Abstract
Structures of ion shock waves are investigated on the basis of the Fokker-Planck equation. The main purpose of this paper is to obtain rigorous solutions of the Fokker-Planck equation. The ion distribution function in the transition region of the shock wave is expanded in terms of the three-dimensional Hermite polynomials. To determine the expansion coefficients, the moment method is employed. By using five expansion coefficients of the lowest order, asymptotic solutions in the vicinities of the upstream and downstream equilibrium states are obtained.
In the downstream region of strong shock wave, the ion distribution function has a double-humped shape. The second peak of the double-humped ion distribution function is lower than that obtained from the Mott-Smith method. In the transition region of weak shock wave, the ion distribution function has only one peak.
