Page 1
High Precision Cavity Simulations
Wolfgang Ackermann, Thomas WeilandInstitut Theorie Elektromagnetischer Felder, TU Darmstadt
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 1
11th International Computational Accelerator Physics ConferenceICAP 2012August 19 - 24, 2012Warnemünde, Germany
Page 2
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 2
Outline
▪ Motivation▪ Computational model
- Problem formulation in 3-D
- Problem formulation in 2-D (boundary condition)
▪ Numerical examples- Field patterns for selected modes
- Resonance frequency and quality factors
▪ Summary / Outlook
Page 3
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 3
Outline
▪ Motivation▪ Computational model
- Problem formulation in 3-D
- Problem formulation in 2-D (boundary condition)
▪ Numerical examples- Field patterns for selected modes
- Resonance frequency and quality factors
▪ Summary / Outlook
Page 4
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 4
Motivation
▪Particle accelerators- FLASH at DESY, Hamburg
http://www.desy.de
TESLA 1.3 GHz
TESLA 3.9 GHz
RF Gun
LaserBunch
CompressorBunch
Compressor
Diagnostics Accelerating Structures Collimator Undulators
250 m
Page 5
23. August 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 5
Motivation
▪ XFEL: Main parameters of the accelerator
http
://xf
el.d
esy.
de/te
chni
cal_
info
rmat
ion/
tdr/t
dr
Page 6
23. August 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 6
Motivation
▪ Linac: Cavities
http
://xf
el.d
esy.
de/te
chni
cal_
info
rmat
ion/
tdr/t
dr
Page 7
23. August 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 7
Motivation
▪ Linac: Cavities
http
://xf
el.d
esy.
de/te
chni
cal_
info
rmat
ion/
tdr/t
dr
Page 8
23. August 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 8
Motivation
▪ Linac: Cavities- Photograph
- Numerical modelhttp://newsline.linearcollider.org
CST Studio Suite 2012
upstream downstream
Page 9
Motivation
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 9
▪Superconducting resonator
9-cell cavity
Beamtube
Downstreamhigher order mode coupler
Input coupler
Upstreamhigher order mode coupler
High precisioncavity simulations
Page 10
Motivation
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 10
▪Superconducting resonator9-cell cavity
Downstreamhigher order mode coupler
Input coupler
Upstreamhigher order mode coupler
Page 11
Motivation
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 11
▪Superconducting resonator9-cell cavity
Downstreamhigher order mode coupler
Input coupler
Upstreamhigher order mode coupler
Variation:Penetration depth
Variation:Coupler orientation
Page 12
Motivation
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 12
▪ Input coupler and coupler to extract unwanted modes
Beam tube
Downstreamhigher order mode coupler
Coaxial input coupler
Coaxial line
Antennas
Page 13
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 13
Outline
▪ Motivation▪ Computational model
- Problem formulation in 3-D
- Problem formulation in 2-D (boundary condition)
▪ Numerical examples- Field patterns for selected modes
- Resonance frequency and quality factors
▪ Summary / Outlook
Page 14
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 14
Computational Model
▪Problem formulation- Local Ritz approach
continuous eigenvalue problem
+ boundary conditions
vectorial function
global index
number of DOFs
scalar coefficient
discrete eigenvalue problem
Galerkin
Page 15
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 15
Computational Model
▪Eigenvalue formulation- Fundamental equation
- Matrix properties
- Fundamental properties
Notation:A - stiffness matrixB - mass matrixC - damping matrix
for proper chosen scalar and vector basis functions
orstatic dynamic
Page 16
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 16
Computational Model
▪Fundamental properties- Number of eigenvalues
- Orthogonality relation
Notation:A - stiffness matrixB - mass matrixC - damping matrixMatrix B nonsingular:
• matrix polynomial is regular• 2n finite eigenvalues
If the vectors and are no longer B-orthogonal:
Page 17
23. August 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 17
Computational Model
▪Numerical formulation- Function definition
Pär
Inge
lströ
m,
A N
ew S
et o
f H(c
url)-
Con
form
ing
Hie
rarc
hica
lB
asis
Fun
ctio
ns fo
r Tet
rahe
dral
Mes
hes,
IEE
E T
RA
NS
AC
TIO
NS
ON
MIC
RO
WA
VE
TH
EO
RY
AN
D T
EC
HN
IQU
ES
,V
OL.
54,
NO
. 1, J
AN
UA
RY
200
6
FEM06: lowest order approximation(edge elements, Nedelec)
scal
arve
ctor
Page 18
23. August 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 18
Computational Model
▪Numerical formulation- Function definition
Pär
Inge
lströ
m,
A N
ew S
et o
f H(c
url)-
Con
form
ing
Hie
rarc
hica
lB
asis
Fun
ctio
ns fo
r Tet
rahe
dral
Mes
hes,
IEE
E T
RA
NS
AC
TIO
NS
ON
MIC
RO
WA
VE
TH
EO
RY
AN
D T
EC
HN
IQU
ES
,V
OL.
54,
NO
. 1, J
AN
UA
RY
200
6
scal
arve
ctor
FEM12: higher order approximation
Page 19
23. August 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 19
Computational Model
▪Numerical formulation- Function definition
Pär
Inge
lströ
m,
A N
ew S
et o
f H(c
url)-
Con
form
ing
Hie
rarc
hica
lB
asis
Fun
ctio
ns fo
r Tet
rahe
dral
Mes
hes,
IEE
E T
RA
NS
AC
TIO
NS
ON
MIC
RO
WA
VE
TH
EO
RY
AN
D T
EC
HN
IQU
ES
,V
OL.
54,
NO
. 1, J
AN
UA
RY
200
6
scal
arve
ctor
FEM20: higher order approximation
Page 20
▪Spherical resonator
Computational Model
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 20
Fem20_G1: 2.1
TM 011: f0 = 65.456 MHz
Fem06_G1: 2.00
Number of elements in thousand
5 20 50 10010
10-1
10-2
10-3
10-4
10-5
Rel
ativ
e Fr
eque
ncy
Err
or
10-62
Page 21
Computational Model
▪Geometry approximation- Tetrahedral mesh types
Linear element Curvilinear element
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 21
Page 22
Computational Model
▪Geometry approximation
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 22
Planar elements Curvilinear elements
1701 tetrahedrons 1701 tetrahedrons
Page 23
Computational Model
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 23
TM 011: f0 = 65.456 MHz
Fem20_G2: 4.0
Fem06_G2: 1.8
▪Spherical resonator
Number of elements in thousand
5 20 50 100102
10-1
10-2
10-3
10-4
10-5
Rel
ativ
e Fr
eque
ncy
Err
or
10-6
Page 24
▪Spherical resonator
Computational Model
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 24
TM 011: f0 = 65.456 MHz
Fem06_G1: 2.0
Fem20_G2: 4.0
Number of elements in thousand
5 20 50 10010
10-1
10-2
10-3
10-4
10-5
Rel
ativ
e Fr
eque
ncy
Err
or
10-62
Page 25
Computational Model
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 25
▪Geometrical model
9-cell cavity
Beamtube
DownstreamHOMcoupler
Input coupler
UpstreamHOMcoupler
High precisioncavity simulations
for closed structures
Page 26
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 26
Outline
▪ Motivation▪ Computational model
- Problem formulation in 3-D
- Problem formulation in 2-D (boundary condition)
▪ Numerical examples- Field patterns for selected modes
- Resonance frequency and quality factors
▪ Summary / Outlook
Page 27
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 27
Computational Model
▪Port boundary condition
Port face, fundamental coupler
Page 28
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 28
Computational Model
▪Port boundary condition
Port face, HOM coupler
Page 29
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 29
Computational Model
▪Problem formulation- Local Ritz approach
vectorial function
global index
number of DOFs
scalar coefficient
Port face
Mixed 2-D vector and scalar basis
Page 30
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 30
Computational Model
▪Problem formulation- Local Ritz approach
continuous eigenvalue problem, loss-free
+ boundary conditions
vectorial function
global index
number of DOFs
scalar coefficient
discrete eigenvalue problem
Galerkin
Page 31
0 5 10 15 200
100
200
300
400
0 2 4 6 8 100
50
100
150
200
Computational Model
▪Wave propagation in the applied coaxial lines- Main coupler
- HOM coupler
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 31
12.5 mm
60.0 mm
3.4 mm
16.0 mm
TEM
TE11 TE21
TEM
TE11 TE21
f0 = 1.3 GHz
f0 = 1.3 GHz
Dispersion relation
propagation
damping
Page 32
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 32
Computational Model
▪Problem formulation- Determine propagation constant for a fixed frequency
algebraic eigenvalue problem
eigenvectorand
eigenvalue
Page 33
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 33
Computational Model
▪Problem formulation- Determine propagation constant for a fixed frequency
algebraic eigenvalue problem
eigenvectorand
eigenvalue
Mode 1 Mode 2 Mode 3 Mode 4 …
Page 34
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 34
▪Problem definition- Geometry
- Task
Numerical Examples
TESLA 9-cell cavity
PECboundary condition
Search for the field distribution, resonance frequency and quality factor
Portboundaryconditions
Port boundary conditions
Page 35
Numerical Examples
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 35
▪Computational model
9-cell cavity
Beamcube
Inputcoupler
Upstream HOM coupler
Distributecomputational load
on multiple processes
Page 36
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 36
Outline
▪ Motivation▪ Computational model
- Problem formulation in 3-D
- Problem formulation in 2-D (boundary condition)
▪ Numerical examples- Field patterns for selected modes
- Resonance frequency and quality factors
▪ Summary / Outlook
Page 37
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 37
Numerical Examples
▪Simulation results- Accelerating mode (monopole #9)
- Higher-order mode (dipole #37)
Page 38
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 38
Numerical Examples
▪Simulation resultsAccelerating mode(monopole #9)
Higher-order mode(dipole #37)
Beam tube
HOM coupler
Coaxialinput coupler
Coaxial line
Beam tube
HOM coupler
Coaxialinput coupler
Page 39
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 39
Numerical Examples
▪Simulation results
1 3 5 7 9 2917 2521 33 37 41 4513
1.900
1.800
1.700
1.600
1.500
1.400
1.300
Freq
uenc
y / G
Hz
Monopolepassband
Mixed first and second dipole passband
Mode Index
Black: 283,130 tetrahedraColor: 1,308,476 tetrahedra
Page 40
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 40
Numerical Examples
▪Simulation results Black: 283,130 tetrahedraColor: 1,308,476 tetrahedra
1 3 5 7 9 Mode Index810642
107
108
109
1010
6
8 mm
4 mm
0 mm
No port on main input coupler
Ext
erna
l qua
lity
fact
or
Penetration depth:
Page 41
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 41
Numerical Examples
▪Simulation results
12 1614 1810 Mode Index8103
42 6
104
105
106
Ext
erna
l qua
lity
fact
or
Mixed first and second dipole passband
Page 42
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 42
Summary / Outlook
▪Summary:Request for precise modeling of electromagnetic fields withinresonant structures including small geometric details:- Geometric modeling with curved tetrahedral elements- Port boundary conditions with curved triangles- Preliminary implementation
▪Outlook:- User-friendly parallel implementation