Progress in Dark Current and Multipacting Modeling in the Analyst Finite Element Package*

1. Progress in Dark Current and Multipacting Modeling in the Analyst Finite Element Package* J. F. DeFord and B. Held Advanced Accelerator Concepts Workshop 2008 Santa Cruz, CA July 29, 2008 * Work supported by the Department of Energy Office of Science SBIR Program (DE-FG02-05ER84373 and DE-FG02-05ER84374)

2. Presentation Topics • Particle tracking on tetrahedral meshes. • Parallel scaling. • Particle emission models. • Multipacting statistics/output data. • Dark current statistics. • Particle-based adaptive mesh refinement. • Ongoing work. Work has greatly benefited from a strong collaboration with I. Gonin, N. Solyak and others in Technical Division at FNAL.

3. What is Analyst??? • Finite-element based support for electromagnetics. • 3D electrostatics, magnetostatics, driven-frequency, and eigenmodes. 2D eigenmodes (RZ and XY). • Particle tracking. • Third-party solvers (ES-PIC, time-domain). • Embedded CAD, meshing, visual/numerical post-processing. • Python-based scripting. • Focus on large problems, parallel processing. • Interface runs on Windows, solvers on Windows/Linux.

4. User interface Embedded “help” Project Workspace Multiple projects & windows Python window

5. Particle tracking on FE meshes • Explicitly track each element (find entrance and exit points). • Use finite-element basis functions instead of interpolated fields. • Use an adaptive time-step. Resonant orbit in spoke cavity (courtesy of I. Gonin, et al., Technical Division, FNAL.

6. Updating equations/process • Use position/momentum at element entrance to determine exit point. • Repeat calculation using exit momentum and compare. • If difference is too large, introduce intermediate node and repeat.

7. Parallel scaling • Particle decomposition: • Distribute particles across processors. • Efficient scaling because particles do not interact. • Domain decomposition (under development): • Distribute mesh across processors (use virtualmachine mechanism). • Potentially poor scaling because particles must be transferred between processors.

8. Parallel job queue/virtual machines • Distributes multiple analyses over cluster nodes based on problem size to make best use of cluster. • Requires batch system be present on distributed memory systems (Sun Grid Engine, PBS, etc.). • For optimization algorithms that can generate concurrent evaluation points, ideal scaling should be attainable. • This capability has been used on a workstation to allow simultaneous use of multiple cores for separate analyses. cpu/core 1 VM 1 Batch system cpu/core 2 cpu/core 3 VM 2 cpu/core 4 VM 2 cpu/core n User interface Batch system Virtual machines Procs./cores

9. Emission models • Fowler-Nordheim field emission: • Secondary emission:

10. Multipacting statistical functions 1A “resonant primary” is a primary resulting in a particle chain that includes at least one particle that survives for n impacts.

11. More multipacting output data • Particle tables. • Per-impact yield vs. location on model surface.

12. Orbit near “equator” of SNS cavity

13. Dark current computations • Similar to multipacting problem only not looking for resonances. • Field emit from surface, track particles until model exit. • Collect statistics on where particles exit, exit energies, etc. • Mark particles so that they can be filtered in various ways, e.g., by which model surface they exited.

14. Field emission in RF cavity RF cavity and mode E-field pattern. Peak field regions. Analytic peak FN emission in peak field region.

15. Field emission (2) Peak surface E-field over 1 RF cycle. Expected FN current density. Field emission region.

16. DC in RF module |E| for pi/2 phase advance per cell. Only particles that exit downstream.

17. Close-up of one cell

18. Output particle spectra Peaks correspond to distinct source regions within structure.

19. Adaptive mesh refinement (AMR) • Idea is to use results from a previous analysis to refine the finite-element mesh in order to reduce errors.

20. AMR: Population metric • Based upon idea that mesh should be refined in regions with relatively large local particle populations. • Metric is given by: where is the total number of particles that traverse the k-th element.

21. AMR: Complexity metric • Based upon an estimate of the complexity of the orbits within an element. • Metric is of the form: where is the total number of particle knots within the k-th element. Track computed within element. Dots are “knots” in track. Particle track from previous element stopped at boundary. Exit location found to begin tracking in next element.

22. Cavity with HOM coupler1 Antenna Antenna housing Second mode resonates at about 810 MHz 1Model of TESLA HOM coupler courtesy of I. Gonin, Technical Division, FNAL.

23. 3 2 Adaptive mesh refinement 1 2 3 1

24. Ongoing work • Adding more user control over primary and secondary models. • More visualization/animation options for particles. • Domain decomposition for tracking runs. • Job management enhancements to support combined field-solve/particle track AMR loop.