Quantifying Wave–Particle Interactions in Collisionless Plasmas: Theory and Its Application to the Alfvén-mode Wave

Abstract

Wave–particle interactions can induce energy transfer at different timescales in collisionless plasmas, which leads to the reshaping of the particle velocity distribution function. Therefore, how to quantify wave–particle interactions is one of the fundamental problems in the heliosphere and in astrophysical plasmas. This study proposes a systematic method to quantify linear wave–particle interactions based on the Vlasov–Maxwellian model. We introduce energy transfer rates with various expressions by using perturbed electric fields and perturbed particle velocity distribution functions. Then, we use different expressions of the energy transfer rate to perform a comprehensive investigation of wave–particle interactions of the Alfvén-mode wave. We clarify the physical mechanisms responsible for the damping of the Alfvén-mode wave in wavevector space. Moreover, this study exhibits for the first time evident signatures of wave–particle interactions between Alfvén-mode waves and resonant/nonresonant particles in the velocity space. These resonant and nonresonant particles can induce energy transfer in opposite directions, which leads to self-regulation of the particle velocity distribution function. Furthermore, this study exhibits a comprehensive dependence of wave–particle interactions of the Alfvén-mode wave on the wavenumber and plasma beta (the ratio between the plasma thermal pressure and the magnetic pressure). These results illustrate that the proposed method would be very useful for quantifying different types of linear wave–particle interactions of an arbitrary wave mode.