Statistical Analysis of Whistler Precursors Upstream of Foreshock Transient Shocks: MMS Observations

Using the high-time-resolution data from the Magnetospheric Multiscale mission, precursor waves upstream of foreshock transient (FT) shocks are statistically investigated using the four-spacecraft timing method. The wave frequencies and wave vectors determined in the plasma rest frame (PRF) are shown to follow the cold plasma dispersion relation for whistler waves. Combining with the feature of the right-hand polarization in the PRF, the precursors are identified as whistler-mode waves around the lower hybrid frequency. The occurrence of whistler precursors is independent of the Alfv & eacute;n Mach number and the FT shock normal angle. More importantly, all the whistler precursors have group velocities pointing upstream in the shock frame, suggesting the dispersive radiation to be a possible generation mechanism. The study improves the understanding of not only the whistler precursors but also the overall FT shock dynamics. The characteristics of the precursor waves upstream of foreshock transient (FT) shocks are determined in the plasma rest frame using the multi-point measurements from the Magnetospheric Multiscale mission with appropriate separation scales. The statistical results demonstrate for the first time that the precursors upstream of FT shocks are lower hybrid frequency whistler-mode waves. The presence or absence of large amplitude whistler precursors does not depend on the FT shock normal angle and the Alfv & eacute;n Mach number. These results have important implications on the nature of the whistler precursors and the dynamics of the FT shocks. Precursor waves upstream of foreshock transient shocks are found to follow the whistler wave dispersion relation in the plasma rest frame The occurrence of whistler precursors is independent of the Alfv & eacute;n Mach numbers and normal angles of the foreshock transient shocks The observed wave characteristics are consistent with that the precursors are generated through the dispersive radiation mechanism