Computational Simulations of Direct Contact Condensation ...
High Precision Cavity Simulations
Transcript of High Precision Cavity Simulations
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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:
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
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
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
▪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
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
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
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
▪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
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
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
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 27
Computational Model
▪Port boundary condition
Port face, fundamental coupler
August 23, 2012 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 28
Computational Model
▪Port boundary condition
Port face, HOM coupler
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
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
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
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
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 …
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
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
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
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)
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
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
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:
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
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