CHARACTERISTIC-FUNCTIONAL APPROACH TO THE STUDY OF STOCHASTIC FLUCTUATIONS IN A MODEL OF IONIZATION GROWTH IN A DISCHARGE GAP

A characteristic-functional approach is introduced to study the space and time stochastic fluctuations of the electron population in a simpl e one-dimensional model of ionization growth. Two electron sources are considered: (a) ionization by direct collisions and (b) photoemission at the cathode due to de-excitation of atoms. The motion of the ions is neglected and the electrons are assumed to move with constant drift velocity. An equation for the characteristic functional G[theta(x),t] = [exp[i integral-L/0 dx theta(x)n(x, t)]] is obtained, where n(x, t) is the electron density, and theta(x) is a conjugate function; from t his, equations for the moments, e.g., the average density and the dens ity-density correlation function, can easily be derived. Similarly to using the method of compounding moments, this technique avoids the use of a probability in function space; however, it has the benefit that the motion in configuration space may be incorporated self-consistentl y, whether the motion is free streaming or diffusion. Numerical exampl es are used to illustrate the time behavior of the mean total populati on in the gap, which shows a good agreement with previous results; in addition, we analyze the time evolution of the associated electron mea n density, the density-density correlation function, and the fluctuati ons around the mean population.