The influence of the electron temperature gradient on the space-charge field in a d.c. discharge

Abstract

The deviations of the space-charge field from its equilibrium value in the d.c. discharge plasma is investigated, taking into account the influence of changed electron temperature. Starting from the plasma-equations, the corresponding steady-state solution in a linear, one-dimensional approximation is found, on the assumption that the ion density disturbance is known and given as a function of the space coordinate, constant in time or only slowly varying with time. As the changed electron temperature influences the electron density, the space-charge field disturbance is no longer restricted (within the limit of the Debye screening length) by the dimension of the positive ion disturbance as is the case of the temperature uninfluenced field. The space charge field now extends widely out of the place of the ion disturbance, the extension being given by the dimension of the electron temperature relaxation length, which in order of magnitude equals the quantityl1=2Ue0/E0. A solution in a closed analytical form (25) is found in the case of a quasineutral plasma. Even in this case of zero Debye length, temperature lengthening of the spacecharge field relaxation takes place. The appropriate numerical examples are given for the case of final (non-zero) Debye length.