Compressible Turbulence as a Source of Particle Beams and Ion Bernstein Waves in Collisionless Plasmas

TL;DR

This work addresses the origin of proton beams and ion Bernstein waves (IBWs) in collisionless plasmas by using high-resolution simulations of compressible turbulence that span MHD to sub-ion scales. The authors demonstrate that MHD-scale dissipation via transit-time damping (TTD) naturally generates suprathermal electron and proton beams, with the proton resonant speed increasing with plasma $eta$, potentially reaching super-Alfvénic values as observed in the solar wind. At sub-ion scales, IBWs arise from intrinsic coupling with fast waves and phase steepening, aided by the turbulent cascade, providing an efficient mechanism for perpendicular heating of suprathermal protons. The results offer a unified cross-scale picture where compressible fluctuations drive energy transfer and dissipation across scales, aligning with solar wind measurements and highlighting the essential role of compressible turbulence in collisionless plasma dynamics.

Abstract

We investigate the source of particle beams and ion Bernstein waves in collisionless plasmas using a high-resolution particle-in-cell simulation of compressible turbulence. At magnetohydrodynamic (MHD) scales, compressible turbulence is damped by transit-time damping, naturally generating suprathermal electrons and proton beams. As the energy cascade reaches sub-ion scales, multiple branches of ion Bernstein waves are excited and contribute to the formation of proton suprathermal tails. Under realistic conditions such as those in the solar wind, these processes remain efficient and provide a natural explanation for the super-Alfvénic proton beams observed in situ. We show that compressive fluctuations, though often understudied, are essential for cross-scale energy transfer and dissipation in collisionless plasma turbulence.

Figures (3)

• Figure 1: Energy distribution of compressible turbulence and the evolution of particle temperatures. (a) Energy distribution of compressibleturbulence in the $k_{\perp}$–$k_{\parallel}$ space. (a1) Zoomed-in view corresponding to the red dashed box in panel (a). (b) 1D integrated PSD. (c) Temporal evolution of the electron temperature components, normalized by initial temperature. (d) The same as panel (c) but for protons. An animation for the temporal evolution of electron number density ($n_e$) is available.
• Figure 2: Dispersion relations at sub-ion scales during the interval $t = 1.51\tau_A$–$1.60\tau_A$. (a)–(c) PSD Traces of the magnetic-field, electric-field, and electron-velocity fluctuation for perpendicular propagating fluctuations ($k_{\parallel} \approx 0$). The black dashed line shows the theoretical dispersion relation of the ion Bernstein wave, the red line corresponds to the lower-hybrid wave, and the green line denotes the fast wave dispersion $\omega = k v_{f}$. (d)–(f) PSD Traces of the magnetic-field, electric-field, and electron-velocity fluctuation for parallel propagating fluctuations ($k_{\perp} \approx 0$). In panels (d)–(f), the black dashed line represents the theoretical dispersion relation of whistler waves.
• Figure 3: Particle velocity distributions corresponding to the spatial region $(x = 0$-$2d_i, y = 0$-$2d_i)$. (a) Electron 2D velocity distribution in the $v_{\parallel}$–$v_{\perp}$ space. Red crosses mark fast magnetosonic speed $v_{f}$ and resonant speed $v_{\mathrm{res}}$. (a1) Electron parallel velocity distribution, with dashed lines indicating $v_{f}$ and $v_{\mathrm{res}}$. (a2) Electron perpendicular velocity distribution. The blue histogram shows the initial distribution at $t=0$, and the red histogram corresponds to $t = 1.55\tau_A$–$1.6\tau_A$. The light red lines indicate the difference between the two histograms. (b) Proton 2D velocity distribution in the $v_{\parallel}$–$v_{\perp}$ space. Red crosses mark $v_{f}$ and $v_{\mathrm{res}}$. (b1) Proton parallel velocity distribution, with dashed lines indicating $v_{f}$ and $v_{\mathrm{res}}$. (b2) Proton perpendicular velocity distribution. The blue histogram shows the initial distribution at $t=0$, and the red histogram corresponds to $t = 1.55\tau_A$–$1.6\tau_A$. The green dashed lines represent a kappa distribution fit with $\kappa=4.2$.