An Introduction to Breakdown Simulations With PIC Codes

C. Nieter, S.A. Veitzer, S. Mahalingam, P. StoltzTech-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

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

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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

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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

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2D simulation geometry (Cylindrical)R

adiu

s (r

)

Normal (Z)

Cavity surface

B-field

Neutral Cu gas

Asperity

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Breakdown simulations: OOPIC Pro physical parameters• Simulation area

– 10m 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

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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

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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

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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

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are needed to see this picture.

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Ionization produces more electrons

• Ions are accelerated towards the surface• Ionization electrons are accelerated away from the

surface

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are needed to see this picture.

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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

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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

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Physics models for breakdown studies are available as an external numerical library

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

TxPhysics contains: secondary electron emission, neutral gas ionization, sputtering, radiation, wall heating, and more

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TxPhysics Web UI brings quick visualization to surface processes

http://txphysics.txcorp.com

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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

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VpStudio is a friendly interface for creating VORPAL input files