Zur nichtlinearen Theorie der Strahl-Plasma-Wechselwirkung I

Beam-plasma-interaction is theoretically investigated on the basis of the non-linear Vlasov equation. The case of amplifying longitudinal waves is described by a non-linear approximation including “quasilinear” and mode-coupling terms. By evaluating the electric field vector E(x, t) and the distribution functions f_a(x, v, t) for the beam and plasma electrons in Fourier series and approximating the non-oscillating parts of the f_a by the first terms in an expansion using Hermite polynomials in velocity space a system of ordinary differential equations for the complex wave number k, the mean and thermal velocities and the quasimoments b_as is obtained, which can be solved numerically, if terms with E for which m + n > 3 are neglected. The numerical results will be given in a further part of the paper.