The theory of light scattering in a plasma is extended by including an external electric field (e.g. the field of a laser beam) in calculating the density fluctuations. It is shown that in the presence of a time constant homogeneous magnetic field there arise density fluctuations with the frequency and the wave number of the external electric field. Expansions of the general expressions are obtained for the case that the frequency is large compared to the electron gyrofrequency. The special case that the external electric field is a transverse wave is discussed in detail.
The light of a second beam may be scattered by these forced density fluctuations. The scattered light has the sum and the difference frequency of the two light beams, i.e. light mixing occurs. In the framework of this theory the effect occurs only if the two beams are parallel. - If one considers the scattering of the same beam that forces the density fluctuations, the scattered light is the second harmonic
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