The thermal self-focusing of a wave beam in an underdense plasma. Part 5. Cubic nonlinear effects

Abstract

In the fifth part of this paper devoted to the problem of the thermal self-focusing of an electromagnetic wave in an underdense plasma, we extend the nonlinear theory of part 4 to include the effect of cubic nonlinearities. These terms describe the stabilizing influence of perturbations to the electrical conductivity. We assume that a stationary state of the type described earlier has been established and consider the spatial nonlinear interaction of the pump wave with the Stokes side-band waves and the density perturbation corresponding to the most unstable linear mode. We show that the system of єquations describing their interaction possesses three invariants. These invariants are used to reduce the problem to quadratures and an implicit solution is obtained in terms of incomplete elliptic integrals of the first and third kinds. From this solution we derive explicit expressions for the saturation level and the nonlinear growth length. The results are applied to the problem of ionospheric modification by microwave transmissions from the proposed solar power satellite systems.