HOM Damping Simulation and Measurement of JLab Ampere Class Cavity

1. HOM Damping Simulation and Measurement of JLab Ampere Class Cavity Haipeng Wang also Robert Rimmer and Frank Marhauser Jefferson Lab, Newport News, Virginia 23606, USA

2. MAFIA wakefield calculation for both broad and narrow bands HOM impedance calculation Critical steps to get correct cavity’s impedance through FFT of wake function: WG WG WG WG WG WG • Generate 3D cavity vacuum CAD drawing with waveguide ports facing to Cartesian coordinates. WG WG • Import CAD geometry, mesh volume with uniform steps (5mm) in beam direction. • Define waveguide port positions and mesh in 2D. • Solve 10 lowest eigen modes in each WG port. • Load WG solutions to each port with zero power input. Check any ignored mode. • Set up “1D current” in Gaussian bunch with s=3cm, 0~10s long, 1q charge at a defined off-axis distance. • Set up wake potential monitor in beam direction at a defined path. • Calculate 1311m long wave (~4days, ~1millon meshes) • Take max. 2n wake data set with rest of them zero out. Do the Cosine window tapering. • FFT wake (get |Wzfft| and Gaussian beam. • Normalized impedance with Zam=|Wzfft|/Bam Zph=Wzfftph-Bph. With correct phase wrapping within -90o to 90o, the real part of impedance Zre should be always >0.

3. Broadband impedances contribute to power deposition or BBU below beam pipe cut-off frequency bunch length 3cm Monopole modes excited by on-axis beam bunch monopole + dipole modes excited by off-axis 5cm beam bunch

4. Broadband HOM power calculation for above cut-off Calculation formula: ~8.5 kW Total ~18kW/cavity 2 Amp 5 cell 1.33 nC can be improved by model measurement or high power computing Obtained from ABCI or MAFIA

5. Copper model bench measurement • S21 from beam pipe to beam pipe. • Labview automation. • Ceramic bead-pull on-axis or off-axis. • End groups staggered relatively at 30o or 60o. • 5, 6, 7-cell stack assembly then 5-cell welded. • Data sets with dummy loads or shorts. • Rotatable coupling antennas.

6. Five-peak fitting program to get real peak, frequency and Q • Multi-peak fitting program is try to find real amplitude at each Lorenz resonance frequency, and filter out the contribution from each neighbor peak. Totally five peaks cab be fitted together. • Each resonance peak is fitted with the Lorenz function. • Total amplitude Am2=(Re1+P2*Re2+P3*Re3+…)2+(Im1+P2*Im2+P3*Im3+…+bp*Bg)2 • P2, P3,…is each peak polarity=+1 or -1. bp is background polarity. Bg is total background. • This fitting program can be also used to find real impedance of each HOM from overlapped HOMs’ spectrum like obtained from MAFIA wakefield FFT..

7. First measurement data do not agree simulation well

8. RF dummy load and single cell aluminum model bench measurement

9. E-antenna rotation changes excitation of the HOMs • Antenna rotation relatively 90 degree can suppress one or other polarization of dipole modes, but once the beam pipe uses absorber, and for those above cut-off modes, this advantage disappear quickly • HOM mode IDs is most complication in the HOM impedance measurement.

10. Multiple beam (1d current) excitation of wake in 3D structure One beam Two beams Monopole modes only Dipole modes, polar 1 Quadruple modes, polar 1 • If there is no structure asymmetry about mid-plane and no asymmetric meshing, wave excitation and reflection have to satisfy the enforced boundary condition. A proper mode suppression should be made. • In reality of the squared (MAFIA) and finite number of meshes, the mode contamination of high Q modes always happen. • Excitation more than three-beam is possible. Three beams Dipole modes, polar 2 Quadruple modes, polar 2

11. Multiple beam excitation of wakes in a single-cell high current cavity with one “Y” waveguide group

12. Mode ID can be labeled to the spectrum from the MAFIA simulations without a bead pulling

13. MAFIA multi-beam wakefield simulation, monopole mode excitation only

14. MAFIA multi-beam wakefield simulation, dipole mode excitation only

15. MAFIA multi-beam wakefield simulation, quadruple mode excitation only

16. Summary • Multiple beam excitation technique used in MAFIA time domain wakefield calculation is very powerful simulation tool. It can selectively choose BC and number of beam, position and polarization to suppress unwanted modes. • FFT of MAFIA wake can get both real and amplitude, narrow and broad band cavity’s impedance if the wake function is properly phase unwrapped and normalized. • Mode identity is most important part of HOM measurement, it can be improved by rotation and position of antennas, bead pulling, and 2D (eigen mode) or 3D (time domain) simulation. • After careful mode ID, calibration and bead-pull, Initial data bellow cut-off frequencies on single-cell aluminum model agrees with simulations. • By this measurement, we bunch-marked our simulation method and data used in the prototype design. • R/Q measurement by calibrated bead-pulling is needed to replace MAFIA 2D R/Q for above cut-off modes. • We need re-measure the 5-cell structure after mode ID is clear from the new simulations.