Wave propagation in a hot nonuniform magnetized plasma

A differential equation for small amplitude wave propagation in a hot nonuniform magnetized plasma is derived from the Vlasov equation by a perturbation expansion in the smallness of the Larmor radius compared to characteristic scale-lengths of the plasma. This equation is developed primarily to study the effects of strong plasma nonuniformities on propagation of waves which have counterparts in a uniform magnetized plasma. It consistently incorporates collisionless Landau-cyclotron damping effects in the wave propagation and is valid for wavelengths comparable to the scale-lengths of nonuniformities. Other features explicitly included in the equation are: (i) multiple ion species and (ii) weak nonlinear effects. An ordering has been established to evaluate the relative importance of finite Larmor radius effects and nonlinear effects.