Microscopic Theory of Density Fluctuations and Diffusion in Weakly Ionized Plasmas

Kinetic equations for the self and distinct parts of the electron density cross-correlation function are obtained for a partially ionized gas by solving a truncated BBGKY hierarchy in the Markovian limit. Assuming a BGK model for the terms representing collisions with the neutrals, these equations are then used to calculate the self and total electron density cross-correlation functions. The expressions obtained for the correlation functions are valid for stationary, homogeneous, partially ionized plasmas. In equilibrium, the expression for the spectral density reduces to that obtained by Dougherty and Farley. In the limit of zero-collision frequencies, the results of Rostoker and Rosenbluth are recovered. For long times and large probe separations analytical expressions are obtained for the cross correlation functions. It is found that the self-correlation function depends on the electron diffusion coefficient and the total electron correlation function depends on the ambipolar diffusion coefficient.