Two-dimensional quasilinear relaxation of a relativistic electron beam in a collisional plasma

Numerical investigation of relaxation of a relativistic electron beam in a collisional plasma with regard for two-dimensionality of the Langmuir noise spectra is carried out in the framework of the quasilinear approximation. Relaxation is shown to have two stages in the general case. On the first (one-dimensional) stage oscillation energy increases mainly due to longitudinal noises and beam deceleration occurs during its insignificant scattering. On the second (two-dimensional) stage oscillation energy increase is mainly conditioned by the growth of oblique noises and accompanied by considerable beam scattering. At the low initial noise level beam relaxation runs as one-dimensional, at high one-relaxation runs as two-dimensional from the very beginning omitling the one-dimensional stage. Particle collision in the plasma, decreasing the rate of Langmuir noise increase and decelerating relaxation, leads to one-dimensionality of the oscillation sectrum too and thus to pulling of the one-dimensional stage of relaxation