1. Update on LHC 800MHz Crab Cavity Conceptual Design Liling Xiao, Zenghai Li Advanced Computations Department, SLAC Presented at LARP-CM12, April 9, 2009

2. L. Xiao, Z. Li, CM122 Baseline Design (CM11) Cell Shape Optimization : (R/Q)_T, Bpeak<100mT for TM110 LOM/SOM/HOM Coupler Design: Qext<200 for LOM/SOM Alternative Cavity Design Multipacting Study Summary Outline

3. L. Xiao, Z. Li, CM123 Baseline Design (CM11) Cell Shape Optimization Cell_l = 187.5 mm, R_disk = 70mm VT > 2.5MV, Maximum kick gradient limited by Bpeak Optimize disk parameters for optimal Epeak and Bpeak TM110-pi Squash or racetrack Squash ratio:0.8

4. L. Xiao, Z. Li, CM124 Ep Bp TM110-pi mode E-field B-field Frequency800MHz (R/Q)_T117ohm/cavity Deflecting Voltage V T 2.5MV Deflecting Gradient Ekick6.67MV/m Epeak25MV/m Bpeak83mT Mode separation (Opt.-SOM)89MHz TESLA TDR cavity peak fields for comparison (Eacc: 25-30MV/m): Ep=50-60MV/m, Bp=107-128mT Crab Cavity RF Parameters

5. L. Xiao, Z. Li, CM125 LOM/SOM  Strongly damps unwanted modes in a compact structure because no cutoff for TEM mode in the coax  Node at the electric field rejects operating mode in the vertical plane LOM/SOM Coax-to-Coax Design d

6. L. Xiao, Z. Li, CM126 There are two additional LOM modes due to the coupling of the cavity modes to the coaxial beampipe TEM modes. Coupler can be optimized to achieve Qext less than 100 for LOM/SOM with a smaller gap. Gap=10mm Q ext vs. Coax Position

7. L. Xiao, Z. Li, CM127  Damp the dipole modes at the horizontal plane and reject the operating TM110 mode at 800MHz.  A two-stub antenna instead of the coupling loop is proposed. LOM Opt. HOM Coupler Design

8. L. Xiao, Z. Li, CM128 HOM FPC LOM/SOM There is significant coupling of input power to the LOM/SOM couplers in this baseline design Drawback in Baseline Design

9. L. Xiao, Z. Li, CM129 Alternative Design  Input coupler is between of the two cells to avoid the cross coupling  Coax TM110-pi coupler rejects operating mode using field symmetry.  LOM/SOM couplers reject operating mode using electric field node.  HOM coupler rejects operating mode using filter. LOM/SOM WG: TM110-0 (TE10:Fc=750MHz) Coax: TM110-pi LOM/SOM HOM

10. L. Xiao, Z. Li, CM1210 LOM/SOM couplers reject operating mode using electric field node. Field symmetry is very important. The center conductors of LOM/SOM couplers will be slightly bent so that the rotating flange can adjust the tips of the center conductors to lie exactly along the E-field node of the operating mode field. Rejection of Operating Mode shift

11. L. Xiao, Z. Li, CM1211 TM110-π coupler rejects operating mode using field symmetry. Coax coupler misalignment00.625mm1.25mm2.5mm F (MHz) for TM110-o mode799.982 Qext@coax>e111.4e93.5e88.2e7 The misalignment of π-mode coupler should be less than 1mm to avoid the cross coupling between the FPC and pi-mode coupler. TM110-0: (R/Q)_T=100Ω/cavityTM110-π: (R/Q)_T=0.3Ω/cavity Rejection of Operating Mode

12. L. Xiao, Z. Li, CM1212 LOM modes F (MHz)587.056587.218608.210608.288 R/Q(Ώ/cavity)54.141.864.571.4 Qext4950129 Vertical Dipole modes F (MHz)888.130889.123899.865906.237985.622996.683 (R/Q)_T(Ώ/cavity)35.31.20.930.916.42.3 Qext414644 5967 Damping requirements for the LOM and SOM modes: Qext < 200. Monopole & Vertical Dipole Modes

13. L. Xiao, Z. Li, CM1213 Horizontal Dipole modes: TM110-o mode is the operating mode F (MHz)799.682 (pi mode) 799.985 (0-mode) 897.095898.974982.510996.130 (R/Q)_T(Ώ/cavity)1.199.50.081.011.24.1 Qext3.6e4>e9143013959321359 Horizontal Dipole Modes

14. L. Xiao, Z. Li, CM1214 2mm E-BC Track3P - Multipacting Studies TM110-0 mode VT=0.1~1.25MV Resonant particles with impact energy between 50~2000eV MP in the Cell - z x yeV Avoid E: 200ev~600ev

15. L. Xiao, Z. Li, CM1215 VT=2.3MV 2-points MP, 0.5,1, 1.5 order Multipacting at the Disk In the disk area at the short axis of the KEKB 509MHz crab cavity, MP were found but it can be processed through.

16. L. Xiao, Z. Li, CM1216 r R_bp=70mm r=13.75mm, Bs=124mT Smaller disk radius can suppress MP but is at risk of higher Bpeak. Larger disk radius is hard to push the MP barrier beyond VT=2.5MV. MP vs. Disk Profile

17. L. Xiao, Z. Li, CM1217 Radius=2mm Radius=4mm Adding grooves along the short axis without changing the operating mode’s RF parameters can suppress MP activities. MP vs Local Geometry E-field B-field

18. L. Xiao, Z. Li, CM1218 There is no MP in the coaxial beampipe. With fully rounded tip of LOM center conductor, MP can be suppressed. MP in LOM Coupler & Coax BP

19. L. Xiao, Z. Li, CM1219 There are MP events in the gap of HOM notch filter. z eV x y MP in HOM Coupler VT

20. L. Xiao, Z. Li, CM1220 There is no MP in FPC and π mode couplers below Pin=100KW. MP in Input & π Mode Couplers Assuming: FPC coupling Qext~1e6 VT=2.5MV, (R/Q)_T=100Ω/cavity Pin=63KW

21. L. Xiao, Z. Li, CM1221 Summary Baseline 800MHz crab cavity design has been proposed. With optimum cell shape, Bpeak=83mT @ VT=2.5MV (Critical Bpeak~100mT) Using coax-to-coax couplers, Qext @ LOM/SOM < 150. (Requirement Qext<200) Strong MP in disk area at the short axis of normal cavity shape. Ad ding a small groove along the cavity surface at the short axis can suppress MP No MP barriers found in LOM/SOM/FPC couplers and coaxial beampipe. If needed, further optimization can be done to fully suppress MP in HOM coupler. Cavity model put on wiki page for cross check and cryostat study. https://twiki.cern.ch/twiki/bin/view/Main/CrabCavityRF Search for eigenmodes below 2GHz in progress. Further simulations planned to analyze RF/thermal/mechanical effects. Thanks to members of LHC Crab Cavity Collaboration for valuable discussions.