Coherence of Ion Cyclotron Resonance in Damped Ion Cyclotron Waves in Space Plasmas

Ion cyclotron resonance is one of the fundamental energy conversion processes through field-particle interaction in collisionless plasmas. However, key evidence for ion (i.e., coherence between electromagnetic fields and phase space density) resulting damping waves (ICWs) has not yet been directly observed. Investigating high-quality measurements plasmas by Magnetospheric Multiscale (MMS) satellites, we find that both wave field vectors bulk velocity disturbed distribution rotate around background magnetic field. Moreover, absolute gyro-phase angle difference center fluctuations functions electric falls range (0, 90) degrees, consistent with ongoing from wave-fields to particles. By invoking plasma kinetic theory, demonstrate correlation our theoretical model matches well observations. Furthermore, ($\delta \mathbf{E'}_{\mathrm {wave,\perp}}$), current density \mathbf{J}_\mathrm {i,\perp}$) transfer rate {i,\perp}\cdot \delta {wave,\perp}}$) exhibit quasi-periodic oscillations, integrated work done on ions are positive, indicates mainly energized perpendicular component via resonance. Therefore, combined analysis MMS observations theory provides direct, thorough, comprehensive ICW