Electron plasma relaxation processes

The solution of the Vlasov equation for the longitudinal electron plasma wave is obtained by using Neumann series method. The electron relaxation process is analytically described by the superposition of expressions for electron streamings and Coulomb collisions. The currently established formula for the longitudinal plasma wave is also explained by the closed-form solution of the Vlasov equation. The expression effectively describes the detailed physical processes of the electron plasma wave relaxation both in space and time.