Van Allen Probes observation of a 360\textdegree phase shift in the flux modulation of injected electrons by ULF waves

We present Van Allen Probe observation of drift-resonance interaction between energetic electrons and ultralow frequency (ULF) waves on 29 October 2013. Oscillations in electron flux were observed at the period of \~450 s, which is also the dominant period of the observed ULF magnetic pulsations. The phase shift of the electron fluxes (\~50 to 150 keV) across the estimated resonant energy (\~104 keV) is \~360\textdegree. This phase relationship is different from the characteristic 180\textdegree phase shift as expected from the drift-resonance theory. We speculate that the additional 180\textdegree phase difference arises from the inversion of electron phase space density (PSD) gradient, which in turn is caused by the drift motion of the substorm injected electrons. This PSD gradient adjusts the characteristic particle signatures in the drift-resonance theory, which indicates a coupling effect between the magnetotail and the radiation belt and helps to better understand the wave-particle interaction in the magnetosphere.