Numerical and analytical study of the electron heating by plasma waves

Electron heating and acceleration by wakefield caused by the laser pulse is studied with help of the space nonuniform Fokker–Planck equation. Relativistic intense laser pulse propagates in a plasma with prescribed values of density and quasi stationary plasma wave spectrum. Electron heating is considered in а frame of plasma-wave interaction on the base of quasilinear theory. Previous to front, the extending distribution function tails is building-up in the course of impulse propagation. Numerical solution has the coincident asymptotic form with the obtained analytical solution. The paper proceeds and evelops the previous work on the subject.