An Introduction to Breakdown
Simulations With PIC Codes
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
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
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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Radius (r)
2D simulation geometry (Cylindrical)
Cavity surface
B-field
Neutral Cu gas
Asperity
Normal (Z)
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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
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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
QuickTime™ and a
YUV420 codec decompressor
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
QuickTime™ and a
YUV420 codec decompressor
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
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
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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, 2ndorder 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
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