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


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


Outline








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


Motivation

▪ Linac: Cavities

http

://xf

el.d

esy.

de/te

chni

cal_

info

rmat

ion/

tdr/t

dr


Motivation

▪ Linac: Cavities

http

://xf

el.d

esy.

de/te

chni

cal_

info

rmat

ion/

tdr/t

dr


Motivation

▪ Linac: Cavities- Photograph

- Numerical modelhttp://newsline.linearcollider.org

CST Studio Suite 2012

upstream downstream

Motivation


▪Superconducting resonator

9-cell cavity

Beamtube

Downstreamhigher order mode coupler

Input coupler

Upstreamhigher order mode coupler

High precisioncavity simulations

Motivation


▪Superconducting resonator9-cell cavity


Input coupler


Motivation


▪Superconducting resonator9-cell cavity


Input coupler


Variation:Penetration depth

Variation:Coupler orientation

Motivation


▪ Input coupler and coupler to extract unwanted modes

Beam tube


Coaxial input coupler

Coaxial line

Antennas


Outline








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


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


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:


Computational Model

▪Numerical formulation- Function definition

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FEM06: lowest order approximation(edge elements, Nedelec)

scal

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Computational Model


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FEM12: higher order approximation


Computational Model


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FEM20: higher order approximation

▪Spherical resonator

Computational Model


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


Computational Model

▪Geometry approximation


Planar elements Curvilinear elements

1701 tetrahedrons 1701 tetrahedrons

Computational Model


TM 011: f0 = 65.456 MHz

Fem20_G2: 4.0

Fem06_G2: 1.8



5 20 50 100102

10-1

10-2

10-3

10-4

10-5

Rel

ativ

e Fr

eque

ncy

Err

or

10-6


Computational Model


TM 011: f0 = 65.456 MHz

Fem06_G1: 2.0

Fem20_G2: 4.0


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


▪Geometrical model

9-cell cavity

Beamtube

DownstreamHOMcoupler

Input coupler

UpstreamHOMcoupler

High precisioncavity simulations

for closed structures


Outline








Computational Model

▪Port boundary condition

Port face, fundamental coupler


Computational Model

▪Port boundary condition

Port face, HOM coupler


Computational Model


vectorial function

global index

number of DOFs

scalar coefficient

Port face

Mixed 2-D vector and scalar basis


Computational Model


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


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


Computational Model

▪Problem formulation- Determine propagation constant for a fixed frequency

algebraic eigenvalue problem

eigenvectorand

eigenvalue


Computational Model

▪Problem formulation- Determine propagation constant for a fixed frequency

algebraic eigenvalue problem

eigenvectorand

eigenvalue

Mode 1 Mode 2 Mode 3 Mode 4 …


▪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


▪Computational model

9-cell cavity

Beamcube

Inputcoupler

Upstream HOM coupler

Distributecomputational load

on multiple processes


Outline








Numerical Examples

▪Simulation results- Accelerating mode (monopole #9)

- Higher-order mode (dipole #37)


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


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


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:


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


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

Documents

High Precision Cavity Simulations