On excitation of electromagnetic waves in the region of plasma resonance in inhomogeneous plasma by nonlinear Langmuir oscillations

Strongly nonlinear free electron oscillations were studied in cold isotropic inhomogeneous plasma. Analytical expressions describing evolution of velocity and density of plasma electrons and strength of self-consistent electric field in time were obtained in the Lagrange variables. Cases of strong and weak spatial inhomogeneity of plasma which are of practical interest are studied. It is shown that in the region of plasma resonance the plasma inhomogeneity leads to parametric excitation of fast electromagnetic waves by the nonlinear Langmuir oscillations. The growth rate of the transverse waves is equal in order of magnitude to the electron plasma frequency multiplied by the plasma inhomogeneity parameter.