Efficient approximations of quasi-linear diffusion coefficients in the radiation belts

[1] Combined pitch angle and energy diffusion are key ingredients in current models of radiation belt electron dynamics. Bounce-averaged quasi-linear diffusion coefficients can be approximated with a recently developed approach based on the ranges of wave normal angle compatible with cyclotron and Landau resonance within a prescribed wave frequency band, as has been demonstrated for a model of chorus waves. The method casts nested, multiple integrals over wave normal angle as a single weighted average, which is further approximated by evaluation at only a few, carefully chosen points. Here, the method is shown to agree well with results for more recent models of chorus, electromagnetic ion cyclotron waves, and whistler mode hiss. Highly oblique magnetosonic waves are also considered, and a related approach is developed which is shown to give a good approximation for their diffusion rates.