Statistical distribution of random electric fields in charged particle gases

The temperature and density dependent probability distribution W = W(E; T, n) of the collective electric fields E in an ideal gas of charged particles each carrying the same charge e (electrons: e = − e₀> 0; ions: e = Ze₀≷ 0) is calculated from first principles of statistical mechanics. It is shown that (i) the collective electric fields act at distances larger than the characteristic repulsion distance D = ; (KT/4πne²)^1/2 of like charged particles, and (ii) the average collective electric field is E_w =(12πnKT)^1/2 for ideal gases of particles of the same charge e. Thus, in a thermal equilibrium gas of like charged particles, the longitudinal microfields are considerably stronger than in a quasi-neutral plasma, since in the latter the random field effects of the negative electrons and positive ions nearly compensate each other.