A statistical study of three-second foreshock ULF waves observed by the Magnetospheric Multiscale mission

Shan Wang,Naoki Bessho,Barbara L Giles,Shing F Fung,Daniel J Gershman,Jonathan Ng,Guan Le,Li-Jen Chen

doi:10.1063/5.0055972

Abstract

We perform a statistical study of 3-s ultra-low frequency (ULF) waves using Magnetospheric Multiscale 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 the drift-bi-Maxwellian distribution functions according to the 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 study suggests that the dispersion equation provides the 3-s ULF waves a fundamental explanation that unifies a rich variety of resonant conditions.

Highlights

Upstream of the Earth’s quasi-parallel bow shock, energetic ions reflected from the shock form an ion foreshock region (Eastwood, 2005a)
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
We have performed a statistical analysis of 3 s ultra-low frequency (ULF) waves to gain a better understanding of the wave generation mechanism and the responsible instability

Summary

INTRODUCTION

Upstream of the Earth’s quasi-parallel bow shock, energetic ions reflected from the shock form an ion foreshock region (Eastwood, 2005a). The propagation direction of the 3 s wave is determined from the Minimum Variance Analysis (MVA) of MMS 1 magnetic field during 07:08:13–07:09:32 UT as [À0.818, À0.517, 0.073] GSE, and the 180 ambiguity from MVA is solved by comparing the order of observed waveforms by multiple spacecraft. The mode propagating sunward in the same direction with the beam ions [Fig. 2(d)] is right-hand and resonant with beam ions as the solution to Eq (1þ) (not shown) It has a similar maximum growth rate with that propagating in the same direction with the SW ions, supporting the co-existence of 30 s ULF wave that is left-hand propagating in the same direction with the SW ions in the SCF and right-hand propagating in the same direction with the beam ions in the PRF

STATISTICAL ANALYSES OF 3 s ULF WAVES

Procedures for the statistical analysis

Statistical results

CONCLUSIONS AND DISCUSSIONS