Tearing Driven Reconnection: Energy Conversion Involving Firehose Kinetic Instabilities (2D Hybrid Möbius Simulations)

Abstract

This study focuses on energy conversion related to tearing-driven magnetic reconnection in the context of weakly collisional astrophysical plasmas. We present results from a two-dimensional hybrid particle-in-cell simulation employing novel periodic conditions with a topology akin to the Möbius strip, which double the computation efficiency as compared to regular periodic conditions. Evaluation of the ion electric work rate ($\mathbf{j}_i \cdot \mathbf{E}$) and pressure strain interaction ($\mathbf{P}_i : \mathbf{\nabla u}_i)$ shows that most of the energy conversion occurs during the nonlinear phase of the instability, where magnetic energy is transferred towards ion kinetic energy (bulk outflows) and internal energy (heating). These energy conversion rates are of the same order but inhomogeneous. Heating predominantly occurs within the magnetic islands, while near the X-points, nearly the same amount of magnetic energy is transferred to bulk plasma flow and heating. The reconnected plasma moreover exhibits an ion temperature higher parallel than perpendicular to the local magnetic field $\mathbf{B}$. This temperature anisotropy is sustained by the islands contraction, but eventually gets regulated by the firehose instabilities, which main effect is to redistribute the internal energy from the parallel to the perpendicular direction.

Figures (13)

• Figure 1: Schematic views of the simulation domain and associated Möbius boundary conditions. (a): 2D simulation domain, with the initial magnetic field $\bm{B}_0$ depicted by blue arrows. The boundaries are periodic in $x$, and have Möbius periodic conditions in $y$. The positions of a particle (with velocity indicated by the black arrow) exiting and re-entering the domain are depicted by purple cells for the $x$ boundary and red cells for the $y$ boundary. (b): Reversal of the magnetic field vector along a Möbius strip.
• Figure 2: Temporal evolution of the magnetic field fluctuations within the current sheet, and plasma variations averaged over the domain. Panel (a) shows the evolution of the magnetic field component $B_y$ in the center of the current sheet, as function of the wave number $k_x \, d_i < 1.6$. Colors indicate the amplitude of $|B_y (y=0)/B_0| (k_x)$ decomposed over $k_x$ using a fast Fourier transform (FFT) in the $x$ direction along the current sheet center. Panel (b) shows the, spatially averaged, variations of the magnetic field $\bm{B}$, plasma bulk velocity $\bm{u}$, and current density $\bm{j}$. The vertical dashed black line ($t = 400 \; \Omega_{ci}^{-1}$) indicates the transition from the linear to non-linear tearing instability.
• Figure 3: Linear growth rates of the tearing instability and examples of some associated magnetic perturbations evolution. Panel (a) provides the temporal evolution of $|B_y (y=0)| (k_x)$ (decomposed using a FFT) for three wavenumbers $k_x \, d_i = 0.02$ (plain curve), $k_x \, d_i = 0.07$ (dashed curve) and $k_x \, d_i = 0.25$ (dotted curve). The two black vertical dashed lines indicate the time interval considered for the linear growth rates estimation $\gamma$, between $t = 250 \, \Omega_{ci}^{-1}$ and $t = 400 \, \Omega_{ci}^{-1}$. Panel (b) gives $\gamma / \Omega_{ci} (k_x \, d_i)$, estimated from $|B_y (y=0)| (k_x)$ decomposed using: a regular FFT (blue), the Welch method (orange) and wavelets (green).
• Figure 4: Global magnetic field evolution during the non-linear stage of the tearing instability. Panels (a), (b) and (c) display, in color, the magnetic field component $B_x / B_0$ for a zoom around $y \in [-40, 40] \, d_i$, and at times $t = 520 \, \Omega_{ci}^{-1}$, $t = 600 \, \Omega_{ci}^{-1}$ and $t = 660 \, \Omega_{ci}^{-1}$, respectively. Grey curves are magnetic field lines, defined as isovalues of the magnetic vector potential's out-of-plane component $A_z$. Panel (d) shows $A_z (x, y=0, t)$: the temporal evolution of $A_z$ in the center of the current sheet. Positions of the principal X-points, defined as local maxima of $A_z (y=0)$, are indicated by the differently colored dotted curves.
• Figure 5: Transition of a primary reconnection X-point into a coalescence site (also reconnecting) between two merging magnetic islands. The three panels present the out-of-plane electric current density $j_z$ within the black sub-box of Figure \ref{['fig:NL_evolution_whole-box']} (a-c), and for the three same times $t = 520, \, 600$, and $660 \, \Omega_{ci}^{-1}$. The $j_z$ values have been smoothed by taking a spatial average of total lengths $d_i/2$ in the $x$ and $y$ directions around each cell.