Specificities of onedimensional dissipative magnetohydrodynamics
Abstract
Onedimensional dynamics of a plane slab of cold (β ≪ 1) isothermal plasma accelerated by a magnetic field is studied in terms of the MHD equations with a finite constant conductivity. The passage to the limit β → 0 is analyzed in detail. It is shown that, at β = 0, the character of the solution depends substantially on the boundary condition for the electric field at the inner plasma boundary. The relationship between the boundary condition for the pressure at β > 0 and the conditions for the electric field at β = 0 is found. The stability of the solution against onedimensional longitudinal perturbations is analyzed. It is shown that, in the limit β → 0, the stationary solution is unstable if the time during which the acoustic wave propagates across the slab is longer than the time of magnetic field diffusion. The growth rate and threshold of instability are determined, and results of numerical simulation of its nonlinear stage are presented.
 Authors:
 National Research Center Kurchatov Institute (Russian Federation)
 Publication Date:
 OSTI Identifier:
 22614069
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Plasma Physics Reports; Journal Volume: 42; Journal Issue: 11; Other Information: Copyright (c) 2016 Pleiades Publishing, Ltd.; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; BOUNDARY CONDITIONS; COMPUTERIZED SIMULATION; DIFFUSION; DISTURBANCES; ELECTRIC FIELDS; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; ONEDIMENSIONAL CALCULATIONS; PLASMA; PLASMA INSTABILITY; SOLUTIONS; SOUND WAVES
Citation Formats
Popov, P. V., Email: popov.pv@mipt.ru. Specificities of onedimensional dissipative magnetohydrodynamics. United States: N. p., 2016.
Web. doi:10.1134/S1063780X16090075.
Popov, P. V., Email: popov.pv@mipt.ru. Specificities of onedimensional dissipative magnetohydrodynamics. United States. doi:10.1134/S1063780X16090075.
Popov, P. V., Email: popov.pv@mipt.ru. 2016.
"Specificities of onedimensional dissipative magnetohydrodynamics". United States.
doi:10.1134/S1063780X16090075.
@article{osti_22614069,
title = {Specificities of onedimensional dissipative magnetohydrodynamics},
author = {Popov, P. V., Email: popov.pv@mipt.ru},
abstractNote = {Onedimensional dynamics of a plane slab of cold (β ≪ 1) isothermal plasma accelerated by a magnetic field is studied in terms of the MHD equations with a finite constant conductivity. The passage to the limit β → 0 is analyzed in detail. It is shown that, at β = 0, the character of the solution depends substantially on the boundary condition for the electric field at the inner plasma boundary. The relationship between the boundary condition for the pressure at β > 0 and the conditions for the electric field at β = 0 is found. The stability of the solution against onedimensional longitudinal perturbations is analyzed. It is shown that, in the limit β → 0, the stationary solution is unstable if the time during which the acoustic wave propagates across the slab is longer than the time of magnetic field diffusion. The growth rate and threshold of instability are determined, and results of numerical simulation of its nonlinear stage are presented.},
doi = {10.1134/S1063780X16090075},
journal = {Plasma Physics Reports},
number = 11,
volume = 42,
place = {United States},
year = 2016,
month =
}

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