ISSN:
1573-8620
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
,
Physics
Notes:
Abstract The description of many physical systems comes down to the solution of a system of two nonlinear equations of the parabolic type. Such systems can be the electron-hole plasma of a semiconductor and a weakly ionized gas plasma, nonequilibrium superconductors, as well as a number of chemical and biological objects, the properties of which are determined by autocatalytic reactions. The formation of complicated nonuniform structures occurs upon the loss of stability in these systems. We shall examine the concrete problem of the development of an ionization-superheating instability in a self-maintained discharge, described by the equation of charged-particle balance of the plasma and the equation of heat balance. The mechanism of this stability is connected with the decrease in the density of gas escaping at constant pressure from a superheated region, and with the rise in electron temperature occurring as a consequence of this (see, e.g., [1]). Self-similar functions for the local values of the charged-particle density and the gas temperature, being solutions of the corresponding balance equations, are of interest for the understanding of the nonlinear state of this process. An ionization-superheating instability in a high-frequency field and a self-similar solution, describing the explosive development of conductivity in a constricting discharge, neglecting the thermal conductivity of the gas and charge recombination, were studied in [2]. Self-similar solutions of a pair of equations of the parabolic type under the conditions of a self-maintained glow discharge are investigated in the present paper. The solutions obtained can be of interest for a whole series of physical systems.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00910507
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