Electrodynamics of linear modes—Conservation relations and perturbation theory

Abstract This chapter presents a unified description of linear electrodynamics of a weakly-dissipative, homogeneous medium entailing arbitrary temporal and spatial dispersion in its dynamics. In an electrodynamic description, one asserts that the “mechanical” field variables (e.g. densities, velocities, pressures, velocity distribution functions, etc.) have been eliminated in favor of the SCF EM-fields. For a plasma, the electrodynamic formulation is based upon the (internal response) susceptibility function which comes from any linearized model dynamics of the plasma. Introducing slowly-varying amplitudes on the electrodynamic fields allows for an expansion of the general space-time convolution-integral constitutive relations and, together with Maxwell's equations, leads to electrodynamic partial differential equations (P.D.E.s), in the slow space-time variables, including the presence of weak dissipation and external sources in the medium. The chapter also offers a dynamic perturbation theory of modes which leads to linear (L) and nonlinear (NL) coupling modes (COM).