Particle and wave subsystems

A plasma is a collection of individual particles coupled together through the electromagnetic field. These coupled particles constitute a collective medium. The reinterpretation of a collection of individual particles and the electromagnetic field as a collective medium requires a formal rearrangement of the ‘bare’ particles and electromagnetic field into a background system of ‘dressed’ particles, sometimes called quasiparticles, and a ‘self-consistent’ field that includes the collective response of the medium. The free oscillations of the selfconsistent field constitute wave subsystems. To identify wave subsystems as distinct subsystems one needs to identify the Lagrangian for the subsystem, and this is obtained from the Lagrangians for the free particles and free fields by an appropriate rearrangement. There are several different ways of carrying out the rearrangement and three are discussed here. All of them lead to explicit expressions for the response tensors of the collective medium. The three approaches are the forward-scattering approach, the Vlasov approach and the oscillating-center approach. A cold plasma approach is also discussed: it may be adapted to give the linear and nonlinear response tensors for an arbitrary (unmagnetized) plasma, and in this sense it is a fourth approach.