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.
Magnetic reconnection is thought to be the dynamical mechanism responsible for many explosive phenomena observed in laboratory, space, and astrophysical plasmas (Yamada et al. 2010;Pucci et al. 2020b;Ji & Daughton 2022). Through magnetic topology reconfiguration, reconnection converts stored magnetic energy into plasma heating, particle acceleration, and bulk flows. This mechanism is central to energy release events in magnetic confinement fusion devices (e.g., tokamak sawtooth crashes (Waelbroeck 1989)), solar flares and coronal mass ejections in the solar corona (Shibata 1996), geomagnetic storms and substorms within planetary magnetospheres (Burch & Phan 2016;Louarn et al. 2015), and high-energy phenomena in astrophysical environments such as accretion disks and relativistic jets (Romanova & Lovelace 1992;Khiali & de Gouveia Dal Pino 2016).
The tearing mode instability, first analyzed by Furth, Killeen, and Rosenbluth (1963) (Furth et al. 1963), is a fundamental mechanism through which magnetic reconnection can develop within current sheets in the resistive magnetohydrodynamic (MHD) framework. Over the past several decades, the tearing mode has been investigated extensively under increasingly complex plasma conditions. Studies have explored its properties with equilibrium shear flows and/or viscosity (Ofman et al. 1991;Mallet et al. 2025;Chen & Morrison 1990;Comisso & Grasso 2016;Grasso et al. 2008;Dahlburg et al. 1997;Tenerani et al. 2015), incorporated Hall and two-fluid effects (Terasawa 1983;Pucci et al. 2017;Shi et al. 2020), and extended to partially ionized plasmas (Paris 1973;Zweibel et al. 2011;Pucci et al. 2020a) and to collisionless or kinetic regimes (Porcelli 1991;Daughton & Karimabadi 2005;Del Sarto et al. 2016).
However, in many natural and laboratory environments reconnection can occur in stratified plasmas in the presence of gravity, magnetic curvature, or other effective accelerations, sometimes leading to heavy-over-light plasma configurations embedded within current sheets. At Earth’s magnetopause, for example, rapid variations in solar wind dynamic pressure accelerate the boundary across the sharp density gradient separating the dense magnetosheath from the tenuous magnetosphere, producing an effective gravitational force that can drive Rayleigh-Taylor modes (Anderson et al. 1968;Gratton et al. 1996) and potentially affect reconnection during southward interplanetary magnetic field conditions. Similar conditions arise at the heliopause, where both acceleration of the heliospheric interface toward the interstellar medium and charge-exchange interactions between interstellar neutrals and heliosheath plasma can generate an effective gravity antiparallel to the density gradient, making the interface unstable to Rayleigh-Taylor modes (Borovikov et al. 2008;Avinash et al. 2014;Pogorelov et al. 2017;Opher et al. 2021;Ruderman 2024). In the laboratory, magnetic confinement devices such as tokamaks and stellarators are also susceptible to interchange-type instabilities (Kruskal & Schwarzschild 1954) and other gravity-driven resistive instabilities that can develop in current sheets (Furth et al. 1963;Coppi 1964;Johnson et al. 1963;Roberts & Taylor 1965;Glasser et al. 1975). These early works however relied on restrictive assumptions -such as constant-ψ, weak gravity, weak magnetic shear, or asymptotic wavelength limits -thereby limiting their ability to capture how tearing modes are modified by gravity and how they transition to gravity-driven instabilities.
In this study, we investigate the effects of favorable and unfavorable stratification on the linear stage of reconnecting instabilities in a plane slab current sheet by including a gravitational acceleration acting normal to the current layer. Here, favorable and unfavorable stratification refer to cases in which the density gradient is parallel or antiparallel, respectively, to the gravitational acceleration. Although configurations with a negative density gradient along the gravitational field direction (unfavorable stratification) can be ideally unstable to interchange or Rayleigh-Taylor modes, we restrict our attention to regimes in which stratification is sufficiently weak to satisfy the Suydam stability criterion (Paris et al. 1982;Gerwin 1979), a necessary condition for ideal stability in a sheared pinch configuration.
With uniform resistivity, it has been shown that a plane sheet pinch is unstable to two resistive instabilities under the constant-ψ approximation (Furth et al. 1963): a longwavelength tearing mode, dominant when gravity is negligible, with a growth rate scaling with the Lundquist number as S -3/5 , and a short-wavelength gravity-driven mode (the G-mode) with a growth rate scaling as S -1/3 . This gravity-driven resistive mode was further extended to stellarator-like geometry in weakly sheared magnetic configurations (Johnson et al. 1963;Coppi 1964;Roberts & Taylor 1965) and generalized to nonlocalized modes man
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