Abstract
We perform a statistical study of 3-s ultra-low frequency (ULF) waves
using MMS observations in the Earth’s foreshock region. The average
phase velocity in the plasma rest frame is determined to be
anti-sunward, and the intrinsic polarization is right-handed. We further
examine the linear instability conditions based on drift-bi-Maxwellian
distribution functions according to observed plasma conditions. The
resulting instability is a solution to the common dispersion equation of
the ion/ion right-hand non-resonant and left-hand resonant
instabilities. The predicted wave propagation is also predominantly
anti-sunward. The cyclotron resonant conditions of the solar wind and
backstreaming beam ions are evaluated, and we find that in some cases,
the anti-sunward propagating waves can be resonant with beam ions, which
was overlooked in previous studies. The result suggests that the
dispersion equation provides the 3-s ULF waves a fundamental explanation
that unifies a rich variety of resonant conditions. In the later stage,
the 3s ULF waves could further develop into Short Large Amplitude
Magnetic Structures, contributing to the turbulence in the foreshock
region.