Three-Wave Interaction and Nonlinear Wave-Particle Scattering

Abstract

A study has been made of three-wave interaction and nonlinear wave-particle scattering for waves propagating parallel to the external magnetic field using quantum techniques. The three-wave interaction refers to longitudinal, transverse, and Alfvén or whistler modes. The waves taking part in the nonlinear wave-particle scattering are transverse, Alfvén, and whistlers. Kinetic equations containing these effects have been derived. It is established the three-wave interaction for Alfvén or whistler modes is impossible.

Kinetic theory of three-wave interaction in a magnetized plasma

“…Corrections due to kinetic effects in the coupling coefficients are then of little importance. The present results thus refer, in particular, to the MO waves, considered by, for example, Lee (1971). The propagation properties of these waves can be very different from those of the' conventional' ordinary waves, and thermal motions are important.…”

“…There are, however, some reasons why the present more general ('hot') form of the coupling coefficient for the interaction between three MO waves should require particular attention. One indication is Lee (1971), where it is shown that MO waves, with frequencies near the harmonics of the cyclotron frequency, can be unstable. But, even when an MO wave is linearly stable, it may be of negative energy (1/w d/d(o 0) 2 e zs < 0), which means that nonlinear 'explosive' instabilities can exist.…”

“…collisionless damping phenomena or propagation of cyclotron harmonic waves). It is evident that particle motions affect the interaction between longitudinal waves, which then have to be treated by means of a kinetic analysis (Harker & Crawford 1968), but transverse waves should also be included in such a description (Earn et al 1971;Cano et al 1969;Lee 1971). Because of the complexity of the results and the wealth of parameters, it is not possible to describe all cases in detail.…”

“…The comparatively simple interaction between three waves, which propagate parallel to B o , has already been treated (e.g. Stenflo 1970; Kim, Harker & Crawford 1971;Krishan & Fukai 1971) from such a point of view. Thus, we aim to derive the coupling coefficients without most of the basic restrictions of other works.…”