Energy Constants Associated with the Nonlinear Theory of Electromagnetic Instabilities

For configurations relevant to transverse electromagnetic instabilities, two independent energy constants are derived within the framework of the fully nonlinear Vlasov-Maxwell equations. It is assumed that the spatial variation in equilibrium and perturbed quantities is perpendicular to a uniform external magnetic field B0. The case B0 = 0 is not excluded, and the spatial variations may be one-or two-dimensional. The energy constants, which are applicable in both the stable and unstable regimes, exhibit precisely how the energy is partitioned between the fields and the individual components of plasma kinetic energy perpendicular and parallel to the propagation direction. The corresponding constants at the quasilinear level of description are also examined.