Quantifying the Effect of Strong Subpacket Structure in VLF Chorus Rising Tones on Radiation Belt Acceleration

Abstract:

Associated with injections of 10s keV electrons into the inner magnetosphere (L ~ 4), strong (|Bw| ~ 1nT; |Ew| ~ 0.03 V/m), long duration (~10 ms) subpacket structure is seen in Van Allen Probes EMFISIS burst mode observations of VLF chorus rising tones (cf. Figure, Panels A, B and D). The strongest subpackets are seen at wave frequencies (f) very near 1⁄4 of the local electron gyrofrequency (f_ce) and are associated with a pronounced steepening of df/dt, the rate of increase of wave frequency with time (cf. Panels A and D; df/dt reaches ~20 Hz/ms in the strongest subpackets). On a wave cycle by wave cycle basis we examine both cyclotron and Landau energy gain for seed electrons with 50 keV – 10 MeV initial energies in non-linear interactions with the obliquely-propagating VLF waves. Maximum energy gain of 5-10 keV/wave cycle occurs for electrons with 1-2 MeV initial energy resulting in a 200 keV – 500 keV total energy increase for electrons resonant with the waves throughout the single subpacket (Panel C). Contributions from cyclotron (n=1) and Landau (n=0) effects are of similar magnitude in these strong subpackets, with Landau effects of the wave electric field perpendicular to B the largest contributor (Panel C). Whistler mode group velocity maximizes at ¼ f_ce and a simple model addresses the build-up of wave amplitude and the steepening of df/dt around ¼ f_ce.