
(Left) MP barriers in 9-cell ICHIRO cavity calculated with Track3P, (Right) MP barriers measured on ICHIRO prototype (K. Saito, KEK).
Simulation MeasurementTrack3P
Track3P Applied to ILC Crab Cavity Multipacting Simulation
• Deflecting field level scanned up to 5 MV/m• No multipacting activities observed in cavity
Nb SEY Curve
00.20.40.60.8
11.21.41.6
0 500 1000 1500 2000impact energy (eV)
delta
E & B field distributions in cell
EB
Multipacting In ILC-CC LOM/HOM Couplers
LOM Coupler
• No resonant trajectories found up to 5 MV/m deflecting gradient
Region scanned for MP
HOM Coupler
• Resonant particle trajectories found for deflecting gradient around 3-5 MV/m
• Impact Energy at 85–240 eV• Soft MP if use Cu antenna• Antenna shape being modified to alienate
resonate trajectories
Cu Nb
Preliminary Studies for LHC Crab Cavity RF Parameters & Couplers
800 MHz Cavity Design For LHC Crab-Cavity
• Scaled from Rama Calaga’s 400 MHz baseline design
RF Parameter vs Cavity Shape
angle=0, A=B,a=b
12
14
16
18
20
22
50 55 60 65 70 75 80A=B (mm)
Bpea
k(m
T)/E
kick
(MV/
m)
3
3.2
3.4
3.6
3.8
4
Epea
k/Ek
ick
Bpeak/EkickEpeak/Ekick
A=B=60mm
12
14
16
18
20
22
0 2 4 6 8 10
angle (degree)
Bpe
ak (m
T)/E
kick
(MV/
m)
3.0
3.2
3.4
3.6
3.8
4.0
Epea
k/E
kick
Bpeak/EkickEpeak/Ekick
A=B=60mm, a=33.75mm
12
14
16
18
20
22
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3ratio: b/a
Bpe
ak (m
T)/E
kick
(MV/
m)
3
3.2
3.4
3.6
3.8
4
Epea
k/Ek
ick
Bpeak/EkickEpeak/Ekick
disk thickness disk angle iris ellipticity
• Maximum kick gradient limited by Bpeak• Optimize disk parameters for optimal Epeak and Bpeak• rbp=riris=70mm, cell length=187.5mm
A=B=60mm, a=33.75mm
100
104
108
112
116
120
0.6 0.8 1 1.2ratio: b/a
(R/Q
)_T
(ohm
/cav
ity)
(R/Q)_T
A=B=60mm
100
104
108
112
116
120
0 2 4 6 8 10angle (degree)
(R/Q
)_T
(ohm
/cav
ity)
(R/Q)_T
angle=0, A=B,a=b
100
104
108
112
116
120
50 60 70 80A=B (mm)
(R/Q
)_T
(ohm
/cav
ity)
(R/Q)_T
Cell Squash Ratio
A
B
B/A A (Fy-Fx) (MHz)0.90 235.97 420.85 240.10 650.80 244.92 89
• Racetrack or Elliptical
• Chose squash ratio to optimize mode spectrum
Fc=1.2GHz @ Riris=70mm
Dispersion Curve
5.50E+08
6.00E+08
6.50E+08
7.00E+08
7.50E+08
8.00E+08
8.50E+08
9.00E+08
9.50E+08
1.00E+09
1.05E+09
1.10E+09
0.7 0.75 0.8 0.85 0.9 0.95 1Cross Section Elliptical Ratio
F (H
z)TM010-1 TM010-2 TM110-1-H (opt.mode) TM110-2-HTM110-1-V (SOM) TM110-2-VTE111-1-H TE111-2-HTE111-1-V TE111-2-V
LOM
HOM(TE111)
SOM
FM
Preliminary Cavity RF Parameters
Frequency 800MHz(R/Q) 117ohm/cavityDeflecting Voltage VT 2.5MVDeflecting Gradient Ekick 6.67MV/mEpeak 24.72MV/mBpeak 82.75mTMode separation (Opt.-SOM) 89MHz
BpEpE-field
TESLA TDR cavity peak fields for comparison
(Eacc: 37-47MV/m):Epeak: 70-90MV/mBpeak: 150-190mT
B-field
Squash ratio: 0.8
LOM/SOM and HOM Damping
• Parameters provided for beam dynamics and damping requirement studies(Frank Zimmermann, Rama Calaga)
• Qext of 102-103 is considered not far off for preliminary designs • Various damping schemes being studied. Optimal choice of damping
scheme will depend on Qext requirements
F (MHz)
R/Q(mono) (ohm/cavity)
R/Q (dipole) (ohm/cavity)
593.6 35.2 LOM
597.4 194.5 LOM
800.0 117.3 H-operating
812.9 0.5 H
889.6 93.4 V-SOM
909.0 6.8 V
Dominate LOM and SOM and HOM modes for a 800-MHz cavity design
1.0E-01
1.0E+00
1.0E+01
1.0E+02
1.0E+03
500 600 700 800 900 1000F (MHz)
R/Q
(ohm
/cav
ity)
H-Dip (R/Q)_tV-SOM (R/Q)_tLOM (R/Q)
KEKB Crab Cavity & Damping Scheme
KEKB crab cavity utilizes a choked coaxial-coupler damping scheme
Courtesy of K. Hosoyama
Conceptual Damping Studies
• LOM/SOM damping Schemes– Waveguide coupler– Coaxial coupler– Coax-to-coax coupler (coaxial-beampipe to coax)– Coax-to-waveguide coupler
• HOM damping– Waveguide coupler - needs to cut off operating mode.
Can it damp the adjacent mode efficiently?– Coupler with choke or filter, e.g. ILC crab cavity HOM
coupler– …
Waveguide LOM/SOM Coupler
• Spacing between cavity and coupler is 25mm.• Waveguide cutoff = 536MHz
– Waveguide with short on one end improves damping – Optimal short position is frequency dependent– Could be optimized to damp both LOM and SOM more effectively
mode F(MHz) Qext
LOM-1 593
597
889LOM-2
8.55e3
8.80e3
SOM 4.86e3
mode F(MHz) Qext
LOM-1 593
597
889LOM-2
3.05e3
2.65e3
SOM 3.93e3
short
Symmetric Waveguide
Shorted Waveguide
Coaxial LOM/SOM Coupler
• Hard to achieve much lower Qext• Not suitable for either LOM or SOM• An option for operating mode input
mode F(MHz) Qext
LOM 593 7.22e5
LOM 597 7.29e5
SOM 890 1.23e5
E-field of SOMZ(TEM)=50ohm
Coupler With Coaxial Beam Pipe To Enhance Damping
Coax-to-coax Coupler• Beamline coaxial to enhance coupling• More compact than coax-to-
waveguide coupler
Coax-to-waveuide Coupler• Beamline coaxial to enhance coupling• More bulkier than coax-to-coax• Maybe easier for assembly
• These two schemes can provide lower Qext• Multipacting and surface field enhancement need to be analyzed
LOM: F=601MHz, Qext=1376
LOM: F=608MHz, Qext=176
SOM: F=893MHz, Qext=209
Beampipe radius adjusted to fit the beamline coax into the beampipe
Coax-to-coax Coupler
• Damping Results are very encouraging• More improvement under way
F=600MHz, Qext=3022
F=604MHz, Qext=2575
F=892MHz, Qext=1263
Coax with a simple short does not yield satisfactory damping
Will use door-knob shape or tapered junction to improve the matching between waveguide and coaxial beampipe
Coax-to-waveguide Coupler
MP region
0.024
0.026
0.028
0.03
0.032
0.034
0.036
0.038
0.04
0.0495 0.05 0.0505 0.051 0.0515 0.052 0.0525 0.053
Z (m)
r (m
)
Eacc=2MV/m, 4th order MP
Impact energy: 540~790MeVLtube=105.6mm
Z=0
Example Of Multipacting Study In Coaxial Coupler
TESLA 1.3GHz Accelerating Cavity
Coax dimensions are important for suppressing MP
Spoke Cavity ?
• Need minimum iris radius of 60mm• Outer radius can be smaller than regular shape (e.g. ~ 170mm for 800 MHz)• Explore possibilities for both 800-MHz and 400-MHz cavities• Optimize spoke shape and end-group to improve R/Q and surface fields• Explore option of opening hole on outer wall for wakefield damping• Multipacting and structural analysis, etc
E-field in a spoke cellSpoke – optimize to minimize surface fields
Goal is to minimize the transverse dimension to fit in tight transverse space of the existing latticeWork in progress
TEM3P: Multi-Physics Analysis
• Finite element based with high-order basis functions– Natural choice: FEM originated from structural analysis!
• Use the same software infrastructure as Omega3P– Reuse solvers framework– Mesh data structures and format
• Multi-physics analysis– EM heating– Thermal radiation– Lorentz force detuning– Mechanical stress
• Parallel large-scale simulations for accurate and reliable multi-physics analysis
– Virtual prototyping through computing
CAD Model
EM Analysis
Thermal Analysis
Mechanical Analysis
TEMP Flow Chart
TEM3P Example: LCLS RF Gun
EM DomainThermal/MechanicalDomain
CAD Model (courtesy of Eric Jongewaard)
TEM3P Mesh: 0.6 million nodes.Materials: Copper + Stainless steelThermal analysis: 7 cooling channelsResult benchmarked with ANSYS
EM Heating
Thermal Analysis:Max temperature
ANSYS: 49.96 degCTEMP3P: 49.82 degC
TEM3P: RF Gun Thermal/Mechanical Analysis Comparison With ANSYS
TEM3P ANSYS
Mechanical Analysis:Max displacement
ANSYS: 3.71e-5 mTEM3P: 3.70e-5 m
Summary
• SLAC parallel electromagnetics and beam dynamics codes facilitate the design and optimization of cavities
• LOM and HOM coupler designs and multipactinganalysis for the ILC crab cavity have been performed
• Design and optimization of the LHC crab cavity are being studied for– Cavity shape and RF parameters– Wakefield damping schemes for LOM, SOM and HOM modes– Multipacting and multi-physics analysis
