1. Wakefield/Impedance Considerations for APS and LHC Crab Cavities Haipeng Wang Thomas Jefferson Lab, Newport News Virginia, USA ICFA Beam Dynamics Mini-Workshop on Deflecting/Crabbing Cavity Research and Applications in Accelerators at Institute of Modern Physics, Lanzhou China July 18-20, 2012

2. Outlines of my talk : Review wakefield simulation and impedance techniques developed in recent years 1.Cover both long-rang and short-range wakefield, broadband and narrow band impedance calculations 2.Long-range wakefied is mostly concerned on the SRF cavities for the coupled-bunch instability in the high current storage rings 3.Multi-beam wakefield excitation--for the spatial mode separation 4.Extrapolation of FFT spectrum--for resolved narrow band impedance peaks Simulation and benchmark experience on various simulation codes 1.3D codes available for the wakefield calculation: MAFIA, CST, GdfidL, T3P and VORPAL 2.Some benchmark results and comparison between different codes Simulation results verses beam impedance budgets 1.APS crab cavities with waveguide dampers 2.LHC 4-rod structure with LOM/DFM/HOM1/HOM2 coaxial couplers designed by Graeme Burt/Ben Hall/Daniel Doherty at Lancaster Univ., UK (Daniel’s talk yesterday, preliminary coupler design and eigen simulation result only)

3. Multiple beam wake excitation scheme was first introduced and demonstrated by MAFIA T3 simulations at ERL 2007 workshop in UK Multi-co-moving beams including image charge with different signs must satisfy the E/M symmetry boundary polarization (if any) with the polarized source field generated from the beams’ self fields, so the field excitation is purely monopole, dipole or quadruple modes as designed. The sum of total charges including the image charges is “q” in order to account for a proper impedance normalization When structure have no symmetric plane, the image charge beam has to be in the place Monopole-one beam Dipoles-one to two beams Quadruples-two to four beams Wakefield monitor (integration line) can be placed behind any lead source beam Asymmetric wake potential recorded by each field monitor will be solely due to the asymmetric structure or meshes, mode spatial mixing or contamination. ERL or colliding beams scheme is possible if working with code developers

4. JLab half scale High Current cavity MAFIA T3 simulation using multi-beam excitation technique

5. Benchmark between MAFIA T3 (wakefield/impedance calculation), E3 (eigen solver) and bench measurement on JLab 5-cell, 1.5GHz High Current cavity)

6. D. Li, R. Rimmer, “Beam Impedance Calculations and Analysis of Higher Order Modes (HOMs) Damped RF Cavities Using MAFIA in Time Domain“, Proceedings of PAC 2001. Impedance extrapolation from half to full wake length to get a resolved impedance peak ds Natural method:  2 =2  1,  2 >>  n Works for both narrow and broad band Z(  ) here

7. MathCAD program developed to post-process wakefield/impedance Important developments and benchmarks: Mityanina: original MathCAD program for MAFIA P3. real part of impedance being negative value has no physics meaning Wang: Proper phase wrapping introduced to get the MAFIA impedance post processing correctly. Benchmark Gdifidl, CST. Calculate HOM power from the WG and coax couplers Marhauser: Track change. Impedance normalization. Window function to cos^2. Implication of Derun Li’s method.

8. ANL’s Baseline Crab Cavity Unit Design with LOM and HOM Waveguide Dampers

11. Input Coupler LOM Damper HOM Dampers Baseline (Mark-I) Alternate (Mark-II) Two design options on the LOM damping, Mark-II design was the final selection

12. Longitudinal Monopole Impedances between Baseline and Alternate Designs

13. SPX Crab Cavity Mark-II Longitudinal Impedance Stability Threshold Monopole Impedance Monopole Stability Threshold

14. 14 SPX Crab Cavity Mark-II Transverse Impedance Vertical dipole Dipole Stability Threshold Vertical Dipole Impedance Stability Threshold

15. 15 SPX Crab Cavity Transverse Impedance Horizontal dipole Dipole Stability Threshold Stability Threshold Horizontal Dipole Impedance

16. Gdfidl verse MAFIA BenchmarkGdfidlMAFIA APS 1-cell crab modelsame drive bunch charge sigmaz=ssigma=2cm charge=1.0*@clight/(sigm az*(2*@pi)**0.5) current=1.0*@c0/(ssigma* sqrt(2*@pi)) Impedance normalization Wake length156.7m1567m Normalization factor when using MathCAD for FFT 2 indexn =# data sample machine“srfnode2”, 4 thread ~3GHz CPU “Mass”, HP workstation ~2GHz CPU softwarecan be parallelsingle node

19. Waveguide Damping Power Rate and Spectra Calculation

20. Coaxial Coupler Design on 4-Rod LHC Crab Cavity by G. Burt, B. Hall and D. Doherty Lancaster Univ. UK Port 1: HOM1 Port 2: LOM Port 3: HOM2 Port 4: DMC 1 (should be short by design) Port 5: DMC 2 Port 6: BP1 Port 7: BP2

22. Port 1: HOM1 Port 2: LOM Port 3: HOM2 Port 4: DMC 1 Port 5: DMC 2 Port 6: BP1 Port 7: BP2 PortLOMHOM1HOM2DMC1DMC2BP1BP2 kW11311.626.64.2 N.A.0.8434.8 ?5.7 ? LOM/HOM damping power with LHC beam current of 581mA, preliminary only Voltage monitor in recent release CST has no phase information anymore which is important for the power calculation. With amplitude only voltage signal, the power rate calculation could be over estimated. The voltage signal also has been re-normalized. LOM notch is not tuned yet Beam pipes are too short for the calculation at this frequency since the port is assumed to be without cutoff frequency. Corrections have not been done yet

26. Summary: Long-range wakefield simulation using multi-beam excitation and Impedance extrapolation techniques have been reviewed. Wakefield simulation, Impedance normalization, port boundary condition and benchmark on different simulation codes are important parts of impedance calculation. Frequent communication with code developer is also essential part of code benchmarking SPX crab cavity with on-cell damper design have been satisfied APS impedance budget and cryogenic cooling design requirement The first-cut wakefield simulation on the Lancaster Univ.’s 4-rod crab cavity (with preliminary coupler design) indicates being satisfied to the LHC 1 Amp’s beam current operation by the impedance budget Power handing and cooling on the coaxial couplers on all LHC crab cavities will be very challenging The HOM damping design is very important part of LHC crab cavity. It should be one of critical requirements in the down selection process.