Microscopic Lagrangian description of warm plasmas 4. Macroscopic approximation

The averaged-Lagrangian method is applied to linear wave propagation and nonlinear three-wave interaction in a warm magnetoplasma, in the macroscopic approximation. The microscopic Lagrangian treated in papers 1–3 is first expanded to third order in perturbation. Velocity integration is then carried out, before applying Hamilton's principle to obtain a general description of wave propagation and coupling. The results are specialized to the case of interaction between two electron plasma waves and an Alfvén wave. The method is shown to be more powerful than the alternative possibility of working from the beginning with a macroscopic Lagrangian density.