Non-linear coupling of waves in a magnetized plasma with particle drift motions

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Abstract
We study non-linear interaction between three monochromatic waves which propagate parallel to the direction of a magnetic field in a plasma. The approach to the problem is hydromagnetic, including temperature effects, and the method of solution is that of coupled mode theory. In particular drift motions of the particles along the magnetic field are considered taking into account relativistic effects. The interaction of two transverse waves and one longitudinal wave is treated as well as that of three longitudinal waves. Besides, the case of two longitudinal waves and one perpendicular wave has been studied in some detail assuming the latter to have a long wavelength. The present paper represents a generalization of the problem of three-wave interaction in a plasma to situations more complex than have been treated before. The most essential limitation consists in the assumptions made for the directions of propagation of the waves.