Two-dimensional instability of fast ionization waves propagating in an external electric field

Abstract

Stability of fast planar ionization waves (IW) propagating in a cold electropositive gas in the presence of constant applied electric field E0 has been investigated. The stationary IW are one-dimensional (1D) nonlinear solutions depending on the variable ξ=x−Vt and connecting two different steady states with constant parameters. The basic system of equations contains the rate equations for the concentrations of electrons and positive ions and the Poisson equation for the electric field. There is a continuum of possible velocities of stationary anode-directed (E0<0) and cathode-directed (E0>0) IW. All stationary IW are stable to small 1D perturbations. It has been shown that in a wide range of the parameters E0/p and V/Ve, where p is the gas pressure and Ve is the electron drift velocity ahead of the wave front, both anode- and cathode-directed IW are unstable to two-dimensional (2D) perturbations having the form f(ξ)exp(iky+λt). The 2D instability is displayed in the form of increasing corrugation of the planar IW. The integral representation of the electric potential perturbation has been employed for calculation of the eigenmodes and the growth rates in the long-wave limit kΔ≪1 where Δ is the characteristic thickness of a stationary IW.