Fig. 1: Comparison of electron pitch-angle transport caused by wave-driven Landau resonant trapping to transport caused by diffusion.

a Observed precipitation caused by Landau resonant interaction with whistler-mode waves. The initial electron (of approximately 10 keV) has a pitch angle α outside the loss cone, corresponding to a large radius of gyration (blue) around the magnetic field line (white curve). But after resonant trapping and acceleration (to 60–150 keV) by whistler-mode waves (purple) observed at Time History of Events and Macroscale Interactions during Substorms (THEMIS) spacecraft on a near-equatorial orbit (cyan curve), the electron’s pitch angle enters the loss cone (yellow) and it is precipitated (red) toward the atmosphere, as observed by Electron Losses and Fields Investigation (ELFIN) spacecraft on a low-altitude polar orbit (green curve). b Normalized electron phase space density profiles (solid curves) from within the loss cone (yellow range, of maximum pitch angle α_LC) to outside it, for weak (grey) and strong (black) diffusion by waves. The electron phase space density within the loss cone remains much smaller than (for weak diffusion) or at most equal to (for strong diffusion) the phase space density of trapped electrons immediately outside the loss cone. c Same as (b) but for Landau resonant nonlinear trapping by intense oblique waves, leading to loss cone overfilling (red) with higher electron phase space density (solid curve) within the loss cone than immediately outside it, and faster electron losses than for strong diffusion.