On the higher-order nonlinear corrections to the theory of plasma emission by a nonlinear beam instability

A recent alternative theory of electromagnetic radiation with frequency in the vicinity of plasma frequency and/or its harmonic, put forth by the present author, invokes a new type of nonlinear beam-plasma instability. The new theory was originally formulated by retaining the second-order nonlinear response of the plasma only. However, in a general nonlinear instability theory it is well known that the third-order correction can have a contribution of the same order of magnitude as the second-order nonlinearity. This article examines the validity of the original formulation of the nonlinear beam instability by reformulating the problem, keeping the full second- and third-order nonlinear responses of the plasma. In the final analysis, however, it is found that the third-order nonlinear correction can indeed be neglected, and that the original formulation of the problem is justified. © 1998 American Institute of Physics.