Quantum Theory of Photon Interaction in a Plasma

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Abstract
The quantum theory of interaction of electromagnetic waves in a plasma is formulated from two different points of view. The first is to consider scattering of light off light (in the form of laser beams) with the plasma acting as a mediator of the interaction; the second is to consider scattering of one of the light beams off a system consisting of the plasma and the other laser beam. Based on the first viewpoint, the light-light scattering cross sections, both elastic and inelastic, are calculated in the lowest order. By summing over the final states of one of the photons, we obtain, based on the above results, the lowest order cross section of scattering of the other photon from the photon-plasma system. In the presence of a second stimulating laser beam, this cross section is enhanced. When both laser beams are very intense, the lowest order perturbation treatment is inadequate. The second viewpoint is then conveniently adopted to include the plasma-laser beam interaction to all orders. The results are discussed and compared with those in previous treatments. Finally, a simple model is considered. In this model, the plasmon is treated as the quantum of a harmonic oscillator which is linearly coupled to a system of phonons. All the previous results are explicitly verified in this model, which is solved exactly.

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