Sub-ion scale current sheets in kinetic Alfvén wave turbulence

TL;DR

The paper demonstrates that fully kinetic 3D PIC simulations initiated from KAW eigenvectors generate sub-ion scale current sheets with thicknesses that scale as $(m_e/m_i)^{-1/2}$ and cluster around the electron skin depth $d_e$, while widths and lengths scale more weakly with mass ratio. Using BFS and DBSCAN to identify sheets, and PCA/convex hull analyses to measure dimensions, the study shows robust, mass-ratio dependent intermittency (scale-dependent kurtosis) and dissipation concentrated in high-current-density regions via J·E' and Pi-D channels, consistent with solar wind observations. The work provides a quantitative link between turbulent KAW cascades and electron-scale dissipation, validating the role of sub-ion current sheets in energy conversion and heating in kinetic plasmas. Limitations include the use of reduced mass ratios and the absence of tearing at realistic ratios, pointing to future work to explore tearing, reconnection, and kinetic instabilities at true electron scales.

Abstract

3D kinetic particle-in-cell (PIC) simulations are performed using the kinetic Alfvén wave (KAW) eigenvector relations from a two-fluid model as initial conditions, in order to study turbulent fluctuations and intermittent structures at sub-ion and electron scales. Simulations with different ion-to-electron mass ratios are set up to investigate the role of electron scales in the formation of intermittent structures. We analyze the current sheet structures that develop in these simulations. Two algorithms, namely Breadth-First Search (BFS) and Density-Based Spatial Clustering of Applications with Noise (DBSCAN), are employed to determine the thickness, length, and width of the current sheets, and both methods are found to yield consistent results. The average current sheet thickness scales inversely with the square root of the ion-to-electron mass ratio, with values close to the electron skin depth ($d_e$), indicating the presence of electron-scale current sheets in the simulations. The widths and lengths of the current sheets show a weaker scaling with the mass ratio. The scale-dependent kurtosis reveals enhanced intermittency at electron scales, consistent with magnetosheath observations. Distributions of scale-dependent properties of the current sheets also align with the electron skin depth of the different simulations and they lie within ranges observed in kinetic scale solar wind turbulence. This study reveals the nature of sub-ion-scale current sheets in KAW turbulence and their role in dissipation.

Figures (12)

• Figure 1: $\delta B_{rms}/B_0$ (left) and $\delta J_{rms}^2$ (right) evolving with time for $S0$ (red), $S1$ and (blue) $S2$ (green) simulations.
• Figure 2: Magnetic spectrum in perpenducular wavevector $k_{\perp}d_i$ at $\omega _{p,i}t=0, 600$ and $1800$ for (a) $S0$, (b) $S1$ and (c) $S2$ simulation (top panel). Bottom panel shows the ratios (d) $\delta B_{\parallel}/\delta B$, (e) $\delta B_{\perp}/\delta B$ and (f) $\delta E/\delta B$ w.r.t $k_{\perp}d_i$ at $k_zd_i=0.314$, from $S2$ simulation, analytical results of KAW(black) and whistler wave(magenta).
• Figure 3: Current density $J_z$ in $x-y$ plane at $\omega _{p,i}t=600$ for S0 (a,b,c), S1(d,e,f) and S2(g,h,i) simulations. The current sheets identified with both BFS (middle panel) and DBSCAN (right panel) are shown in black clusters. The white cross lines shows the maxima of each cluster and solid red lines indicate the thickness of the identified clusters.
• Figure 4: Current density $J_z$ structures in 3D at $\omega _{p,i}t=700$ for S0 ($m_r=25$), S1 ($m_r=50$) and S2 ($m_r=100$) simulations identified with BFS algorithm (top) and DBSCAN (bottom).
• Figure 5: Visualization of an isolated current sheet identified using BFS with the maximum current density point marked by a red sphere; (a) shows the thickness with a black line and (b) shows the width with a magenta line and the length with a blue dotted line.