A Statistical Examination of Interactions Between 1-Hz Whistler Waves and Ions in the Earth's Foreshock

Abstract

The 1 Hz whistler wave precursors attached to shock-like structures are often observed in the foreshock. Using observations from the Magnetospheric Multiscale mission, we investigate the interactions between 1 Hz waves and ions. Incoming solar wind ions do not cyclotron-resonate with the wave, since typically the wave is right-handed in their frame. We demonstrate that solar wind ions commonly exhibit 180° gyro-phase bunching from the wave magnetic field, understanding it with a reconciled linear theory and non-linear trapping theory for non-cyclotron-resonant modulations. Along the longitudinal direction, solar wind ions experience Landau resonance, exhibiting either modulations at small wave potentials or trapping in phase-space holes at large potentials. The results also improve our understanding of foreshock structure evolution and 1 Hz wave excitation. Shock-like structures start with having incoming solar wind and remotely reflected ions from further downstream. The ion-scale 1 Hz waves can already appear during this stage. The excitation may be due to shock-like dispersive radiation or kinetic instabilities resonant with these remotely reflected ions. Ions reflected by local shock-like structures occur later, so they are not always necessary for generating 1 Hz waves. The wave leads to ion reflection further upstream, which may cause reformation of shock-like structures. In one event, locally reflected ions exhibit non-cyclotron-resonant modulation in the early stage, and later approach the anomalous cyclotron resonant condition with gyro-phases ∼270°. The latter is possibly due to nonlinear trapping in regions with an upstream-pointing magnetic field gradient, linked to reformation. Some additional special features, such as frequency dispersions, are observed, encouraging further investigations.