Nonlinear Interaction of an Electromagnetic Wave with a Plasma Layer in the Presence of a Static Magnetic Field. I. Theory of Harmonic Generation

The theory of electromagnetic wave propagation through an anisotropic ionized layer, including the effects of the nonlinear terms in the Boltzmann transport equation, is presented. The method of solution of the nonlinear equations involves an expansion of all of the dependent variables in a Fourier series in time. The differential equations describing wave propagation are then solved, for each frequency in the series, for plane wave propagation, including all of the reflections within the plasma layer. A solution in closed form has been obtained, under small signal conditions, for the field at the $h\mathrm{th}$ harmonic in the Fourier series. A discussion of the properties of the wave at the second harmonic frequency as a function of the dc magnetic field strength, the electron density, the electron-neutral particle collision frequency, the field strength of the incident wave, and the thickness of the plasma layer is given.