Higher Nonlinearities

Abstract

It is natural to ask whether the next terms in the expansion in the used parameters may be important. Besides these parameters β ~ k ² υ ² _Te /ω ² _pe [see (2.44)] in the nonlinear third-order responses. The corrections corresponding to an expansion in this parameter are traditionally named electron nonlinearities [24, 44]. We stress here that only few works give correct expressions for the electron nonlinearities. The reason is that in a number of pioneer works (see, e.g., [44]), some definite methods were used to average over the high frequency ω _pe , and thus some terms (which are of the same order as ones taken into account in these works) were lost. The correct result can be obtained using the consistent method of the present approach (see also [24, 30, 45]). A necessity of accounting for the electron nonlinearities appears in the case in which strong compensation of the two main contributions (connected with direct third-order and polarizational effects) in the Σ^eff takes place, i.e., when the response Σ^eff becomes sufficiently small. Because of the compensation we have to take into account the electron nonlinearities as well as to calculate higher order effects in the wave fields.