Oscillation centres and mode coupling in nonuniform Vlasov plasma
Abstract
The general coupling coefficient for three electromagnetic linear modes of an inhomogeneous and relativistic plasma is derived from the oscillationcentre viewpoint. A concise and manifestly symmetric formula is obtained; it is cast in terms of Poisson brackets of the singleparticle perturbation Hamiltonian and its convective timeintegral along unperturbed orbits. The simplicity of the compact expression obtained is shown to lead to a new insight into the essence of threewave coupling and of the ManleyRowe relations governing such interactions. Thus, the interaction Hamiltonian of the three waves is identified as simply the trilinear contribution to the singleparticle (new) Hamiltonian, summed over all nonresonant particles. The relation between this work and the Lietransform approach to Hamiltonian perturbation theory is discussed.
 Publication:

Journal of Plasma Physics
 Pub Date:
 August 1979
 DOI:
 10.1017/S002237780000996X
 Bibcode:
 1979JPlPh..22..105J
 Keywords:

 Coupled Modes;
 Nonuniform Plasmas;
 Perturbation Theory;
 Plasma Oscillations;
 Relativistic Plasmas;
 Vlasov Equations;
 Frequency Shift;
 Hamiltonian Functions;
 Lie Groups;
 Transformations (Mathematics);
 Plasma Physics