Bounce-averaged diffusion coefficients for superluminous wave modes in the magnetosphere

In this study, we present a first evaluation of bounce-averaged diffusion coefficients of superluminous wave (R-X and L-O) modes at two locations: L=6.5L=6.5 and 4.5. We show that, analogous to the local diffusion coefficients, bounce-averaged momentum diffusion coefficients play a dominant role for pitch angles αα above a critical angle αcαc, namely, 〈Dpp〉>|〈Dpα〉|>〈Dαα〉〈Dpp〉>|〈Dpα〉|>〈Dαα〉. We also demonstrate that for a Gaussian distribution of wave normal angle θθ (X=tanθ), diffusion coefficients are sensitively dependent on the peak XmXm. As XmXm increases, 〈Dpp〉〈Dpp〉 and 〈Dαα〉〈Dαα〉 are found to increase in cases of interest: Xm=tan25∘, tan45∘ and tan65∘. We have estimated wave amplitudes for particular stochastic acceleration timescale for 1 MeV electrons and found that the required wave amplitudes Bte∼86Bte∼86 to ∼170pT for a timescale τ=1day. These results indicate that superluminous wave modes may have a significant potential for both stochastic acceleration of trapped electrons (with higher pitch angles) and loss process of untrapped electrons (with smaller pitch angles).