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