Stability of the steady-state conditions of the Joule heating of a low-temperature plasma

An analysis is made of the stability of the imhomogeneous state of a flat discharge in a thermal plasma with a rising temperature dependence of the electrical conductivity sigma(T). For the case of a power dependence of sigma(T) and for conditions where, in the base state, the vectors of the electrical current and the heat flux are mutually orthogonal, the stability of a bounded plasma with respect to three-dimensional perturbations was investigated. On the basis of an exact solution of the boundary-value problem, the existence of neutral two-dimensional and three-dimensional perturbations, branching-off from the base state in the incident section of the volt-ampere characteristic, was established. An investigation was made of the spectrum of the one-dimensional perturbations in a discharge with an external ohmic load, and the possibility of the supression of such perturbations with a sufficiently large value of the load is shown. Attention must be drawn to the possibility, in principle, of the appearance of three-dimensional steady-state structures in the region of linear instability