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

Abstract

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 = 6.5 and 4.5. We show that, analogous to the local diffusion coefficients, bounce-averaged momentum diffusion coefficients play a dominant role for pitch angles α above a critical angle α c , namely, 〈 D pp 〉 > | 〈 D p α 〉 | > 〈 D α α 〉 . We also demonstrate that for a Gaussian distribution of wave normal angle θ ( X = tan θ ), diffusion coefficients are sensitively dependent on the peak X m . As X m increases, 〈 D pp 〉 and 〈 D α α 〉 are found to increase in cases of interest: X m = tan 25 ∘ , tan 45 ∘ and tan 65 ∘ . We have estimated wave amplitudes for particular stochastic acceleration timescale for 1 MeV electrons and found that the required wave amplitudes B te ∼ 86 to ∼ 170 pT for a timescale τ = 1 day . 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).