A general model of particle acceleration by plasma waves coupled with adiabatic radial diffusion in a planetary magnetic field is developed. The model assumes that a spectrum of lower hybrid waves is present to resonantly accelerate ions transverse to the magnetic field. The steady state Green's function for the combined radial diffusion and wave acceleration equation is found in terms of a series expansion. The results provide a rigorous demonstration of how a quasi-Maxwellian distribution function is formed in the absence of particle collisions and elucidate the nature of turbulent heating of magnetospheric plasmas. The solution is applied to the magnetosphere of Neptune for which a number of examples are given illustrating how the spectrum of pickup N+ ions from Triton evolves. ¿ American Geophysical Union 1994