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Lsp Simulations of RF and BeamDriven Breakdown in Hydrogen


sims. P. Hanlet, et al., EPAC, 2006. 9 ... The bunch 'length' is roughly d=bct/2 ... Proton beam density and impact ionization rate: ... – PowerPoint PPT presentation

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Title: Lsp Simulations of RF and BeamDriven Breakdown in Hydrogen

Lsp Simulations of RF and Beam-Driven Breakdown
in Hydrogen
  • D. V. Rose, C. Thoma, D. R. Welch, and R. E.
  • Voss Scientific, LLC
  • Albuquerque, New Mexico 87108

Low Emittance Muon Collider Workshop,
FermiLab April 21-25, 2008
Work supported by Muons, Inc. (with a special
thank you to Rolland Johnson)
  • Lsp simulation code
  • Particle-in-cell model description
  • MCC model
  • Computational representations of the H2 breakdown
  • 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

Lsp is a general purpose particle-in-cell (PIC)
  • A number of electromagnetic (explicit and
    implicit), electrostatic, and magnetostatic field
    solvers are implemented
  • Kinetic and fluid particle descriptions are
  • 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,
  • … 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,
  • Moderately and strongly-coupled plasmas

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
Physical Model the Test Cell (TC)
400 MeV H-
2.5 cm
5 cm
3 cm
11.4 cm
RF Power Feed
0D, 1D, and 2D simulation models
Idealized region between electrodes, independent
of spatial gradients and physical boundaries, but
can treat transient effects (RF field, presence
of a beam)
2.5 cm
Idealized region spanning space between
electrodes, spatial (1D) and temporal gradients
and physical boundaries are added. (RF field,
beam injection through electrode)
(modest size calculation)
Axi-symmetric approximation (?/ ?q 0), radial
gradients are added, RF power can be feed in
via a port.
(call in sick)
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.

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
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.
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).

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.
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
  • The bunch length is roughly dbct/2 (I assume
    a worst-case short bunch of one-half of the sine
    wave) d13.3 cm

Estimate proton energy inside gas cell
I used the SRIM dE/dx stopping power tables and
fit simple functions for proton stopping 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 is roughly 209 MeV
Beam-impact ionization cross-section estimate
  • Impact ionization cross-section for protons on
    hydrogen gas gives s4.5x10-23 m2 for 209 MeV
  • Note I ignore additional energy loss of the
    proton beam in the gas as it traverses the AK gap.

(for Eb gt 5 MeV)
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 to beam impact
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.

Impact ionization of H2 gas by the proton beam
rapidly drives the breakdown, as expected
10 MV/m case at 325 psia below the Paschen limit
25 MV/m case at 325 psia at the Paschen limit
0D calculations including proton beam impact
ionization indicate that SF6 reduces electron
density growth rate slightly
Comparison of electron densities with and without
Electron and negative ion SF6 densities.
Note I do not include beam impact ionization of
any SF6 species.
1D simulation model RF fields and proton impact
We inject 3 proton bunches into the 1D
simulation region through one of
the electrodes. The electron density increases
significantly due to proton impact ionization of
the H2.
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
  • F. C. Young, et al., Phys. Plasmas 1, 1700
  • F. C. Young, et al., Phys. Rev. Lett. 70, 2573
  • J. M. Neri, et al., Phys. Fluids B 5, 176 (1993).
  • B. V. Oliver, et al., Phys. Plasmas 6, 582
  • 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
  • D. V. Rose, et al., Nucl. Instrum. Meth. Phys.
    Res. A 464, 299 (2001).
  • D. R. Welch, et al., Phys. Plasmas 9, 2344
  • D. V. Rose, et al., Phys. Plasmas 6, 4094 (1999).
  • C. L. Olson, et al., Il Nuovo Cimento 106A, 1705
  • B. V. Oliver, et al., Phys. Plasmas 3, 3267
  • GeV proton beam propagation in the atmosphere
  • D. V. Rose, et al., Phys. Rev. ST-AB 9, 044403
  • D. V. Rose, et al., Phys. Plasmas 9, 1053
  • Laser-matter interaction and generation of ion

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
  • 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
  • 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.)