Eigenmode Calculation for the BC0 Vacuum Chamber

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1 Eigenmode Calculation for the BC0 Vacuum Chamber W. Ackermann, W.F.O. Müller, T. Weiland Institut für Theorie Elektromagnetischer Felder, Technische Universität Darmstadt Status Meeting December 19, 2013 TEMF, TU Darmstadt December 19, 2013 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 1

2 Computational Model Bunch compressor 0 - Vacuum chamber (construction) technical details 19. Dezember 2013 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 2

3 Computational Model Bunch compressor 0 - Vacuum chamber (electric model) vacuum model beam tube vacuum pump 19. Dezember 2013 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 3

4 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 beam tube vacuum chamber hard-edged magnets particle trajectories 19. Dezember 2013 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 4

5 Implementation 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 shunt impedance reference points local coordinate system di t 19. Dezember 2013 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 5

6 - Computational mesh tetrahedrons DOF 19. Dezember 2013 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 6

7 - Field pattern of the electric field strength Mode 1 f = MHz Mode 2 f = MHz Mode 3 f = MHz Mode 4 f = MHz Mode 5 f = MHz 19. Dezember 2013 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 7

8 - Field pattern of the electric field strength Mode 6 f = MHz more than 1000 modes have been examined (all modes up to 4 GHz). Mode 1294 f = MHz Mode 1295 f = MHz 19. Dezember 2013 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 8

9 - Field pattern of the electric field strength Mode 6 f = MHz - Components of the electromagnetic force 19. Dezember 2013 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 9

10 - Field pattern of the electric field strength Mode 6 f = MHz - Components of the electromagnetic force Point: result of integration Line: integrand 19. Dezember 2013 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 10

11 - Field pattern of the electric field strength Mode 1294 f = MHz - Components of the electromagnetic force 19. Dezember 2013 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 11

12 - Field pattern of the electric field strength Mode 1294 f = MHz - Components of the electromagnetic force 19. Dezember 2013 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 12

13 - Field pattern of the electric field strength Mode 1295 f = MHz - Components of the electromagnetic force 19. Dezember 2013 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 13

14 - Field pattern of the electric field strength Mode 1295 f = MHz - Components of the electromagnetic force 19. Dezember 2013 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 14

15 Summary / Outlook Summary: - Computational model for BC0 available from DESY - Trajectories used for field evaluation can be determined analytically due to hard-edge magnet approximation (applicable to extract points and local coordinate systems) - Field pattern for various modes have been determined with the help of real-valued eigenanalysis - Postprocessing of all modes (>1000) up to 4 GHz did not identify any harmful modes for the selected trajectories December 19, 2013 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 15

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