A statistical examination of ion dynamics at 1-Hz whistler waves in the
Earth's foreshock
Abstract
The 1-Hz whistler wave precursor attached to shock-like structures are
often observed in foreshock. Using observations from the Magnetospheric
Multiscale mission, we investigate the interactions between 1-Hz waves
and ions. Incoming solar wind ions do not gyro-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 picture
for non-resonant ions and non-linear trapping theory of anomalous
resonance. 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. In one event, locally-reflected ions exhibit
anomalous resonance in the early stage, and later approach to the
gyro-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 like frequency dispersions are observed,
requiring better explanations in the future.