STOCHASTICALLY STABLE FLUCTUATIONS IN A MODEL OF ELECTRICAL-DISCHARGEWITH EXTERNAL ILLUMINATION

A Markov description of the electron population in a model of electric al discharge between parallel plates in the presence of an external il lumination source is developed. Electron production is assumed to be d ue to ionizing collisions in the gas, as well as photoelectric emissio n at the cathode; the electrons are assumed to move with a constant dr ift velocity towards the anode, where they are lost. The Markov descri ption is based on a discretized distribution of electrons within the g ap, from where macroscopic equations for the mean electron density and the density-density correlation function are obtained in the limit to the continuum. The results show the existence of stochastically stabl e solutions only when stationary discharges are obtained by means of a nonvanishing external illumination. In addition, the variance-to-mean ratio in the steady state shows a discontinuity when the conditions o f the discharge are those for which the breakdown Townsend criterion i s satisfied. Numerical examples are used to illustrate the results.