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, the key evidence for ion cyclotron resonance (i.e., the coherence between electromagnetic fields and the ion phase-space density) and the resulting damping of ion cyclotron waves (ICWs) has not yet been directly observed. Investigating the high-quality measurements of space plasmas by the Magnetospheric Multiscale (MMS) satellites, we find that both the wave electromagnetic field vectors and the bulk velocity of the disturbed ion velocity distribution rotate around the background magnetic field. Moreover, we find that the absolute gyrophase angle difference between the center of the fluctuations in the ion velocity distribution functions and the wave electric field vectors falls in the range of (0, 90)°, consistent with an ongoing energy conversion from wave fields to particles. By invoking plasma kinetic theory, we demonstrate that the field–particle correlation for the damped ICWs in our theoretical model matches well with our observations. Furthermore, the wave electric field vectors ( δEwave,⊥′ ), ion current density (δ J i,⊥), and energy transfer rate ( δJi,⊥·δEwave,⊥′ ) exhibit quasiperiodic oscillations, and the integrated work done by the electromagnetic field on the ions is positive, indicating that ions are mainly energized by the perpendicular component of the electric field via cyclotron resonance. Therefore, our combined analysis of MMS observations and kinetic theory provides direct, thorough, and comprehensive evidence for ICW damping in space plasmas.