Lsp Simulations of RF and BeamDriven Breakdown in Hydrogen

1
Lsp Simulations of RF and Beam-Driven Breakdown
in Hydrogen

• D. V. Rose, C. Thoma, D. R. Welch, and R. E.
  Clark
• Voss Scientific, LLC
• Albuquerque, New Mexico 87108

Low Emittance Muon Collider Workshop,
FermiLabApril 21-25, 2008
Work supported by Muons, Inc. (with a special
thank you to Rolland Johnson)
2
Outline

• Lsp simulation code
• Particle-in-cell model description
• MCC model
• Computational representations of the H2 breakdown
  experiment
• 0D model results for H2
• Comparison with RF breakdown experiment
• Addition of SF6
• Impact ionization of gas due to H beam
• Addition of SF6
• 1D model
• Sample RF breakdown calculation
• Sample beam-driven and RF breakdown calculation
• Discussion
• Additional physics (1D electrode emission models,
  realistic beam emittance, etc)
• Extension to 2D models (computational
  constraints, scaling)
• Summary

3
Lsp is a general purpose particle-in-cell (PIC)
code

• A number of electromagnetic (explicit and
  implicit), electrostatic, and magnetostatic field
  solvers are implemented
• Kinetic and fluid particle descriptions are
  available
• 1, 2, and 3 physical dimensions Cartesian,
  cylindrical, and spherical coordinate systems
• Lsp has been used successfully for a number of
  accelerator and pulsed power applications
• LTD drivers Sandia National Labs (SNL) LTDR,
  6-MV facility
• Heavy ion accelerators LBNL NDCX I II
• IVA accelerators SNL RITS-3, RITS-6, AWE Hydros,
  Darht
• and plasma physics applications
• Ion beam sources
• Laser-plasma, laser-material interactions
• Electron beam diodes for x-ray radiography and
  pumping excimer lasers
• Charged particle beam propagation
• EMP applications
• Magnetic confinement of plasmas
• Wave-wave and wave-particle interactions,
  instabilities
• Moderately and strongly-coupled plasmas

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PIC code model

• Charged and neutral plasma species are treated
  macro-particles, each representing 10x real
  particles. (x can be greater than 10!)
• EM fields are determined from Maxwells
  equations, solved on a finite grid, with source
  terms provided by particle charge densities
  and/or currents mapped onto the grid.
• Particle motion governed by fields interpolated
  from grid to particle positions (typically
  second-order accurate)

See C. Birdsall and A. Langdon, Plasma Physics
via Computer Simulation and R. Hockney and J.
Eastwood, Computer Simulation Using Particles
5
Physical Model the Test Cell (TC)
B0
400 MeV H-
2.5 cm
5 cm
3 cm
11.4 cm
RF Power Feed
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0D, 1D, and 2D simulation models
Idealized region between electrodes, independent
ofspatial gradients and physicalboundaries, but
cantreat transient effects (RF field,presence
of a beam)
0D
2.5 cm
(cheap)
0D
Idealized region spanning space between
electrodes, spatial (1D)and temporal gradients
and physical boundaries are added.(RF field,
beam injection throughelectrode)
1D
(modest sizecalculation)
1D
Axi-symmetric approximation(?/ ?q 0), radial
gradients are added, RF power can be feed in
via a port.
2D
2D
(call in sick)
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0D Lsp simulations of RF breakdown in hydrogen

• Lsp model (particle-in-cell Monte Carlo collision
  model or PIC-MCC) previously benchmarked for RF
  breakdown in helium C. Thoma, et al. IEEE Trans.
  Plasma Sci. 34, 910 (2006).
• Here, we carry out similar calculations in
  hydrogen, for direct comparison to experiments
  P. Hanlet, et al., EPAC, 2006 M. BastaniNejad,
  et al., PAC 2007.
• PIC-MCC model uses cross-section data compiled
  from Boltzmann code calculations and experimental
  data D. V. Rose, et al., ICOPS 2007, C. Thoma,
  et al., Voss Sci. Report VSL-0621 (2006).
• Here, the model is compared with experimental
  data for gas pressures less than the electrode
  breakdown limits.

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0D Lsp calculations in 805 MHz RF field indicate
no breakdown at 10 MV/m (blue dot), and breakdown
for fields at 25 and 50 MV/m (red dots),
consistent with measurements.
P. Hanlet, et al., EPAC, 2006
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0D simulations of RF breakdown are in agreement
with experiments in H2 at 0.002 g/cm3
Seed plasma population has a density of 1010
cm-3, a very small fraction of the initial
neutral gas density (6x1020 cm-3). The 25 MV/m
simulation shows a very slow growth in
electron density (red curve) and the 50 MV
simulation (blue curve) shows an extremely
rapid breakdown of the gas.
At 25 MV/m, breakdown is initially slow but
finite (borderline Paschen level).
50 MV/m is well above Paschen level.
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Addition of low levels of SF6

• SF6 is a electro-negative gas and the electron
  attachment channel provides a possible mechanism
  to reduce the electron density, potentially
  raising the Paschen curve limit (increasing the
  breakdown strength of the H2).
• Here, we explore 0D calculations of an H2/SF6
  mixture (ratio of H2 to SF6 densities 10-4).
• To the 0D simulations we add three species,
  neutral SF6, SF6-, and SF6.
• The attachment and ionization cross sections for
  SF6 are composed of experimental and theoretical
  model data D. V. Rose, et al., ICOPS 2007, C.
  Thoma, et al., Voss Sci. Report VSL-0621 (2006).

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0D Calculations with SF6 dopant show rapid
reduction in (seed) electron density
For this small level of SF6, electron density
prevented from increasing due to attachment of
electrons to SF6.
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Add streaming proton beam

• Based on Rols email (3-27-08), the planned
  experiment would use 400 MeV proton bunches in an
  805 MHz bucket
• The proton speed incident on the gas cell b
  0.713
• The bunch length is roughly dbct/2 (I assume
  a worst-case short bunch of one-half of the sine
  wave) d13.3 cm

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Estimate proton energy inside gas cell
I used the SRIM dE/dx stopping power tables and
fit simple functions for protonstopping in
Stainless Steel (vacuum vessel wall material) and
Tungsten (electrode material)
I assume 1D material layers composed of 5.1 cm of
stainless and 2.5 cm of tungsten.
A simple calculation shows that the average
proton energy entering the gas isroughly 209 MeV
(b0.58).
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Beam-impact ionization cross-section estimate

• Impact ionization cross-section for protons on
  hydrogen gas gives s4.5x10-23 m2 for 209 MeV
  protons.
• Note I ignore additional energy loss of the
  proton beam in the gas as it traverses the AK gap.

(for Eb gt 5 MeV)
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Proton beam density and impact ionization rate

• I assume a cylindrical beam bunch, 13.3 cm
  long, 1-cm in radius, with 1010 protons the
  density is then nbeam2.4x108 cm-3.
• For beam impact ionization only, the electron
  density in the gas evolves as

(I assume ngas 6x1020 cm-3 as used in the 0D
simulations already presented.)
So, in 1 ns, you should expect to generate 1012
cm-3 electron density due tobeam impact
ionization.
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Adding proton impact ionization to the 0D model

• The mean-free path for impact ionization is
  l1/(ngass)4x10-3 cm (for the parameters I used
  on the previous slide), which is much smaller
  than the AK gap.
• Optionally, we can temporally switch on and off
  the impact ionization algorithm to simulate the
  ion bunches entering and leaving the gas cell.
  (not used here)
• Adding a more detailed estimate of the ion bunch
  energy distribution and emittance would be a
  useful refinement of the 0D calculations.

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Impact ionization of H2 gas by the proton beam
rapidly drives the breakdown, as expected
10 MV/m case at 325 psia belowthe Paschen limit
25 MV/m case at 325 psia atthe Paschen limit
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0D calculations including proton beam impact
ionization indicate that SF6 reduces electron
density growth rate slightly
Comparison of electron densitieswith and without
SF6.
Electron and negative ion SF6 densities.
Note I do not include beam impact ionization of
any SF6 species.
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1D simulation model RF fields and proton impact
ionization
We inject 3 protonbunches into the 1D
simulation region through one of
theelectrodes. The electron densityincreases
significantlydue to proton impactionization of
the H2.
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Aside Our group members have done extensive
modeling of intense ion beam propagation
experiments and theoretical analysis

• 1 MeV proton beam propagation in 1-10 Torr gases
  (helium, air, etc., Gamble II generator, Naval
  Research Laboratory)
• P. F. Ottinger, et al., Nucl. Instrum. Meth.
  Phys. Res. A 464, 321 (2001).
• P. F. Ottinger, et al., Phys. Plasmas 7, 346
  (2000)
• F. C. Young, et al., Phys. Plasmas 1, 1700
  (1994).
• F. C. Young, et al., Phys. Rev. Lett. 70, 2573
  (1993).
• J. M. Neri, et al., Phys. Fluids B 5, 176 (1993).
• B. V. Oliver, et al., Phys. Plasmas 6, 582
  (1999).
• Heavy ion beam propagation in lt1 Torr gases
• P. K. Roy, et al., Nucl. Instrum. Meth. Phys.
  Res. A 544, 225 (2005).
• S. A. MacLaren, et al., Phys. Plasmas 9, 1712
  (2002).
• D. V. Rose, et al., Nucl. Instrum. Meth. Phys.
  Res. A 464, 299 (2001).
• D. R. Welch, et al., Phys. Plasmas 9, 2344
  (2002).
• D. V. Rose, et al., Phys. Plasmas 6, 4094 (1999).
• C. L. Olson, et al., Il Nuovo Cimento 106A, 1705
  (1993).
• B. V. Oliver, et al., Phys. Plasmas 3, 3267
  (1996).
• GeV proton beam propagation in the atmosphere
• D. V. Rose, et al., Phys. Rev. ST-AB 9, 044403
  (2006).
• D. V. Rose, et al., Phys. Plasmas 9, 1053
  (2002).
• Laser-matter interaction and generation of ion
  beams

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Status Summary

• 0D modeling of RF breakdown in H2 consistent with
  experimental results.
• Addition of proton beam impact ionization rapidly
  increases electron density in gap
• 0D calculations consistent with simple analytic
  estimates.
• 1D calculations of proton bunches propagating
  across the electrode gap give density increases
  consistent with 0D calculations (no channel for
  rapid electron removal).
• SF6 dopant (preliminary results)
• 0D calculation including addition of SF6 dopant
  to H2 (providing electron attachment) showed
  substantial reduction in electron density near
  Paschen-curve field-stress levels.
• Adding proton beam impact ionization reduced, but
  did not eliminate, electron density growth (more
  complete analysis, including HSF6- should be
  included).
• Next Steps (proposals)
• Add electrode physics (e.g., Fowler-Nordheim
  breakdown) to 1D simulations?
• 2D simulations? (Extension to 2D will require
  revisiting an implicit MCC scattering model
  rather than the explicit PIC-MCC model used here
  due to computational constraints.)