1. IMPEDANCE OF Y-CHAMBER FOR SPS CRAB CAVITY By Phoevos Kardasopoulos Thanks to Benoit Salvant, Pei Zhang, Fred Galleazzi, Roberto Torres-Sanchez and Alick MacPherson Impedance Meeting Date: 14/04/14

2. Contents Overview Methodology Review Existing Y-Chamber (COLDEX) Evaluation of Designs for Crab Cavities Presentation of recommended impedance design Issues Related to Bellows Conclusions Objective of this talk: Present revised Y-chamber design for SPS crab cavity installation and seek approval from impedance group, so that the design can proceed to fabrication by the vacuum group. 1

3. Contents Overview Methodology Review Existing Y-Chamber (COLDEX) Evaluation of Designs for Crab Cavities Presentation of recommended impedance design Issues Related to Bellows Conclusions 2

4. Overview Y-Chamber’s purpose to switch objects in and out of the beam line. 3

5. Overview Y-Chamber’s purpose to switch objects in and out of the beam line. 4

6. Overview Current Y-Chamber: Used by COLDEX. Opening angle: 12 degrees. Transverse displacement: 340mm. Crab Cavities: Opening angle: 16 degrees. Transverse displacement: 510mm. Expected number of cycles(in and out) = O(1000). Redesign needed: Mechanical redesign needed to accommodate Crab Cavities. Take opportunity to redesign Y-Chamber to reduce impedance. Mechanical design must have required reliability. 5

7. Previous Research Previous research has been conducted: B. Spataro et al Impedance of the LHC recombination chambers. LHC Project Note 254. 03/05/2001 On trapped modes in the LHC recombination chambers: experimental results. LHC Project Note 254. LHC Project Note 266. 14/08/2001 LHC Recombination chamber. Possibility of trapped modes above the cut off frequency. 6

8. Contents Overview Methodology Review Existing Y-Chamber (COLDEX) Evaluation of Designs for Crab Cavities Presentation of recommended impedance design Issues Related to Bellows Conclusions 7

9. Methodology Initial 12 o Y-chamber model received from Benoit. CST used to perform simulations on the models. Selection criteria: Based on CST simulations High frequency : Frequency domain Eigenmode solver. Low frequency: Time domain Wakefield solver Results for new designs compared to baseline results of initial Y-chamber model. 8

10. Methodology – High Frequency 9

11. Methodology – Low Frequency Use time domain solver and look at imaginary part of impedance for different source-wake bunch configurations Separate simulations for the monopole, dipole, and quadrupole. (1) (2) (3) (4) (5) 1)Monopole - Beam and test beam on the beam axis 2)Horizontal Dipolar - Beam offset from the beam axis in x 3)Horizontal Quadrupolar - Test beam offset from the beam axis in x 4)Vertical Dipolar- Beam offset from the beam axis in y 5)Vertical Quadrupolar - Test beam offset from the beam axis in y Source bunch wake bunch 10

12. Methodology – Low Frequency 11

13. Contents Overview Methodology Review Existing Y-Chamber (COLDEX) Evaluation of Designs for Crab Cavities Presentation of recommended impedance design Issues Related to Bellows Conclusions 12

14. Current Y-Chamber 12 degree version currently installed at COLDEX at SPS LSS4 There are 3 of these currently in the SPS. Two at LSS4, COLDEX(Crab Cavity) testing area. Legacy design: Reasons behind design are unclear. 13

15. Current Y-Chamber Two Models:. Simplified model. Received from Benoit Imported from Catia. Realistic model. Drawn in SolidWorks, imported as ACIS. Baseline model. As-Installed Stainless Steel Boundaries All Beam pipe connection inner diameter = 155 mm 14

16. Current Y-Chamber Two Models: Simplified model. Received from Benoit Imported from Catia. Realistic model. Drawn in SolidWorks, imported as ACIS. >200 reduced curvature elements. Baseline model. As-Installed 15 Stainless Steel Boundaries All Beam pipe connection inner diameter = 155 mm

17. Eigenmode Results – Simple Y-Chamber Frequency (GHz)Shunt Impedance (KOhms)Q Factor 0.69693.767402 0.91044.668415 1.06714.157979 1.07822.507812 1.15517.436662 1.23215.025872 1.34313.727823 1 Transverse mode identified 48 kOhms/m at 1.40 GHz Cut off frequency at 1.48 GHz Waveguide theory, Pipe radius 77.5mm 16 Results from Eigenmode Simulations

18. Wakefield Solver - Simple Y-Chamber Frequency (GHz)Shunt Impedance (KOhms)Q Factor 0.69693.767402 0.91044.668415 1.06714.157979 1.07822.507812 1.15517.436662 1.23215.025872 1.34313.727823 17 Results from Eigenmode Simulations

19. Low Frequency Transverse (d=5mm) CST Convention: Inductive impedance is - ve 18 Bunch length = 300 Charge =1e-9 Wakelength = 20000 Direct Testbeams

20. Low Frequency Transverse 19 Bunch length = 300 Charge =1e-9 Wakelength = 20000 Direct Testbeams

21. Low Frequency Longitudinal Y-Chamber ≈ 2.8 ± 0.2 mOhms 20

22. 12 Degree Model Comparison 21

23. 12 Degree Model Comparison SPS ≈ 20 MOhms/m 22

24. 12 Degree Model Comparison ModelZ L (mOhms) Zx (kOhms/m) Zy (kOhms/m) Baseline 12 o 2.8 ± 0.20.330.31 Undulated 12 o 2.8 ± 0.20.330.31 SPS: Total Longitudinal 5 Ohms Total Transverse 20MOhms/m 23

25. Contents Overview Methodology Review Existing Y-Chamber (COLDEX) Evaluation of Designs for Crab Cavities Presentation of recommended impedance design Issues Related to Bellows Conclusions 24

26. Alternate Designs Analysed Scaled up of 12 degree. Provided by F. Galleazzi. Scaled up with undulations. Ellipsoid Conical. Proposed. All Designs: 16 Degree angle, stainless steel boundaries, 155mm pipe diameter 25

27. High Frequency Longitudinal Impedance 26

28. High Frequency Longitudinal Impedance 27

29. High Frequency Transverse Impedance Proposed Design - No significant transverse modes why? 28

30. Low Frequency Impedance Comparisons ModelZ II (mOhms)Zx (kOhms/m)Zy (kOhms/m) Baseline 12 Degree 2.80.330.31 16 Degree3.730.271.67 16 Degree Undulations 3.690.410.53 Ellipsoid1.650.250.85 Proposed0.430.210.85 SPS: 5 Ohms Longitudinal 20MOhms Transverse 29

31. Candidate Design Question: Is this design acceptable for the impedance working group? Question: What other aspects are important, aperture? Question: Can we proceed to develop mechanical design with vacuum group? 30

32. Contents Overview Methodology Review Existing Y-Chamber (COLDEX) Evaluation of Designs for Crab Cavities Presentation of recommended impedance design Issues Related to Bellows Conclusions 31

33. Bellows Suggested by Cedric Garion TE-VSC-DLM Are there issues with the bellows? 32

34. Bellow Impedance (Valid up to first cut off frequency) Effective Impedance ≈0.65 mOhms 33 (http://cdsweb.cern.ch/record/118026/files/p1.pdf)

35. Bellow Impedance Cut off frequency at 1.47 GHz Waveguide theory, Pipe radius 78mm Effective Impedance ≈0.65 mOhms Should we be worried at we approach cut-off 34

36. Bellow Impedance 35

37. Contents Overview Methodology Review Existing Y-Chamber (COLDEX) Evaluation of Designs for Crab Cavities Presentation of recommended impedance design Issues Related to Bellows Conclusions 36

38. Conclusions Current 12 degree Y-Chamber has been modelled in CST. Impedances have been calculated cross checked with previous calc.. Consistency cross check between time and frequency domain. Crab cavity Y-Chambers designs 4 models have been modelled & impedances calculated. Results Scaled up version of current Y-Chamber has increased impedance. Reducing the volume reduces the impedance. Candidate design: Shunt impedance: lowest significant: 3.92 kOhms @ 1.12 GHz Most significant:: 5.25 kOhms @ 1.39 GHz No transverse mode below cut off Contribution from bellows: TE-VSC Design has negligible Impedance Next step: Can impedance working group endorse Y-Chamber design for next step. 37