application of a complex eigenmode solver to the tesla 1.3 ... 2013-08-09.… · august 19, 2013 |...

Application of a Complex EigenmodeSolver to the TESLA 1.3 GHz Structure

W. Ackermann, C. Liu, W.F.O. Müller, T. WeilandInstitut für Theorie Elektromagnetischer Felder, Technische Universität Darmstadt

Status MeetingAugust 9, 2013DESY, Hamburg

August 19, 2013 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Wolfgang Ackermann | 1


Outline

Motivation

Computational model

- Problem formulation

- Planar ports of arbitrary shape

(here: coax lines and cylindrical beam tubes)

Numerical examples

- 1.3 GHz structure (single cavity)

Summary of all modes up to the 5th dipole passband

Summary / Outlook


Outline

Motivation

Computational model




Numerical examples



Summary / Outlook

Motivation


Superconducting resonator9-cell cavity

Downstreamhigher order mode coupler

Input coupler

Upstreamhigher order mode coupler


Outline

Motivation

Computational model




Numerical examples



Summary / Outlook

Computational Model


Geometrical model

9-cell cavity

Beamtube

DownstreamHOMcoupler

Input coupler

UpstreamHOMcoupler

High precision cavity simulations using FEM

on tetrahedral mesh


Computational Model

Port boundary condition

Port face, fundamental coupler


Computational Model

Port boundary condition

Port face, HOM coupler


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


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


Outline

Motivation

Computational model




Numerical examples



Summary / Outlook

Numerical Examples


100

200

500100020005000

Monopole

Dipole

Quadrupole

Sextupole

2.46 2.48 2.50 2.52 2.54 2.56 2.58 2.600.00

0.01

0.02

0.03

0.04

Real

Imag

inar

y

Controlling the Jacobi-Davidson eigenvalue solver- Evaluation in the complex frequency plane- Select best suited eigenvalues in circular region around user-specified complex target

Real and imaginary part of the complex frequency


Numerical Examples

Quality factor versus frequency

Calculations kindly performed by Cong Liu


Numerical Examples

Simulation study based on mesh density variations- Grid 1

- Grid 2

- Grid 3

315.885 tetrahedrons1.932.746 complex DOF

1.008.189 tetrahedrons6.238.328 complex DOF

3.081.614 tetrahedrons19.177.820 complex DOF


Numerical Examples

Accuracy considerations (1st monopole passband)

Mod

e In

dex

Mod

e In

dex

Grid Index

Grid index:1) 315.885 tetrahedrons, 1.932.746 complex DOF2) 1.008.189 tetrahedrons, 6.238.328 complex DOF3) 3.081.614 tetrahedrons, 19.177.820 complex DOF

Relative error in ppmResonance frequency in GHz

Grid Index


Numerical Examples


Mod

e In

dex

Mod

e In

dex

Grid Index Grid Index


Relative error in %Quality factor in 106


Numerical Examples


Mod

e In

dex

Mod

e In

dex

Grid Index


Relative error in %Shunt impedance in MΩGrid Index


Numerical Examples

Collection of the first 194 modes (selected page)

Magnitude of the electric field strength(longitudinal cut)

Magnitude of the magnetic flux density(longitudinal cut)

Magnitude of the electric field and themagnetic flux density (longitudinal cut)

Resonance frequency, quality factorand shunt impedances


Numerical Examples

Comparison to MAFIA calculations (fres monopole)

Ref

eren

ce: (

TE

SLA

200

1-33

)M

onop

ole,

Dip

ole

and

Qua

drup

ole

Pas

sban

dsof

the

TE

SLA

9-c

ell C

avity

, R

. Wan

zenb

erg,

Sep

tem

ber

14, 2

001

Mod

e In

dex

Mod

e In

dex

TE modes

MAFIA:step size 1mm12.000 grid points


Numerical Examples

Comparison to MAFIA calculations (R/Q monopole)

Mod

e In

dex

Mod

e In

dex

TE modes

Ref

eren

ce: (

TE

SLA

200

1-33

)M

onop

ole,

Dip

ole

and

Qua

drup

ole

Pas

sban

dsof

the

TE

SLA

9-c

ell C

avity

, R

. Wan

zenb

erg,

Sep

tem

ber

14, 2

001

MAFIA:step size 1mm12.000 grid points


Numerical Examples

Geometry Modifications

CST cavity-construction macro:Modification of eachindividual cell possible

+ attachedbeam tubes and couplers


Numerical Examples


Monopole #2

Monopole #9


Summary / Outlook

Summary:Accurate complex eigenmode solver available

- FEM up to 2nd order edge elements

- Geometric modeling with curved tetrahedral elements

- Port boundary conditions with curved triangles

- Application to the 1.3 GHz structure(calculation of all modes up the 5th dipole passband)

Outlook:- Application to 1.3 GHz and 3.9 GHz cavity strings

application of a complex eigenmode solver to the tesla 1.3 ... 2013-08-09.… · august 19, 2013 |...

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