Nonlinear Wave-Particle Interactions with a Whistler Precursor Upstream of an Interplanetary Shock

On January 8, 2018, a relatively weak quasi-perpendicular interplanetary shock was observed by the four spacecraft of NASA’s Magnetospheric Multiscale (MMS) mission. The shock had an Alfvén Mach number of $2.4 \pm 0.3$, and the shock normal was oriented at $(64 \pm 7)^\circ$ to the background magnetic field. A high-amplitude whistler precursor, with magnetic field perturbations up to 0.25 of the background field, was detected upstream of the shock. Due to its large amplitude and slightly oblique propagation (wave vector $\mathbf{k}$ at $15^\circ$ to the magnetic field), the precursor exhibits a significant parallel electric field component. The associated wave potential traps and modulates core electrons (below 100 eV) on spatial scales comparable to the precursor wavelength ($\sim$150 km). Modulation of the electron core distribution induces a positive slope in the parallel distribution function $f(v_{//})$ and a corresponding current. Using a 1D linear kinetic model, we find that the electron distribution is unstable to an electron-acoustic mode. The model’s dispersion relation matches that of the observed broadband electrostatic waves propagating predominantly parallel to the background magnetic field, as determined via phase differencing of electric field data from the MMS4 antennas. The fully kinetic particle-in-cell (PIC) code VPIC reproduces localized spikes in the parallel electric field, characteristic of nonlinear wave–particle interactions. This reveals a previously unreported mechanism where nonlinear processes upstream drive electron trapping and generate electron-acoustic waves. It raises important questions about how coherent wave structures regulate energy redistribution and electron thermalization.