Resistive instabilities of current sheets in stratified plasmas with a gravitational field

TL;DR

This paper analyzes the linear stability of a plane slab current sheet in the presence of gravity and density stratification, focusing on how favorable and unfavorable stratification alter tearing-mode dynamics and induce a gravity-driven G-mode. Using a boundary-layer approach with outer ideal-MHD and inner resistive regions, the authors derive a dispersion relation that captures the transition from tearing to G-modes, and they confirm the predictions with numerical solutions for both linear and tanh density profiles. The key findings show that favorable stratification suppresses reconnection, while unfavorable stratification destabilizes and shifts the spectrum toward rapid gravity-driven growth with a scaling $ ext{growth} imes au_a \nsim S^{-1/3}$ in the G-mode regime; the classical constant-$ extpsi$ tearing scaling $ ext{growth} imes au_a sim S^{-3/5}$ is recovered only in the weak-stratification limit. Overall, gravity-modified tearing and G-modes provide a framework for understanding reconnection in astrophysical and laboratory plasmas with density gradients under effective gravity, and the results are robust to the choice of smooth density profiles. Further work could incorporate dispersive and kinetic effects to extend these insights to finer scales.

Abstract

Magnetic reconnection can develop spontaneously via the tearing instability, often invoked to explain disruptive instabilities in fusion devices, solar flares, the generation of periodic density disturbances at the tip of helmet streamers, and flux transfer events at the Earth's dayside magnetopause. However, in many such environments the presence of gravity, magnetic field curvature or other forms of acceleration often result in situations of a heavy-over-light plasma in an effective gravitational field with an embedded current sheet. This paper studies the linear stability of a slab current sheet with respect to reconnecting modes in the presence of a density gradient under the effect of a constant gravitational acceleration. We show that the presence of stratification and gravity modify the properties of the tearing mode instability both in the case of favorable and unfavorable stratification. Favorable stratification suppresses reconnection while unfavorable stratification strongly destabilizes the tearing mode. Furthermore, we show that the classical constant-ψ regime effectively does not exist, even for weak unfavorable stratification, for S>>1. Instead, the gravity-modified tearing progressively transitions into the G-mode, which is a gravity-driven reconnecting mode with a growth rate scaling as S^-1/3. As a consequence, unfavorable stratification only permits rapidly reconnecting modes.

Figures (8)

• Figure 1: The analytical (solid lines) and numerical (dashed lines) dispersion relation for different favorable stratification values ($A\leq0$) for $S=10^6$.
• Figure 2: The analytical (solid lines) and numerical (dashed lines) dispersion relation for different unfavorable stratification values ($A\geq0$) for $S=10^5$.
• Figure 3: Dispersion relation obtained by solving the eigenvalue problem numerically for the hyperbolic tangent density profile given in equation (\ref{['58']}) for $A\leq0$ and $S=10^6$ (left panel) and $A\geq0$ and $S=10^5$ (right panel).
• Figure 4: The analytical (dotted line) and numerical (solid and dashed lines) dispersion relation highlighting the effect of stratification on the tearing mode and the region of instability of G-modes for the density profiles given in equations (\ref{['6']}) and (\ref{['58']}) for $S= 10^{5}$ and $A = 0.01$. The green dot-dashed line corresponds to $A=0$.
• Figure 5: Numerically solved normalized tearing mode eigenfunctions for $S = 10^7$ and $ka = 0.5$ for three values of $A$: velocity field stream function $\hat{\phi}$ (left panel) and magnetic field flux function $\hat{\psi}$ (right panel).