Pitch angle and energy diffusion coefficients from resonant interactions with ion-cyclotron and whistler waves

General relations for quasi-linear diffusion coefficients in pitch angle and energy are applied to resonant particle interactions with ion-cyclotron and whistler waves. Expressions for the diffusion coefficients, valid for any distribution of wave energy with frequency and wave normal angle, are derived and normalized to be independent of the ambient magnetic field intensity and the electron density. The results illustrate how resonant particle diffusion rates vary with pitch angle and energy, and how the diffusion rates depend upon the distribution of wave energy.