An Introduction to Breakdown Simulations With PIC Codes

1. C. Nieter, S.A. Veitzer, S. Mahalingam, P. Stoltz Tech-X Corporation MTA RF Workshop 2008 Particle-in-Cell (PIC) codes are being used to model RF cavities and the physics important to breakdown under high gradient conditions. This is an introduction to two such codes, with some simulation results Much of this work was funded under the auspices of DOE through the SBIR program contract #DE-FG02-07ER84833 An Introduction to Breakdown Simulations With PIC Codes

2. Tech-X is a Computational Physics Research Company Based in Boulder, CO • Tech-X is employee owned, focused on computational plasma, accelerator, and fusion science, and high-performance computing • Founded in 1994, currently 57 employees, 38 with Ph.D. • Funded largely by the SBIR program (DOE, DOD, NASA) but also by commercial software sales, consulting, SCIDaC and other government grants • http://www.txcorp.com

3. Tech-X Corporation Numerical simulation of breakdown requires accurate simulation codes We are using two Particle-in-Cell (PIC) FDTD codes to model breakdown OOPIC Pro: 2-Dimensional, R-Z geometry, serial VORPAL: 3-Dimensional,Cartesian, massively parallel Both are self-consistent (We solve Poisson’s Eq with particles and EM fields) Physical processes include Self-consistent particle-field interactions Field emission from conducting surface Impact ionization of bulk neutral gas Ion-induced secondary electron production Physical sputtering of neutral gas We numerically measure indicators of cavity breakdown Number of particles as a function of time Evolution of particle densities and particle fluxes Radiated power from impurities (line and continuum) Surface heating from particle bombardment The bulk of new physics modules are implemented in the TxPhysics numerical library and linked to OOPIC Pro and VORPAL

4. Tech-X Corporation OOPIC Pro 2-Dimensional electrostatic and electromagnetic solvers Cartesian and R-Z geometries Simple and intuitive GUI interface Version 2.0 just released Improved performance Parallel solvers (Linux and now Mac OS X) Native Mac OS X build User-defined cross-sections for Monte Carlo Collisions and ionization simulations

5. Tech-X Corporation 2D simulation geometry (Cylindrical) Cavity surface Radius (r) B-field Neutral Cu gas Asperity Normal (Z)

6. Tech-X Corporation Breakdown simulations: OOPIC Pro physical parameters Simulation area 10m x 10 m cylinder Conical surface defect (stair step boundary) 2 m high x 2 m wide Electric Field boundary condition Normal to surface (up to 60 MV/m) Applied Magnetic Field Normal, Parallel, Oblique to surface (up to 3.0 T) Field emitter Fowler-Nordheim,  Background gas pressure 2.3x1026 #/m3 (7000 Torr) Applied RF signal f = 805 MHz

7. Tech-X Corporation Breakdown simulations: OOPIC Pro computational parameters Number of computational cells 50 x 50 (Cylindrical R-Z) Cell spacing 0.2 m Timestep 1x10-14 seconds Particle weighting 1 simulation particle = 1x106 real particles Neutral gas region 30 x 30 cells Solver Electrostatic simulation with multigrid Poisson solver Computation time 6 hours (serial) to simulation 2.6 ns

8. Tech-X Corporation An applied RF field controls the dynamics When the RF field is pointing towards the surface field emission occurs from the defect When the RF field is pointing away from the surface field emission is suppressed Field enhancement Asperity

9. Tech-X Corporation Electrons ionize neutral gas near the surface defect Background Cu neutral gas is ionized by electrons which are field emitted from the surface Electrons stream out of simulation, unless they are trapped by the potential of plasma ions

10. Tech-X Corporation Ionization produces more electrons Ions are accelerated towards the surface Ionization electrons are accelerated away from the surface

11. Tech-X Corporation Number of particles increases as does radiated power Ionization electrons can become trapped by the enhanced potential of the plasma ions, causing further ionization Impurity (plasma) radiation levels increase rapidly Positive feedback continues until breakdown occurs

12. Tech-X Corporation Future directions (current SBIR Phase II) New Physics X-rays from electron/surface impacts (like Integrated Tiger Series model) Coupling radiation back to ion temperature Allow outgoing radiation to couple to plasma (opacity modeling) Repopulation of background gas with sputtered atoms New User Interfaces Translation of OOPIC input files to VORPAL using VpStudio Web UI for visualization of VORPAL simulations (VorpalView or TxView) New Simulations Better understand effects of magnetic field on breakdown Automated optimization in OOPIC and VORPAL Allow user to specify a quantity to be maximized or minimized as a certain model parameter is varied

13. Tech-X Corporation Physics models for breakdown studies are available as an external numerical library TxPhysics contains: secondary electron emission, neutral gas ionization, sputtering, radiation, wall heating, and more For example, electron-induced secondary electron emission is shown above. Both OOPIC Pro and VORPAL use physics modules from TxPhysics. Other codes that use TxPhysics include LSP (ATK Mission Systems), WARP (LBNL), and HYDRA (LLNL). http://txphysics.txcorp.com

14. Tech-X Corporation TxPhysics Web UI brings quick visualization to surface processes http://txphysics.txcorp.com

15. Tech-X Corporation VORPAL enables accurate, detailed numerical simulation of many plasma physics problems • Hybrid electrodynamics, both Particle-in-Cell (PIC) and Fluid models • Fields solved on discrete mesh, 2nd-order accurate • Self-consistent charged particle dynamics • Cut-cell geometries • C++, MPI, Massively parallel (domain decomposition), 1000+ processors

16. Tech-X Corporation VpStudio is a friendly interface for creating VORPAL input files