Generalized Ponderomotive Forces and Three-Wave Interaction

Abstract

The subject of this article is a unified Hamiltonian approach to the theory of nonlinear interactions among waves and particles. The unifying feature of the approach is a generalization of the concept of “ponderomotive force”. The formulation can be said to retain the conceptual simplicity of the familiar ponderomotivepotential method [l–3], but to remove the approximations [4]. The essence of the approach is to replace the usual method of time-averaging by the performance of a canonical transformation. The transformation is designed to eliminate the terms in the Hamiltonian of a particle which are linear in the wave potentials, replacing them with bilinear terms at combination frequencies. The new entity (the “oscillation center”) thus has no first order uttering motion. The transformation formalism leads to explicit expressions for the required nonlinear currents, which can be decomposed into the current of oscillation centers and the “polarization” corrections [4]. The oscillation-center representation is thus quite analogous to the more familiar guiding-center representation in strong magnetic fields.