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Title: One-dimensional radiation-hydrodynamic scaling studies of imploding spherical plasma liners

Abstract

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. 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 formore » a wide range of liner-plasma initial conditions.« less

Authors:
; ; ; ;  [1];  [2]
  1. Physics Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
  2. Propulsion Research Center, Technology Hall S-226, University of Alabama in Huntsville, Huntsville, Alabama 35899 (United States)
Publication Date:
OSTI Identifier:
22046890
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 18; Journal Issue: 7; Other Information: (c) 2011 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; APPROXIMATIONS; ARGON; ELECTRON TEMPERATURE; ION TEMPERATURE; MACH NUMBER; ONE-DIMENSIONAL CALCULATIONS; PLASMA; PLASMA DENSITY; PLASMA JETS; PLASMA PRESSURE; PLASMA PRODUCTION; PLASMA SIMULATION; RADIANT HEAT TRANSFER; RADIATION TRANSPORT; SHOCK WAVES; SPHERICAL CONFIGURATION; THERMAL CONDUCTION

Citation Formats

Awe, T. J., Adams, C. S., Davis, J. S., Hanna, D. S., Hsu, S. C., and Cassibry, J. T.. One-dimensional radiation-hydrodynamic scaling studies of imploding spherical plasma liners. United States: N. p., 2011. Web. doi:10.1063/1.3610374.
Awe, T. J., Adams, C. S., Davis, J. S., Hanna, D. S., Hsu, S. C., & Cassibry, J. T.. One-dimensional radiation-hydrodynamic scaling studies of imploding spherical plasma liners. United States. doi:10.1063/1.3610374.
Awe, T. J., Adams, C. S., Davis, J. S., Hanna, D. S., Hsu, S. C., and Cassibry, J. T.. 2011. "One-dimensional radiation-hydrodynamic scaling studies of imploding spherical plasma liners". United States. doi:10.1063/1.3610374.
@article{osti_22046890,
title = {One-dimensional radiation-hydrodynamic scaling studies of imploding spherical plasma liners},
author = {Awe, T. J. and Adams, C. S. and Davis, J. S. and Hanna, D. S. and Hsu, S. C. and Cassibry, J. T.},
abstractNote = {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. 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.},
doi = {10.1063/1.3610374},
journal = {Physics of Plasmas},
number = 7,
volume = 18,
place = {United States},
year = 2011,
month = 7
}
  • 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'smore » 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.« 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 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
  • The dynamics of imploding foil plasmas is considered using first-order theory to model the implosion and to investigate the effects of magnetohydrodynamic instabilities on the structure of the plasma sheath. The effects of the acceleration-produced magnetohydrodynamic (MHD) Rayleigh-Taylor instability and a wall-associated instability are studied for a variety of plasma implosion times for several pulsed power drivers. The basic physics of these instabilities is identified and models are developed to explain both linear and nonlinear behavior. These models are compared with the results of detailed two-dimensional magnetohydrodynamic simulations. Expressions for linear Rayleigh-Taylor growth are developed showing its dependence on drivingmore » current, plasma conductivity, and density gradient scale length. A nonlinear saturation model, based on magnetic field diffusion, is developed. The model for a wall instability involves the interaction of the plasma sheath with the electrode wall and the material ablated from the electrode. The growth of this instability is shown to be limited by field diffusion. Comparison with two-dimensional simulations has been excellent.« less
  • Novel experimental data are reported that reveal helical instability formation on imploding z -pinch liners that are premagnetized with an axial field. Such instabilities differ dramatically from the mostly azimuthally symmetric instabilities that form on unmagnetized liners. The helical structure persists at nearly constant pitch as the liner implodes. This is surprising since, at the liner surface, the azimuthal drive field presumably dwarfs the axial field for all but the earliest stages of the experiment. These fundamentally 3D results provide a unique and challenging test for 3D-magnetohydrodynamics simulations.