Calculation of Complex Eigenmodes for TESLA 1.3 GHz and ...€¦ · Calculation of Complex...
Transcript of Calculation of Complex Eigenmodes for TESLA 1.3 GHz and ...€¦ · Calculation of Complex...
Calculation of Complex Eigenmodes for TESLA 1.3 GHz and BC0 structures
W. Ackermann, C. Liu, W.F.O. Müller, T. Weiland Institut für Theorie Elektromagnetischer Felder, Technische Universität Darmstadt
Status Meeting July 9, 2014 DESY, Hamburg
July 10, 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 1
July 10, 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 2
Outline
▪ Eigenvalue calculation for the 1.3 GHz TESLA 9-cell structure - Acceleration mode below cut-off frequency of the beam tubes,
calculation of field maps for various main coupler penetration depths
- Higher order modes above the cut-off frequency of the beam tubes,
influence of different boundary conditions to terminate the beam tubes
▪ Postprocessing of the field data calculated for BC0 - Longitudinal loss parameter
- Kick parameter
July 10, 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 3
Outline
▪ Eigenvalue calculation for the 1.3 GHz TESLA 9-cell structure - Acceleration mode below cut-off frequency of the beam tubes,
calculation of field maps for various main coupler penetration depths
- Higher order modes above the cut-off frequency of the beam tubes,
influence of different boundary conditions to terminate the beam tubes
▪ Postprocessing of the field data calculated for BC0 - Longitudinal loss parameter
- Kick parameter
10. Juli 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 4
Motivation
▪ Linac: Cavities - Photograph
- Numerical model http://newsline.linearcollider.org
CST Studio Suite 2014
upstream downstream
Motivation
July 10, 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 5
▪Superconducting resonator 9-cell cavity
Downstream higher order mode coupler
Input coupler
Upstream higher order mode coupler
Motivation
July 10, 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 6
▪Superconducting resonator modeling Beam tube
Downstream higher order mode coupler
Input coupler
Upstream higher order mode coupler
Parameter variation 0, 2, 4, 6, 8, 10 mm
0 m
m
10 m
m
Numerical Modeling
July 10, 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 7
▪Superconducting resonator modeling
Input coupler
Upstream higher order mode coupler
Beam tube
Downstream higher order mode coupler
Procedure - discretize ¼ of the structure - copy the resulting mesh
Numerical Modeling
▪Field reconstruction using the Kirchhoff integral - Field values inside a closed surface can be determined once the surface field components are available
- Kirchhoff integral
July 10, 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 8
Numerical Modeling
July 10, 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 9
▪Superconducting resonator modeling
Upstream higher order mode coupler
Beam tube
Mesh density control Level 0, blue Level 1, orange Level 3, red
First cell
July 10, 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 10
Computational Model
▪Port boundary condition
Port face, HOM coupler
July 10, 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 11
Computational Model
▪Port boundary condition
Port face, fundamental coupler
Numerical Modeling
July 10, 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 12
▪Superconducting resonator
Beam tube
Downstream higher order mode coupler
Input coupler
Upstream higher order mode coupler
0 mm
Penetration 8 mm
Sampled area -15mm to +15 mm, step 1 mm
Numerical Results
July 10, 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 13
▪Superconducting resonator - Convergence study
Main coupler depth Number of tets Resonance freqency Quality factor
8 mm 366 955 1.300055 GHz 2.832 106
8 mm 720 324 1.300032 GHz 2.753 106
8 mm 1 320 954 1.300012 GHz 2.735 106
8 mm 2 131 752 1.300005 GHz 2.670 106
8 mm 3 284 180 1.300002 GHz 2.667 106
Estimated accuracy
Numerical Results
July 10, 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 14
▪Superconducting resonator - Eigenvalue calculation
Main coupler depth Number of tets Resonance freqency Quality factor
0 mm 3 290 937 1.300003 GHz 12.605 106
2 mm 3 288 250 1.300002 GHz 8.304 106
4 mm 3 286 608 1.300002 GHz 5.571 106
6 mm 3 285 819 1.300002 GHz 3.812 106
8 mm 3 284 180 1.300002 GHz 2.667 106
10 mm 3 282 786 1.300002 GHz 1.909 106
Complex-valued field components are available within the FEM or the Kirch- hoff‘s integral formulation for any specified main coupler penetration depth. File format for ASTRA input has been provided by DESY (thanks to Martin).
July 10, 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 15
Outline
▪ Eigenvalue calculation for the 1.3 GHz TESLA 9-cell structure - Acceleration mode below cut-off frequency of the beam tubes,
calculation of field maps for various main coupler penetration depths
- Higher order modes above the cut-off frequency of the beam tubes,
influence of different boundary conditions to terminate the beam tubes
▪ Postprocessing of the field data calculated for BC0 - Longitudinal loss parameter
- Kick parameter
July 10, 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 16
Numerical Examples
▪ Influence of boundary conditions at the beam tube - Close tube using PEC material
- Close tube using PMC material
Electric BC Electric BC
Magnetic BC Magnetic BC
HOM and MAIN couplers always modeled using port BC
July 10, 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 17
Numerical Examples
▪ Influence of boundary conditions at the beam tube - Infinite tube using port boundary conditions
- “Cavity” boundary condition
Port BC Port BC
“Cavity“ BC “Cavity“ BC
July 10, 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 18
Numerical Examples
▪ Influence of boundary conditions at the beam tube - Infinite tube using port boundary conditions
- “Cavity” boundary condition
Port BC Port BC
“Cavity“ BC “Cavity“ BC Port BC Port BC
July 10, 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 19
Numerical Examples
▪Quality factor versus frequency (1.3 GHz structure)
Calculations kindly performed by Cong Liu
July 10, 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 20
Numerical Examples
▪Quality factor versus frequency - Comparison using different beam-tube boundary conditions
100
200500 100020005000
2.80 2.85 2.90 2.95 3.00 3.05
0.00
0.01
0.02
0.03
0.04
Real
Imag
inary
CC – three cavities
100
200500 100020005000
2.80 2.85 2.90 2.95 3.00 3.05
0.00
0.01
0.02
0.03
0.04
Real
Imag
inary
EE - electric, electric
2.80 2.85 2.90 2.95 3.00 3.051
2
3
4
5
6
7
8
FrequencyGHz
Quali
tyFa
ctor
July 10, 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 21
Numerical Examples
▪Quality factor versus frequency - Comparison using different beam-tube boundary conditions
EE - electric, electric
MM – magnetic, magnetic
CC – three cavities PP – port, port
July 10, 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 22
Numerical Examples
▪Quality factor versus frequency - Comparison using different beam-tube boundary conditions
EE002 EE003
MM002
PP002
EE001
MM001
PP001
MM003
PP003
EE004
MM004
PP004
July 10, 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 23
Numerical Examples
▪Quality factor versus frequency - Comparison
CC002
CC001
CC003
Some of the modes can not be represented by single cavities using “EE”, “MM” or “PP” BC.
July 10, 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 24
Outline
▪ Eigenvalue calculation for the 1.3 GHz TESLA 9-cell structure - Acceleration mode below cut-off frequency of the beam tubes,
calculation of field maps for various main coupler penetration depths
- Higher order modes above the cut-off frequency of the beam tubes,
influence of different boundary conditions to terminate the beam tubes
▪ Postprocessing of the field data calculated for BC0 - Longitudinal loss parameter
- Kick parameter
Computational Model
▪Bunch compressor 0 - Vacuum chamber (construction)
10. Juli 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 25
technical details
Computational Model
▪Bunch compressor 0 - Vacuum chamber (electric model)
10. Juli 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 26
vacuum model
beam tube vacuum pump
Computational Model
▪Bunch compressor 0 - Particle trajectories
• Hard-edged magnets: analytical calculation of particle trajectories • Determination of local coordinates aligned to tangential direction • Specification of sample points to evaluate eigenmode fields
10. Juli 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 27
beam tube
hard-edged magnets particle trajectories
vacuum chamber
Implementation
▪Eigenvalue solver and auxiliary programs - Postprocessing
• Change point evaluation from existing ‘line’ to new ‘arbitrary list’ • Specify list of points along selected trajectory • Evaluate field components for all determined modes and all points • Transform field components to the particles coordinate system • Perform path integration to determine loss and kick parameter
10. Juli 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 28
local coordinate system
0 1 2 3 4 5 6di t
reference points
Implementation
▪Eigenvalue solver and auxiliary programs - Definition of the longitudinal loss and kick parameter
• Resulting energy
• Kick parameter
10. Juli 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 29
Longitudinal loss parameter
Excitation Amplitude
Simulation Results
▪Eigenvalue solver using real-value arithmetic - Computational mesh
10. Juli 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 30
1.758.316 tetrahedrons 10.671.742 DOF
Simulation Results
▪Eigenvalue solver - Field pattern of the electric field strength
10. Juli 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 31
Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
f = 376.4 MHz
f = 378.2 MHz
f = 384.9 MHz
f = 391.5 MHz
f = 397.5 MHz
Simulation Results
▪Eigenvalue solver - Field pattern of the electric field strength
10. Juli 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 32
Mode 6 f = 376.4 MHz
… more than 1000 modes have been examined (all modes up to 4 GHz).
f = 4037.2 MHz
f = 4037.4 MHz
Mode 1294
Mode 1295
Simulation Results
▪Eigenvalue solver - Frequency distribution
10. Juli 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 33
Mode index 0 200 400 600 800 1000 1200
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Res
onan
ce fr
eque
ncy
/ GH
z
Modes up to 4 GHz considered, 1298 eigensolutions detected, calculation based on real arithmetic
Simulation Results
▪Eigenvalue solver - Loss parameter
10. Juli 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 34
0 200 400 600 800 1000 12000.00.51.01.52.02.53.03.5
Null
0 200 400 600 800 1000 12000.0
0.1
0.2
0.3
0.4
0.5Min
0 200 400 600 800 1000 12000.00.10.20.30.40.50.6
Mid
0 200 400 600 800 1000 12000.000.050.100.150.200.250.300.35
Max
k / V
/nC
mode index
k / V
/nC
k / V
/nC
k
/ V/n
C
mode index
Simulation Results
▪Eigenvalue solver - Loss parameter
10. Juli 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 35
k / V
/nC
mode index 0 200 400 600 800 1000 1200
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
path „null“
TESLA 2001-33 R. Wanzenberg
path „mid“
path „max“
path „min“
Comparison to the TESLA 1.3 GHz structure
Simulation Results
▪Eigenvalue solver - Kick parameter
10. Juli 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 36
0 200 400 600 800 1000 1200
20
10
0
10
20Null x
0 200 400 600 800 1000 1200
1000
500
0
Null y
0 200 400 600 800 1000 1200
10
8
6
4
2
0Null z
0 200 400 600 800 1000 1200
20
10
0
10
20
30Min x
0 200 400 600 800 1000 12001500
1000
500
0
500
Min y
0 200 400 600 800 1000 1200
1.5
1.0
0.5
0.0Min z
k x /
Vs/
Cm
k x
/ V
s/C
m
Simulation Results
▪Eigenvalue solver - Kick parameter
10. Juli 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 37
0 200 400 600 800 1000 1200
1000
500
0
500Mid y
0 200 400 600 800 1000 120030
20
10
0
10
20
30Mid x
0 200 400 600 800 1000 1200
2.0
1.5
1.0
0.5
0.0Mid z
0 200 400 600 800 1000 1200
1000
500
0
500Max y
0 200 400 600 800 1000 1200302010
010
2030
Max x
0 200 400 600 800 1000 12001.2
1.0
0.8
0.6
0.4
0.2
0.0Max z
k x /
Vs/
Cm
k x
/ V
s/C
m
Simulation Results
▪Eigenvalue solver - Accuracy estimation
10. Juli 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 38
0 200 400 600 800 1000 120050
40
30
20
10
0
Modeindex
Rela
tivee
rror
in
0 200 400 600 800 1000 12000.350.300.250.200.150.100.05
0.00
Modeindex
Rela
tivee
rrori
n
0 200 400 600 800 1000 1200
2.5
2.0
1.5
1.0
0.5
0.0
Modeindex
Rela
tivee
rrori
n
0 200 400 600 800 1000 1200
4
2
0
2
4
Mode index
Rela
tivee
rrori
n
null min
mid max
Mode 915
Loss parameter
Kick parameter
Error definition
Simulation Results
▪Eigenvalue solver - Accuracy estimation path “min”
10. Juli 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 39
2000 1000 0 1000 2000
2000
1000
0
1000
2000
300 200 100 0 100 200 300300
200
100
0
100
200
300
2000 1000 0 1000 2000
2000
1000
0
1000
2000
Mode 915 Mode 914 Mode 916
Real part
Imag
inar
y pa
rt
Real part Real part
Integrand
July 10, 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 40
Summary / Outlook
▪Summary: - Eigenvalue calculations concentrating on the accelerating mode for the TESLA 1.3 GHz structure performed based on various main coupler penetration depth
- Field maps for the various setups provided
- Comparison of the eigenvalue distribution (fourth dipole passband) using different beam-tube boundary conditions
- Postprocessing of the BC0 vacuum chamber modes, determination of longitudinal loss and kick parameter
Motivation
July 10, 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 42
▪HOM Coupler power flow
Motivation
July 10, 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 43
▪HOM Coupler - Poynting
Motivation
July 10, 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 44
power flow ▪HOM Coupler
- Poynting
Motivation
July 10, 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 45
▪HOM Coupler - Poynting