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Title: One-dimensional radiation-hydrodynamic simulations of imploding spherical plasma liners with detailed equation-of-state modeling

Abstract

This work extends the one-dimensional radiation-hydrodynamic imploding spherical argon plasma liner simulations of Awe et al.[Phys. Plasmas 18, 072705 (2011)] by using a detailed tabular equation-of-state (EOS) model, whereas Awe et al. used a polytropic EOS model. Results using the tabular EOS model give lower stagnation pressures by a factor of 3.9-8.6 and lower peak ion temperatures compared to the polytropic EOS results. Both local thermodynamic equilibrium (LTE) and non-LTE EOS models were used in this work, giving similar results on stagnation pressure. The lower stagnation pressures using a tabular EOS model are attributed to a reduction in the liner's ability to compress arising from the energy sink introduced by ionization and electron excitation, which are not accounted for in a polytropic EOS model. Variation of the plasma liner species for the same initial liner geometry, mass density, and velocity was also explored using the LTE tabular EOS model, showing that the highest stagnation pressure is achieved with the highest atomic mass species for the constraints imposed.

Authors:
;  [1]; ;  [2];  [3]
  1. Physics Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
  2. Prism Computational Sciences, Inc., Madison, Wisconsin 53711 (United States)
  3. Propulsion Research Center, University of Alabama in Huntsville, Huntsville, Alabama 35899 (United States)
Publication Date:
OSTI Identifier:
22068826
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 19; Journal Issue: 10; Other Information: (c) 2012 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ARGON; DENSITY; ELECTRONS; EQUATIONS OF STATE; EXCITATION; ION TEMPERATURE; LTE; MAGNETOHYDRODYNAMICS; ONE-DIMENSIONAL CALCULATIONS; PLASMA; PLASMA SIMULATION; SPHERICAL CONFIGURATION; STAGNATION; THERMODYNAMICS

Citation Formats

Davis, J. S., Hsu, S. C., Golovkin, I. E., MacFarlane, J. J., and Cassibry, J. T.. One-dimensional radiation-hydrodynamic simulations of imploding spherical plasma liners with detailed equation-of-state modeling. United States: N. p., 2012. Web. doi:10.1063/1.4757980.
Davis, J. S., Hsu, S. C., Golovkin, I. E., MacFarlane, J. J., & Cassibry, J. T.. One-dimensional radiation-hydrodynamic simulations of imploding spherical plasma liners with detailed equation-of-state modeling. United States. doi:10.1063/1.4757980.
Davis, J. S., Hsu, S. C., Golovkin, I. E., MacFarlane, J. J., and Cassibry, J. T.. 2012. "One-dimensional radiation-hydrodynamic simulations of imploding spherical plasma liners with detailed equation-of-state modeling". United States. doi:10.1063/1.4757980.
@article{osti_22068826,
title = {One-dimensional radiation-hydrodynamic simulations of imploding spherical plasma liners with detailed equation-of-state modeling},
author = {Davis, J. S. and Hsu, S. C. and Golovkin, I. E. and MacFarlane, J. J. and Cassibry, J. T.},
abstractNote = {This work extends the one-dimensional radiation-hydrodynamic imploding spherical argon plasma liner simulations of Awe et al.[Phys. Plasmas 18, 072705 (2011)] by using a detailed tabular equation-of-state (EOS) model, whereas Awe et al. used a polytropic EOS model. Results using the tabular EOS model give lower stagnation pressures by a factor of 3.9-8.6 and lower peak ion temperatures compared to the polytropic EOS results. Both local thermodynamic equilibrium (LTE) and non-LTE EOS models were used in this work, giving similar results on stagnation pressure. The lower stagnation pressures using a tabular EOS model are attributed to a reduction in the liner's ability to compress arising from the energy sink introduced by ionization and electron excitation, which are not accounted for in a polytropic EOS model. Variation of the plasma liner species for the same initial liner geometry, mass density, and velocity was also explored using the LTE tabular EOS model, showing that the highest stagnation pressure is achieved with the highest atomic mass species for the constraints imposed.},
doi = {10.1063/1.4757980},
journal = {Physics of Plasmas},
number = 10,
volume = 19,
place = {United States},
year = 2012,
month =
}
  • One-dimensional radiation-hydrodynamic simulations are performed to develop insight into the scaling of stagnation pressure with initial conditions of an imploding spherical plasma shell or ''liner.'' Simulations reveal the evolution of high-Mach-number (M), annular, spherical plasma flows during convergence, stagnation, shock formation, and disassembly, and indicate that cm- and {mu}s-scale plasmas with peak pressures near 1 Mbar can be generated by liners with initial kinetic energy of several hundred kilo-joules. It is shown that radiation transport and thermal conduction must be included to avoid non-physical plasma temperatures at the origin which artificially limit liner convergence and, thus, the peak stagnation pressure.more » Scalings of the stagnated plasma lifetime ({tau}{sub stag}) and average stagnation pressure (P{sub stag}, the pressure at the origin, averaged over {tau}{sub stag}) are determined by evaluating a wide range of liner initial conditions. For high-M flows, {tau}{sub stag} {approx} {Delta}R/v{sub 0}, where {Delta}R and v{sub 0} are the initial liner thickness and velocity, respectively. Furthermore, for argon liners, P{sub stag} scales approximately as v{sub 0}{sup 15/4} over a wide range of initial densities (n{sub 0}) and as n{sub 0}{sup 1/2} over a wide range of v{sub 0}. The approximate scaling P{sub stag} {approx} M{sup 3/2} is also found for a wide range of liner-plasma initial conditions.« less
  • We have performed three-dimensional (3D) simulations using smoothed particle hydrodynamics (SPH) in order to study the effects of discrete plasma jets on the processes of plasma liner formation, implosion on vacuum, and expansion. It was found that the pressure histories of the inner portion of the liner from 3D SPH simulations with a uniform liner and with 30 discrete plasma jets were qualitatively and quantitatively similar from peak compression through the complete stagnation of the liner. The 3D simulations with a uniform liner were first benchmarked against results from one-dimensional radiation-hydrodynamic simulations [T. J. Awe et al., Phys. Plasmas 18,more » 072705 (2011)]. Two-dimensional plots of the pressure field show that the discrete jet SPH case evolves towards a profile that is almost indistinguishable from the SPH case with a uniform liner, thus indicating that non-uniformities due to discrete jets are smeared out by late stages of the implosion. The processes of plasma liner formation and implosion on vacuum were shown to be robust against Rayleigh-Taylor instability growth. Finally, interparticle mixing for a liner imploding on vacuum was investigated. The mixing rate was found to be very small until after the peak compression for the 30 jet simulations.« less
  • This work presents scaling relations for the peak thermal pressure and stagnation time (over which peak pressure is sustained) for an imploding spherical plasma liner formed by an array of merging plasma jets. Results were derived from three-dimensional (3D) ideal hydrodynamic simulation results obtained using the smoothed particle hydrodynamics code SPHC. The 3D results were compared to equivalent one-dimensional (1D) simulation results. It is found that peak thermal pressure scales linearly with the number of jets and initial jet density and Mach number, quadratically with initial jet radius and velocity, and inversely with the initial jet length and the squaremore » of the chamber wall radius. The stagnation time scales approximately as the initial jet length divided by the initial jet velocity. Differences between the 3D and 1D results are attributed to the inclusion of thermal transport, ionization, and perfect symmetry in the 1D simulations. A subset of the results reported here formed the initial design basis for the Plasma Liner Experiment [S. C. Hsu et al., Phys. Plasmas 19, 123514 (2012)].« less
  • We describe a new particle-based two-fluid fully electromagnetic algorithm suitable for modeling high density (n{sub i} {approx} 10{sup 17} cm{sup -3}) and high Mach number laboratory plasma jets. In this parameter regime, traditional particle-in-cell (PIC) techniques are challenging due to electron timescale and lengthscale constraints. In this new approach, an implicit field solve allows the use of large timesteps while an Eulerian particle remap procedure allows simulations to be run with very few particles per cell. Hall physics and charge separation effects are included self-consistently. A detailed equation of state (EOS) model is used to evolve the ion charge statemore » and introduce non-ideal gas behavior. Electron cooling due to radiation emission is included in the model as well. We demonstrate the use of these new algorithms in 1D and 2D Cartesian simulations of railgun (parallel plate) jet accelerators using He and Ar gases. The inclusion of EOS and radiation physics reduces the electron temperature, resulting in higher calculated jet Mach numbers in the simulations. We also introduce a surface physics model for jet accelerators in which a frictional drag along the walls leads to axial spreading of the emerging jet. The simulations demonstrate that high Mach number jets can be produced by railgun accelerators for a variety of applications, including high energy density physics experiments.« less
  • Z-pinch implosions driven by the SATURN device [D. D. Bloomquist {ital et} {ital al}., {ital Proceedings} {ital of} {ital the} 6{ital th} {ital Institute} {ital of} {ital Electrical} {ital and} {ital Electronics} {ital Engineers} ({ital IEEE}) {ital Pulsed} {ital Power} {ital Conference}, Arlington, VA, edited by P. J. Turchi and B. H. Bernstein (IEEE, New York, 1987), p. 310] at Sandia National Laboratory are modeled with a two-dimensional radiation magnetohydrodynamic (MHD) code, showing strong growth of the magneto-Rayleigh{endash}Taylor (MRT) instability. Modeling of the linear and nonlinear development of MRT modes predicts growth of bubble-spike structures that increase the time spanmore » of stagnation and the resulting x-ray pulse width. Radiation is important in the pinch dynamics, keeping the sheath relatively cool during the run-in and releasing most of the stagnation energy. The calculations give x-ray pulse widths and magnitudes in reasonable agreement with experiments, but predict a radiating region that is too dense and radially localized at stagnation. We also consider peaked initial density profiles with constant imploding sheath velocity that should reduce MRT instability and improve performance. Krypton simulations show an output x-ray power {approx_gt}80 TW for the peaked profile. {copyright} {ital 1996 American Institute of Physics.}« less