Wave energy flow conservation for propagation in inhomogeneous Vlasov- Maxwell equilibria

~ave energy flow conservation is demonstrated for Hermitian differential operators that arise m the Vlasov-Maxwell theory for propagation perpendicular to a magnetic field. The energy fl~w can be related ~o the. bilinear concomitant, for a solution and its complex conjugate, by usmg the Lagrange Identity ofthe operator. This bilinear form obeys a conservation law and is shown to describe the usual Wentzel-Kramers-Brillouin (WKB) energy flow for asympt?tic~lly. homogeneous regions. The additivity and lack of uniqueness of the energy flow expressIOn IS dISCUSsed for a general superposition of waves with real and complex wavenumbers. Furthermore, a global energy conservation theorem is demonstrated for an inhomogeneity in one dimension and generalized reflection and transmission coefficients are thereby obtained.