1. Crabbing Cavity Multipacting Simulation with VORPAL C.D. Zhou, D. Smithe, C. Nieter, P. Stoltz Beam Dynamics Mini-Workshop on Deflecting/Crabbing Cavity Research and Applications in Accelerators IMP, Lanzhou China

2. Use VORPAL as a basis for a new computational multipacting tool VORPAL is a mature electromagnetic, particle-in-cell simulation framework Originally a laser-plasma simulation code Electromagnetics solved in time domain (all modes self- consistent) Particle dynamics solved using Particle-in-Cell algorithm (fully self-consistent) Full self-consistency means VORPAL can estimate saturation and multi-mode effects

3. Finite-difference leapfrog-Yee algorithm, coupled with the Dey-Mittra curved boundary algorithm, enables cavity simulations with VORPAL Five Deflecting Modes (GHz): f0f0 f1f1 f2f2 f3f3 f4f4 3902.8103910.4043939.3364001.3424106.164 Convergence of frequency with grid resolution

4. Normal modes of an electromagnetic system are obtained easily The filter diagonalization method* is used to extract eigenmodes. It provides complex frequency (ω and Q), and full field profiles for each mode, and can correlate amplitude and phase of a mode to the excitation source for use in computing the wake potential. Handles degeneracies with some extra steps. Analysis tool is integrated in VorpalComposer. No further post-processing is needed *G. R. Werner and J. R. Cary, “Extracting degenerate modes and frequencies from time-domain simulations with filter- diagonalization,” J. Comp. Phys. 227, 5200 (2008).

5. Recent simulation on dual GPUs achieved update speed of 250 Mcells/sec GPU Dual Nvidia Tesla 2070 (Fermi): 250Mcells/sec (0.4mm resolution run out to ~100 periods in about 1/2 hour!) CPU 2.1 GHz Intel Core 2: 1.1 Mcells/sec

6. VORPAL can model all the processes involved in multipacting ● FDTD electromagnetics w/cutcell boundaries ● Particle-in-Cell (PIC) for the electron motion ● Variety of algorithms for calculating the secondary electron yield

7. VORPAL provides the most standard functional parameterization of SEY User defined SEY yield function Function parameters can be varied between runs Time dependence can be introduced Common parameterization:

8. Furman-Pivi emission model is the most complete but is available for few materials Phenomenological model Three types of secondaries True secondaries Diffuse secondaries Elastic secondaries Model gives emission angle and energy for secondaries M.A. Furman and M.T.F. Pivi, “Probabilistic model for the simulation of secondary electron emission”, Phys. Rev. ST Accel. Beams 5, 124404 (2002).

9. VORPAL provides maximal flexibility by importing user-defined SEY ● SEY data stored in a separate file ● Allows SEY data to be imported from a variety of sources ● Custom models ● Experimental data ● SEY interpolated to the impact energy ● Allows use of proprietary data 8 0 10 0 12 0.494115 14 0.755894 16 0.967458 18 1.15104 20 1.31573 22 1.46641 24 1.60604 26 1.73662 28 1.85958 30 1.97596 E (ev) SEY Sample SEY data file

10. Field scaled particles modify the Lorentz force for each particle Standard Lorentz force equation Modified Lorentz force equation with scaling parameter Field scale parameter, α fs, is contained in the particle data structure Field scaling allows running multiple power levels in the same simulation. Quick and detailed analysis of multipacting is possible.

11. Gyro-radius scales inversely with scaling parameter demonstrating proper scaling for magnetic field Distance traveled scales linearly with the scaling parameter demonstrating proper scaling for electric field Field scaled particles now allow particles to experience different fields in the same simulation

12. Simulation of multipacting in coaxial waveguide demonstrates these features Coaxial waveguide is common and well understood Analytical models exist Availability of numerical and experimental data Widely used in many application areas Despite relative simplicity the coaxial geometry tests complex features Cut-Cell electromagnetics Electron emission from curved surface Particle dynamics near curved surface Traveling wave in coaxial waveguide

13. Particle trajectories and resonances

14. Now one can quickly and easily identify multipacting bands in a single simulation Vorpal Results Somersalo Results Somersalo E, Yla-Oijala P, Proch D, Sarvas J. Computational Methods for Analyzing Electron Multipacting in RF Structures. Particle Accelerators. 1998;59:107. Vorpal results from single simulation on 16 processors taking approximately 4 hours of wall time

15. VORPAL simulations automatically capture single-sided, double-sided and hybrid resonances First order Second order Third order Fourth order Time of each impact. Slope of line corresponds to multipacting order.

16. Hard/Soft barriers from impact energy Solid lines are the zero crossings for the SEY yield and dashed line is the peak. Energies near the SEY peak will be harder to process away. Impact energies for 2nd resonanceImpact energies for 3rd resonance VORPAL allows you to see the impact energies to help understand if the barriers are hard or soft.

17. Compact crab cavity designs leave some uncertainly in the various operating parameters of the structure and the potential for disruptive multipacting. We use the VORPAL simulation framework to characterize a four rod compact cavity design being developed jointly by Lancaster University and Jefferson National Laboratory. Determine the frequencies of the LOM and HOM modes of interest for the structure and the spatial structure of these modes. Initial simulations to measure the crabbing of the beam and simulations to look for potential areas of multipacting have been done. Characterization of Four Rod Crab Cavity Design via VORPAL Simulations

18. Four rod cavity structure plus HOM, LOM and power couplers imported from CAD file

19. A prototype four-rod compact crab cavity drawn natively in VORPAL using the new geometry macros

20. Operating and HOM dipole modes are rung between 300-3000 MHz Freq (GHz) 0.5 1.0 1.5 2.0 2.5 3.

21. Mode reconstruction shows transverse B fields for the dipole modes 400 MHz890 MHz1050 MHz 1400 MHz1700 MHz 2000 MHz

22. Freq (GHz) 0.5 1.0 1.5 2.0 2.5 3. Accelerating monopole modes are rung between 300-3000 MHz

23. Monopole frequencies benchmarked against CST VORPAL (MHz) CST (MHz) % difference 370.0375.21.4 395.0400.01.3 886.0892.90.8 960.0971.11.1 1058.01071.01.2 1150.01159.20.8 VORPAL (MHz) CST (MHz) % difference 1429.01439.90.8 1530.01537.70.5 1550.01557.60.5 1675.01697.61.3 1720.01732.10.7 1894.01908.80.8

24. Operating mode was excited with the full cavity including all the coupler structures Electric field in beam axis direction at two different phases in the presence of the input and HOM couplers.

25. Hot-test confirms the transverse cavity shunt impedance R/Q (trans) [400 MHz] 802 Ohms 798.2 Ohms G. Burt, et al.VORPAL(2.54MV) Z (m) Y (m) Z (m) Bx Ey

26. Hot-test shows the crabbing by the operating mode Phase space and velocity versus beam position before (blue) and after (green) beam moves through the cavity Py vs PxPy vs Z (beam fram)

27. Crabbing varies linearly with the peak cavity voltage

28. Simulation of multipacting in the capacitive gap Electrons seeded in the gap (left image) between the fingers of the cavity structure get accelerated out of the gap before multipacting is established (right image). Initial position of the seed electrons Electron positions towards the end of one RF cycle

29. Simulation of multipacting near the beam pipe. Electrons seeded at the junction (left image) of the beam pipe and cavity can produce a multipacting population (right image). Initial position of the seed electrons Electron positions towards the end of many RF cycles

30. Simulation of multipacting in the power coupler structure Electrons seeded in the power coupler structure (left image) can produce a multipacting population (right image). Initial position of the seed electrons Electron positions towards the end of many RF cycles

31. Charge density of electrons towards the end of many RF cycles in the power coupler structure The left and right images are at different points in a RF cycle when the electrons are at the inner and outer radii of the coax

32. Growth in the electron population during multipacting Multipacting may be an issue in these locations Electron population in the beam pipe Electron population in the power coupler

33. VORPAL features for multipacting simulations coaxial multipacting Four rod crab cavity study 1) Cavity shape specification 2) Cold-test of cavity 3) Cold-test of couplers/dampers 4) Hot-test with beam dynamics 5) Multipacting Summary

35. Crab cavities are being considered for luminosity upgrades at a variety of accelerator facilities across the would. Due to space constraints many of the crab cavity designs under consideration are compact designs whose geometries differ from the tradition elliptical cavity shapes often used for superconducting radio frequency cavities. These novel shapes leave some uncertainly in the various operating parameters of the structure and the potential for disruptive multipacting. We use the VORPAL simulation framework to characterize a four rod compact cavity design being developed jointly by Lancaster University and Jefferson National Laboratory. We determine the frequencies of the LOM and HOM modes of interest for the structure and the spatial structure of these modes. Initial simulations to measure the crabbing of the beam and simulations to look for potential areas of multipacting have been done. Characterization of Four Rod Crab Cavity Design through Numerical Simulations

36. Field levels also shows agreement with previous results

37. Field scaled particles now allow particles to experience different fields in the same simulation The range and spacings of the field scale parameter can be specified. fieldScaleEndPoints = [100.0 1000.0] fieldScaleIncrement = 3.0 Alternatively specific values for the field scale parameter can be given. Allows for focused search around suspected resonances fieldScaleValues = [100.0 200.0 500.0 1000.0]

38. Additional work: Simulations of Multipacting in RF Filter Structure

39. Multipacting simulations of RF filter structure

40. VORPAL correctly models the coupling between the two waveguides

41. Once resonances are identified Monte-Carlo emission algorithms can be applied to study saturation

42. Full Monte-Carlo simulation shows multipacting population spreading out in coax The coaxial waveguide geometry and the initial location of the seed electrons

43. We observe multipacting trajectories

44. Trajectories can be a hybrid of single and double sided multipacting Solid lines are the inner and outer coaxial radii

45. 1) Cavity shape specification 2) Cold-test of cavity 3) Cold-test of couplers/dampers 4) Hot-test with beam dynamics 5) Multipacting Four Rod Compact Cavity Studied with VORPAL

46. The amplitude of the x component of the magnetic field as a function of z, B x (z) R/Q (trans) [400 MHz] 802 Ohms 798.2 Ohms G. Burt, et al. VORPAL(2.54MV) Z (m) Y (m)

47. The amplitude of the y component of the electric field, Ey(z) Z (m) Y (m) R/Q (trans) [400 MHz] 802 Ohms 798.2 Ohms G. Burt, et al. VORPAL(2.54MV)