Nonlinear wave interaction in an inhomogeneous magnetized Vlasov-Poisson plasma

The first and second order dielectric functions are calculated for an inhomogeneous magnetized Vlasov-Poisson plasma. The expression derived for the linear dielectric function generalizes previous results by including higher order terms in the background inhomogeneity. The corresponding quadratic response function is derived in a form exhibiting the Manley-Rowe symmetry when resonant wave-particle interactions are neglected. Particularly interesting applications of these results would be the inclusion of modes which only exist in the presence of the inhomogeneity (like the various drift modes) in the nonlinear theory.