Frequency Mixing of Electromagnetic Waves in Plasmas by Collisional Processes.

The problem of calculating the scattered electromagnetic radiation at mixed frequencies when two or more electromagnetic waves pass through a plasma is considered. The Boltzmann equation for the spherical moments of the electron distribution function was obtained and solved in the perturbative limit. A system of diagrams was developed to enable easy identification and calculation of all terms of a given order. Nonlinear currents induced by parallel pencil beams of linearly and circularly polarized waves are calculated. The current at another frequency was calculated for the case of perpendicular propagation of the initial waves. The energy re-radiated from these currents in these cases was calculated. The re-radiation from the currents throughout the volume where the two waves are present can be made to add coherently under certain conditions forming a narrow beam.