Particle-sounding of the spatial structure of kinetic Alfvén waves

Kinetic Alfvén waves (KAWs) are ubiquitous throughout the plasma universe. Although they are broadly believed to provide a potential approach for energy exchange between electromagnetic fields and plasma particles, neither the detail nor the efficiency of the interactions has been well-determined yet. The primary difficulty has been the paucity of knowledge of KAWs' spatial structure in observation. Here, we apply a particle-sounding technique to Magnetospheric Multiscale mission data to quantitatively determine the perpendicular wavelength of KAWs from ion gyrophase-distribution observations. Our results show that KAWs' perpendicular wavelength is statistically 2.4[Formula: see text] times proton thermal gyro-radius. This observation yields an upper bound of the energy the majority proton population can reach in coherent interactions with KAWs, that is, roughly 5.76 times proton perpendicular thermal energy. Therefore, the method and results shown here provide a basis for unraveling the effects of KAWs in dissipating energy and accelerating particles in a number of astrophysical systems, e.g., planetary magnetosphere, astrophysical shocks, stellar corona and wind, and the interstellar medium.