Kinetic study of high-frequency instability in gas discharges

Abstract

It is well kno~ [i] that instability can develop in a gas-discharge plasma because of the presence of a decreasing segment in the dependence of electron drift velocity on the applied electric field. This instability is analogous to the Gunn effect in semiconductors [2]. The linear stage of development of such instability was studied in [I, 3, 4]. Depending on the value of the parameter VuTm = E2/(4vnekTe), the rate of instability development is determined either by the frequency ~m -" (at T m v u >> i), or byv u(~mvu << i) [3] (where ~u is the inelastic collision frequency, which defines the relaxation rate of the symmetrical component of the electron distribution function, T m = i/(4~o), o is the plasma conductivity, E is the electric field intensity, n e is the electron concentration, and T e is the mean electron energy). In the second case instability development is not described by the transfer equations, and it is necessary to calculate the electron distribution function. To analyze the role played by kinetic effects, we shall consider homogeneous development of Gunn-type instability, using model inelastic collision integrals. Self-similar solutions of the kinetic equation will be found for constant current in the circuit. Numerical solution of the kinetic equation will show that the full solution over time periods of the order of Vu -I approaches selfsimilarity.