Thermodynamics of Shear Equilibration During Magnetic Reconnection Onset in Mixed-Equilibrium Current Sheets

TL;DR

This study probes how magnetic shear and a strong guide field govern the thermodynamic response during reconnection onset in a mixed-equilibrium current sheet, using a 2D PIC simulation. The authors apply a generalized first-law framework, tracking heat density and work density alongside electromagnetic power densities to dissect the local energy exchange at the x-line. They find an early stage where magnetic pressure decreases while thermal pressure increases, driven mainly by ion compression, with electron heating showing complex, anisotropic behavior linked to parallel and perpendicular electric fields. The results reveal a two-stage equilibration of the local beta for electrons and ions and highlight strong coupling between compressive work, heat transfer, and electromagnetic energy exchange, offering mechanistic insight relevant to MMS observations of reconnection dynamics in high-guide-field environments.

Abstract

Magnetic shear across the polarity inversion line (PIL) plays an important role in the explosive nature of reconnection onset and in the equilibration of current sheets, acting as a source of free energy that can enhance or inhibit the onset process under certain conditions. In this study, we use a 2D PIC simulation to examine the local interaction between the reconnection guide field and thermodynamic variables during reconnection onset in a region of initially depleted thermal energy and enhanced magnetic energy in a large guide field background. We identify critical stages of the equilibration process, characterize intervals based on whether the pressure evolution is driven by changes in density or temperature, and discuss what these intervals imply about the evolution of local heat and work density. Finally, we examine power densities associated with electromagnetic field time evolution and electromagnetic energy transfer and compare to those related to thermodynamic changes.

Figures (4)

• Figure 1: Initial Current Sheet Equilibration via Guide Field Amplification. (a) mean $P_{tot}$, $P_M$, and $P_{th}$ profiles for a cut normal to the current sheet in black, green, and red, respectively. (b) $P_{th}$, $n$ and $T$ profiles for a cut normal to the current sheet in black, blue, and red, respectively. (c) $P_M$ and the $B_x$ and $B_y$ contributions to it for a cut normal to the current sheet in black, blue, and green, respectively. In all panels, solid lines indicate the state of the variables at $t \sim 5 \ \Omega^{-1}_{ci}$ while dotted lines indicate the initial state of the variables.
• Figure 2: The Onset Interval and X-line Pressure Evolution. (a) $P_{tot}$, $P_M$, and $P_{th}$ in the x-line reference frame (in solid black, green, and red, respectively) with horizontal dashed lines of the same color scheme indicating the initial asymptotic values of their respective variables. (b) $\partial_t P_{tot}$, $P_M$, and $P_{th}$ in the x-line frame and in black,green,and red, respectively. (c) $\beta/\beta_0$, $\beta_i/\beta_{i0}$, and $\beta_e/\beta_{e0}$ in the x-line frame, where the "$0$" subscript indicates the initial asymptotic value. (d) Electron out-of-plane current density $J_{ez}$ of the x-line just after the onset interval, with the primary x-line circled. (e-h) space vs time plots of the $P_{th}$, $P_M$, outflow component of Poynting flux $S_x$ (used to visually identify the x-line), and the $\beta/\beta_0$ along the PIL, respectively. The x-line analyzed throughout this study is also circled in panels e-h.
• Figure 3: Thermodynamic Contributions to Pressure Evolution at the X-line. Panels (a-b) show $P/P_0$, $T/T_0$, and $n/n_0$ at the x-line for electrons (a), and ions (b). Panels (c-d) show $\partial_t P$, $n\partial_t T$, and $T\partial_t n$ for electrons (c), and ions (d). Panels (e-f) show $\partial_t T$, $\partial_t T_\parallel$, and $\partial_t T_\perp$ for electrons (e) and ions (f). Regions in yellow and blue indicate intervals of $\partial_t Q>0$ and $\partial_t Q<0$, respectively for electrons (panels c and e) and ions (panels d and f).
• Figure 4: Comparison of Power Densities at the x-line. Panel (a) shows the ion and electron $\partial_tQ$,ion and electron $J_\perp E_\perp$ terms, and the time evolution of the electric field pressure perpendicular to the local magnetic field $\partial_tP_{E\perp}$ . Panel (b) shows the ion and electron $\partial_tW$ (with the axis range chosen to emphasize $\partial_tW_e$),ion and electron $J_\parallel E_\parallel$ terms, and the time evolution of the electric field pressure parallel to the local magnetic field $\partial_tP_{E\parallel}$. The diagrams on the right represent the proposed local thermodynamic processes at play in the early and late stages of reconnection onset.