Nonlinear wave-particle interaction and conditions for the applicability of quasilinear theory

Abstract

In this paper it is shown that the usual conditions of the broad wave packet and overlapping of the trapping intervals of neighboring harmonics are not sufficient for the applicability of the quasilinear theory. The additional important condition is phase randomization in wave-wave interaction. In order for this randomization to occur during a time of wave evolution, i.e. of the inverse growth rate, the mismatch between the frequency of the three-wave nonlinear driver and that of the plasma eigenmode must exceed significantly the growth rate. If this condition is not fulfilled, quasilinear theory is applicable only for wave spectra smoothed by a procedure of averaging over neighboring harmonics inside the trapping interval. Experimental tests done with a warm beam moving through a traveling tube qualitatively support this point of view. At the same time, as it is shown in the paper, nonlinear interaction of waves has the tendency for steepening and modulation of the spectral energy density at a typical k scale of the order of inverse trapping length.