On Nonlinear Generation of Second Harmonic and Sum and Difference Frequencies in a Homogeneous Plasma

A new mechanism for the generation of even harmonics and sum and difference frequencies in a plasma, which consists of simultaneous application of a d.c. electric field and two alternating electric fields, has been analysed. The Boltzmann transfer equation for electrons in a homogeneous plasma in the presence of a d.c. electric field and two a.c. electric fields has been solved, and explicit expressions for the harmonic and combination frequency components of current density have been obtained. These expressions have been substituted in the general wave equation and the solution has been used to investigate two specific phenomena viz. the nonlinear growth of the second harmonic and sum and difference frequency waves in a plasma, and the magnitude of these frequency components in the wave reflected from a plasma-free space interface when the two incident electromagnetic waves are both travelling perpendicular to the direction of the externally applied d.c. electric field. A short discussion of the results is also given.