Scattering Potential in Fully Ionized Gases

Abstract

Recent methods for calculating the probability $W\left(E\right)\mathrm{dE}$ that a test particle in a plasma experiences an electrical field of magnitude $E\pm \frac{1}{2}\mathrm{dE}$ are discussed. In particular, the assumption is analyzed that the distribution $W\left(E\right)\mathrm{}$ in a system of true charges can be calculated from an auxiliary system of uncorrelated virtual particles which, formally, do not interact although they are the sources of shielded Coulomb fields of the type introduced by Debye and Hückel. It is shown that the electrostatic energy of the auxiliary system, calculated as a volume integral over the average energy density $\frac{{〈E^2〉}_{\mathrm{Av}}}{8\pi }$, is identical with the interaction energy of the true particles as obtained by the Debye-Hückel theory. The distribution of the micropotential $W\left(\Psi \right)d\Psi$ in a plasma is also calculated from the auxiliary system and used for deducing a scattering potential $\Psi \mathrm{}\left(r\right)\mathrm{}$ which has a natural cutoff at a distance equal to the average distance between neighboring ions. An approximate analytical expression for $\Psi \mathrm{}\left(r\right)\mathrm{}$ is given and the physical nature of the scattering potential is discussed.