Interaction between electrostatic whistlers and electron holes in the auroral region

Electron holes have been discovered in several key regions of the magnetosphere in the past few years. These small-scale structures seem to play an important role in the global dynamics of the magnetosphere, being most often associated with parallel electron beams and strong ion heating, as shown by the Fast Auroral Snapshot (FAST) spacecraft in the auroral region. Electrostatic whistler waves (EWW) in the VLF frequency range are often associated with these electron holes, suggesting that the generation of whistler waves is related to the holes. We present a model of the interaction between EWW and electron holes. Our analysis is based on the mechanical description of the energy exchange between particles and waves; by the use of the Hamiltonian formalism, action-angle variables, and canonical perturbation theory, we show that trapped electrons, owing to their periodic motion in the potential structure of the electron hole, enter into a resonance with the wave and can destabilize it at large parallel phase velocity relative to the electron thermal velocity. We derive the growth rate of EWW and compare our model with previous ones. Application to FAST observations shows that this linear instability is able to generate EWW with a normalized growth rate γ/ω varying from a few percents at low frequency (above the lower-hybrid frequency) up to ∼10% at higher frequency (below the electron plasma frequency).