Nonlinear Interaction of an Electromagnetic Wave with a Plasma Layer in the Presence of a Static Magnetic Field. III. Theory of Mixing

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Abstract
The Boltzmann transport equation coupled with Maxwell's equations has been solved under a small signal, plane-wave assumption for a uniform, weakly ionized plasma layer with a constant collision frequency in the presence of a static magnetic field. The effects of the nonlinear terms in the equations are included. The amplitudes of the sum and difference frequency waves produced within the plasma layer by two incident waves of different frequencies, which propagate in the extraordinary mode within the plasma, are derived as functions of the plasma and incident wave parameters. Resonances in the amplitudes of these waves occur for values of the static magnetic field in the neighborhood of plasma resonance for the waves at the fundamental and combination frequencies. The magnetic-field strength for which a given resonance occurs is a sensitive function of the electron density. This provides a mechanism through which the electron density in a plasma layer can be determined by a measurement of magnetic-field strength.