Particle trapping in the beat potential produced by the mixing of two coherent waves lies outside the domain of the conventional weak-turbulence theory of induced wave–particle scattering in plasma. A reformulation of the theory is presented which is applicable to this extended domain. The formulation is based upon a canonical transformation to ’’oscillation-center variables’’ and in particular affords a simpler method for deriving the ’’linear’’ matrix elements of weak-turbulence theory. This method is first illustrated in the problem of the nonlinear Landau damping of longitudinal plasma modes. The power of the method is then usefully exploited in two more difficult situations, namely, the cases of electrostatic waves in the presence of a uniform magnetic field, and electromagnetic waves in an arbitrarily relativistic plasma. The application of the transformation to the extended strong-interaction regime is demonstrated.
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Shayne Johnston (1976) studied this question.