Reconnection-Driven Turbulent Fluctuations in the Magnetically Dominated Collisionless Regime

TL;DR

This work analyzes how magnetic reconnection in magnetically dominated, collisionless plasmas generates turbulent fluctuations across kinetic scales. Using large-scale 3D PIC simulations that resolve from system size down to the electron inertial length $d_e$, the authors compute second- and higher-order structure functions for velocity and magnetic fields along three principal directions in the reconnection layer. They find a near-Kolmogorov velocity cascade with slope $1/3$ and a steeper magnetic cascade with slopes in the range $0.6$–$0.8$, with strong intermittency in the magnetic field, especially along the outflow, and a guide field that increases anisotropy and suppresses magnetic amplitude while leaving velocity scaling largely unchanged. These results illuminate how reconnection energy conversion cascades across scales and has implications for heating and particle acceleration in high-energy astrophysical plasmas, highlighting the crucial role of guide-field strength in shaping turbulence statistics.

Abstract

Magnetic reconnection is a fundamental plasma process that converts magnetic energy into bulk flow energy, thermal energy, and nonthermal particle acceleration. Despite its importance, the statistical properties of the turbulent fluctuations generated by collisionless reconnection, which are essential for understanding how this energy conversion proceeds, remain poorly understood. Here, we employ large-scale 3D particle-in-cell simulations to investigate the turbulence characteristics of velocity and magnetic field fluctuations generated by collisionless reconnection in a magnetically dominated plasma. We characterize their statistical properties by computing structure functions along different directions within the reconnection layer. We find that the square root of the second-order velocity structure function follows a power-law scaling with a slope near $\sim1/3$ at intermediate to large scales, consistent with Kolmogorov-like turbulence, a behavior robust along the inflow, outflow, and guide-field directions. The square root of the second-order magnetic structure function consistently exhibits a steeper slope, in the range $\sim 0.6 - 0.8$. The presence of a finite guide field does not systematically modify the slope of the velocity fluctuations, while it progressively steepens the scaling of the magnetic fluctuations in the guide-field and inflow directions. We also measure higher-order structure functions, which reveal strong magnetic intermittency along the outflow direction and weaker intermittency in the inflow and guide-field directions. In addition, the local anisotropies of both velocity and magnetic field fluctuations are greater for stronger guide fields. These results provide a first systematic characterization of the multiscale nature of turbulence in collisionless reconnection layers, with important implications for plasma heating and particle acceleration.

Figures (10)

• Figure 1: Velocity slices (top two rows) and magnetic field slices (bottom two rows), respectively, taken at the $z$ location where the flux ropes are visually most prominent, and taken at the center of the $y$ axis. The left panels do not include a guide field, whereas the middle and right panels include a guide field of strength $B_g=0.3B_0$ or $B_g=B_0$ (oriented along the $z$-axis), respectively. $\rho=n_0m$ is the mass density and $\pmb{B}_g=B_g\hat{z}$.
• Figure 2: Top and middle panels: Square root of the second-order structure function (SF) for the velocity (red) and magnetic field (blue). The SF is computed for separations along the $z$-axis at each position $(x,y_{\rm mid})$, where $y_{\rm mid}$ denotes the midpoint in $y$ for each $x$ within the reconnection region. The resulting ${\rm SF}(x, y_{{\rm mid}}, \Delta z)$ are then averaged over all $x$ values, denoted as $\langle{\rm SF}(\Delta z)\rangle_{x,y_{\rm mid}}$. The shaded area represents the standard deviation. The black dashed line indicates the expected slope for Kolmogorov-type fluctuations. Left panels show results without a guide magnetic field; the middle and right panels include guide fields $B_g=0.3B_0$ and $B_g=B_0$, respectively. Bottom panel: The distribution of the $\sqrt{{\rm SF}(x, y_{\rm mid},\Delta z)}$'s slope. The slope is fitted over separations in the range 2–30$d_e$. The red and blue dashed lines represent the mean slopes for the velocity's and magnetic field's structure function, respectively.
• Figure 3: Top and middle panels: Square root of the second-order structure function (SF) for the velocity (red) and magnetic field (blue). The SF is computed for separations along the $x$-axis at each position $(y, z)$. The resulting ${\rm SF}(\Delta x,y,z)$ are then averaged over all $y$ and $z$ values, denoted as $\langle{\rm SF}(\Delta x)\rangle_{y,z}$. The shaded area represents the standard deviation. The black dashed line indicates the expected slope for Kolmogorov-type fluctuations. Left panels show results without a guide magnetic field; the middle and right panels include guide fields $B_g=0.3B_0$ and $B_g=B_0$, respectively. Bottom panel: The distribution of the $\langle{\rm SF}(\Delta x,y)\rangle_z$'s slope. The slope is fitted over separations in the range 2–30$d_e$. The red and blue dashed lines represent the mean slopes for the velocity's and magnetic field's structure function, respectively.
• Figure 4: Top and middle panels: Square root of the second-order structure function (SF) for the velocity (red) and magnetic field (blue). The SF is computed for separations along the $y$-axis at each position $(x, z)$. The resulting ${\rm SF}(\Delta y,x,z)$ are then averaged over all $x$ and $z$ values, denoted as $\langle{\rm SF}(\Delta y)\rangle_{z,x}$. The shaded area represents the standard deviation. The black dashed line indicates the expected slope for Kolmogorov-type fluctuations. Left panels show results without a guide magnetic field; the middle and right panels include guide fields $B_g=0.3B_0$ and $B_g=B_0$, respectively. Bottom panel: The distribution of the $\langle{\rm SF}(\Delta y, x)\rangle_z$'s slope. The slope is fitted over separations in the range 2–30$d_e$. The red and blue dashed lines represent the mean slopes for the velocity's and magnetic field's structure function, respectively.
• Figure 5: Mean slopes of $\sqrt{{\rm SF}({x,y_{\rm mid}, \Delta z)}}$ (left), $\sqrt{{\rm SF}(\Delta x,y,z)}$ (middle), $\sqrt{{\rm SF}( x,\Delta y,z)}$ (right) as a function of the guide field strength. The slope is fitted over separations in the range 2–30$\, d_e$. The black dashed line indicates the expected slope for Kolmogorov-type fluctuations, $1/3$, while the black dotted-dashed line indicates the slope $2/3$.