Self-adjoint formulation of plasma heating in the ion-cyclotron range of frequencies

It is shown that second-order (ρ/L) corrections in the expression for the equilibrium distribution function are required to obtain a self-adjoint system of equations for ion cyclotron range of frequencies (ICRF) wave propagation in a nonuniform plasma (ρ denotes the ion-Larmor radius and L the gradient scale length). Self-adjointness results in energy conservation in the absence of absorption mechanisms, as expected. A Lagrangian density is obtained, which yields both the wave operator and its adjoint, and directly results in the conservation law of the truncated system.