Wakefield computation of PETRAIII taper section Laura Lünzer

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1 Wakefield computation of PETRAIII taper section Laura Lünzer 16. Dezember 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Laura Lünzer

2 Geometry of tapered structure Undulator plates Ingoing pipe Vacuum tank Tapered section Outgoing pipe Source: R. Wanzenberg 16. Dezember 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Laura Lünzer 1

3 Geometry of tapered structure Elliptical beam pipe (11 mm x 66 mm) 16. Dezember 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Laura Lünzer 2 Source: R. Wanzenberg

4 Geometry of tapered structure Undulator plates: length 4 m (model with shorter plates) Variable gap: 5-25 mm 16. Dezember 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Laura Lünzer 3 Source: R. Wanzenberg

5 Wake potential calculations Bunch length: 1cm Undulator gap: 6mm Resolution: 1mm Standard parameter calculations: 1. Large differences in longitudinal wake potential 2. Transversal grid resolution very critical 3. Usual 10 lines / sigma rule appears to be misleading 16. Dezember 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Laura Lünzer 4

6 Structure simplification (CST PS) Bunch length: 1cm Undulator gap: 6mm Resolution: 1mm Influence of vacuum tank Structure simplification with less than 2% difference in long. wake potential. 16. Dezember 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Laura Lünzer 5

7 Simulation simplification (CST PS) Influence of undulator plate length Bunch length: 1cm Undulator gap: 6mm Resolution: 0.5 mm Structure simplification with less than 3% difference in long. wake potential. 16. Dezember 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Laura Lünzer 6

8 Mesh simplification (PBCI) Bunch length: 1cm Undulator gap: 6mm Influence of anisotropic mesh Δ ~ 62 µm. N = points on moving window Mesh refinement only in critical direction (small side of pipe) Less than 1% error with simplified mesh 16. Dezember 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Laura Lünzer 7

9 New in PBCI: Symmetry boundary condition Bunch length: 1cm Undulator gap: 6mm Resolution: 0.25 mm Influence of symmetrized problem Calculation of only ¼ of the structure Less than 0,05% error with symmetric boundary 16. Dezember 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Laura Lünzer 8

10 PBCI calculations Δ ~ 8 µm. N = points on moving window Slow convergence for longitudinal wake potential: 1.Only possible with anisotropic mesh refinement and symmetry boundary condition 2. Sim. time at finest grid: ~ 56 hrs on 2040 cores 16. Dezember 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Laura Lünzer 9

11 PBCI calculations Estimated maximum error relative to simulation at finest grid resolution (Estimated) convergence order: 1.2 ~1,8 % error at 640 lines / sigma Grid convergence of longitudinal wake potential: 1.Only possible with anisotropic mesh refinement 2.Sim. time at finest grid: ~16 hrs on 2040 cores Estimated error ~0,96% at 1280 lines / sigma 16. Dezember 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Laura Lünzer 10

12 CST-PS Simulations Grid convergence of longitudinal wake potential: 1.Sim. time at finest grid (~ grid points): ~15 hrs 16. Dezember 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Laura Lünzer 11

13 CST-PS Simulations (Estimated) convergence order: 1.9 Estimated maximum error relative to simulation at finest grid resolution ~ 0,7% ~3 % error at 160 lines / sigma Grid convergence of longitudinal wake potential: 1.Sim. time at finest grid (~ grid points): ~15 hrs 2.Finer simulations possible 16. Dezember 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Laura Lünzer 12

14 Boundary Approximation Problem is stronly geometry dominated - Slower convergence in PBCI (and MAFIA) - Better convergence in CST PS - Nevertheless, absolute accuracies obtained in both cases are comparable due to the higher resolution in PBCI - Simulation issues in CST PS Different behavior for different PBA types Stability problems for high grid resolution 16. Dezember 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Laura Lünzer 13

15 Boundary Approximation Wake Potential (entry section only) Perfect Boundary Approximation: 1. large differences for different PBA at fixed resolution 2. Obvious mesh problem (error?) in PBA and FPBA-E results 16. Dezember 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Laura Lünzer 14

16 Boundary Approximation Wake Potential (entry section only) Perfect Boundary Approximation: 1. leads to different results for low resolutions 2. behavior changes suddenly at higher resolutions 3. strange oscillations at high resolution. Stability problem? 16. Dezember 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Laura Lünzer 15

17 Loss Factor K z = V / nc K z = V / nc Loss Factor calculation: 1. PBCI and CST calculations converge from different sides 2. Upper and lower estimation possible 16. Dezember 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Laura Lünzer 16

18 Loss Factor K z = V / nc Bunch length: 1cm Undulator gap: 6mm Estimated Error at highest resolution ~3% 16. Dezember 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Laura Lünzer 17

19 PBCI simulations Longitudinal wake potential for different gap widths 16. Dezember 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Laura Lünzer 18

20 PBCI simulations Loss factors for different gaps 16. Dezember 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Laura Lünzer 19

21 Thank you very much for your attention 5. April 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Laura Lünzer

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