Calculating Quasi-Linear Diffusion Rates Using Different Methods to Specify the Wave Spectrum

Quasi-linear diffusion theory is widely used in radiation belt modeling to describe resonant interactions between charged particles and electromagnetic waves. The diffusion rates depend on the wave spectrum and properties of the background plasma. For decades many studies have used variations of a longstanding method to specify the wave spectrum. Recently, a new method was proposed, and it was suggested the resulting diffusion rates can differ by orders of magnitude. Large differences in the diffusion rates would cause significant changes in the relativistic electron flux predicted by radiation belt models. We calculate quasi-linear diffusion rates using three methods to specify the wave spectrum: two variations of the longstanding method and the new method. All three methods have the same wave power at each frequency, but the weighting of wave energy with respect to wave normal angle is different. We use input parameters typical of wave observations in the inner magnetosphere, including lower band and upper band chorus, hiss waves, electromagnetic ion cyclotron waves and fast magnetosonic waves. We find very small differences between the new method and the method used to calculate diffusion rates for the British Antarctic Survey Radiation Belt Model. We conclude that the uncertainties in modeling global variations in the radiation belts are more likely due to statistical sampling of wave data, rather than the method of calculating diffusion rates.