1. Simulation Technology & Applied Research, Inc. 11520 N. Port Washington Rd., Suite 201, Mequon, WI 53092 P: 262.240.0291 info@staarinc.com www.staarinc.com 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. Simulation Technology & Applied Research, Inc.www.staarinc.com 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. Simulation Technology & Applied Research, Inc.www.staarinc.com 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. Simulation Technology & Applied Research, Inc.www.staarinc.com User interface Embedded “help” Project Workspace Python window Multiple projects & windows

5. Simulation Technology & Applied Research, Inc.www.staarinc.com 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. Simulation Technology & Applied Research, Inc.www.staarinc.com 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. Simulation Technology & Applied Research, Inc.www.staarinc.com Parallel scaling Particle decomposition: – Distribute particles across processors. – Efficient scaling because particles do not interact. Domain decomposition (under development): – Distribute mesh across processors (use virtual machine mechanism). – Potentially poor scaling because particles must be transferred between processors.

8. Simulation Technology & Applied Research, Inc.www.staarinc.com 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 cpu/core 2 cpu/core 3 cpu/core n cpu/core 4 VM 1 VM 2 Batch system VM 2 Virtual machinesBatch systemUser interfaceProcs./cores

9. Simulation Technology & Applied Research, Inc.www.staarinc.com Emission models Fowler-Nordheim field emission: Secondary emission:

10. Simulation Technology & Applied Research, Inc.www.staarinc.com Multipacting statistical functions Function nameSymbolDefinition CounterCF(n)Total number of resonant primaries 1. Normalized counterNCF(n) Enhanced counterEF(n) Normalized enhanced counterNEF(n) YieldYF(n) Growth factorR(n) DistanceD(n) 1 A “resonant primary” is a primary resulting in a particle chain that includes at least one particle that survives for n impacts.

11. Simulation Technology & Applied Research, Inc.www.staarinc.com More multipacting output data Particle tables. Per-impact yield vs. location on model surface.

12. Simulation Technology & Applied Research, Inc.www.staarinc.com Orbit near “equator” of SNS cavity

13. Simulation Technology & Applied Research, Inc.www.staarinc.com 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. Simulation Technology & Applied Research, Inc.www.staarinc.com Field emission in RF cavity RF cavity and mode E-field pattern. Analytic peak FN emission in peak field region. Peak field regions.

15. Simulation Technology & Applied Research, Inc.www.staarinc.com Field emission (2) Field emission region. Peak surface E-field over 1 RF cycle. Expected FN current density.

16. Simulation Technology & Applied Research, Inc.www.staarinc.com DC in RF module |E| for pi/2 phase advance per cell. Only particles that exit downstream.

17. Simulation Technology & Applied Research, Inc.www.staarinc.com Close-up of one cell

18. Simulation Technology & Applied Research, Inc.www.staarinc.com Output particle spectra Peaks correspond to distinct source regions within structure.

19. Simulation Technology & Applied Research, Inc.www.staarinc.com 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. Simulation Technology & Applied Research, Inc.www.staarinc.com 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. Simulation Technology & Applied Research, Inc.www.staarinc.com 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. Particle track from previous element stopped at boundary. Track computed within element. Dots are “knots” in track. Exit location found to begin tracking in next element.

22. Simulation Technology & Applied Research, Inc.www.staarinc.com Antenna housing Antenna Second mode resonates at about 810 MHz Cavity with HOM coupler 1 1 Model of TESLA HOM coupler courtesy of I. Gonin, Technical Division, FNAL.

23. Simulation Technology & Applied Research, Inc.www.staarinc.com Adaptive mesh refinement 3 2 1 1 2 3 # elements# tracks (M)Time (sec.) 33K7.9781/1110 89K31.3499/5428 262K1092.26K/27.0K 853K33916.6K/112K

24. Simulation Technology & Applied Research, Inc.www.staarinc.com 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.