Resonant Wave-Wave Interactions of Electromagnetic and Electrostatic Waves in a Homogeneous Magnetized Plasma

Abstract

General expressions of the matrix elements for nonlinear resonant wave-wave interactions of electromagnetic and electrostatic waves in a homogeneous magnetized plasma are derived from the Vlasov-Maxwell equations. The kinetic wave equations obtained for electromagnetic waves are represented by three-order tensors in the rotating and Cartesian coordinates. The waves are allowed to propagate at arbitrary angles to the uniform magnetic field, and no restrictions are imposed upon the mean Larmor radius, the frequencies, or the wave numbers. By electrostatic approximation of the dielectric tensor and the matrix elements the kinetic equations can be also applicable to the case in which the three waves are electrostatic altogether or partially electrostatic. The matrix elements in the limit of parallel or perpendicular propagation to the magnetic field are given.