Observations of Rapidly Growing Whistler Waves in Front of Space Plasma Shock due to Resonance Interaction between Fluctuating Electron Velocity Distributions and Electromagnetic Fields

The whistler-mode wave extending from the fast-magnetosonic wave branch is a fundamental perturbation of electromagnetic fields and plasmas in various environments including planetary space, laboratory, and astrophysics. The origin and evolution of the waves is a long-standing question due to the limited instrumental capability in resolving highly variable plasma and electromagnetic fields. Here, we analyze observational data with a high time resolution from the Magnetospheric Multiscale spacecraft in front of the terrestrial bow shock (e.g., foreshock). We develop a novel approach to extract the three-dimensional fluctuating electron velocity distributions (δfe(V)) from their background (fe0(V)), and have successfully captured the coherent resonance between fluctuating electrons (δfe(V)) and wavelike electromagnetic fields (δB, δE) at an unprecedentedly high frequency (>1 Hz) for investigating wave–particle interactions. We provide that the unstable whistler wave grows rapidly over a timescale that is much shorter than the proton gyro-period. Regarding the energy origin for the waves, we find the ion distributions consisting of the solar wind ion flows and the ion beams reflected from the shock play crucial roles in providing the free energy and determining the eigenmode disturbances of fields and electrons. The quantification of wave growth rate and the characterization of wave–particle interactions for the instability driver can significantly advance the understandings of wave evolution and energy conversion between multisource multispecies particles and wave electromagnetic fields