Collisionless relaxation of a disequilibrated current sheet and implications for bifurcated structures

Abstract

Current sheets are ubiquitous plasma structures that play the crucial role of being energy sources for various magnetic phenomena. Although a plethora of current sheet equilibrium solutions have been found, the collisionless process through which a disequilibrated current sheet relaxes or equilibrates remains largely unknown. Here we show, through analyses of phase-space distributions of single-particle orbit classes and particle-in-cell simulations, that collisionless transitions among the orbit classes are responsible for this process. Bifurcated current sheets, which are readily observed in geospace but whose origins remain controversial, are shown to naturally arise from the equilibration process and thus are likely to be the underlying structures in various phenomena; comparisons of spacecraft observations to particle-in-cell simulations support this fact. The bearing of this result on previous explanations of bifurcated structures is also discussed.

Equilibrium selection via current sheet relaxation and guide field amplification

“…Our classification of particle orbits in the finite b g case is different from that in the b g = 0 case 29 in the following aspects. First, the meandering class in the b g = 0 case is redefined here as the single-well class, because a single-well χ no longer guarantees meandering (i.e., repeatedly crossing the origin) if b g is finite.…”

“…When b g = 0, i.e., there is no guide field, χ can have either a single-well shape (for ) or a double-well shape (for ). Particle orbits can then be classified into four distinct classes, and current sheet relaxation can be characterized by transitions among the orbit classes 29 . When b g is finite, however, χ is asymmetric and is necessarily single-welled when , but the exact condition for double-welled χ becomes more complicated (see Methods).…”

“…Also, the relaxation process manifests the general solution of current sheet equilibria, providing a more profound insight than the multitude of specific solutions that have been found so far. For instance, Yoon et al 29 showed that current sheet equilibration—heating and pinching—is achieved via particle orbit class transitions, or, in other words, that a particular equilibrium solution can be represented by the fractional population in each orbit class. A useful by-product of this analysis was the prediction of bifurcated current sheets 30 , whose origins had remained controversial for over a decade.…”

“…A crucial limitation to the analysis in Yoon et al 29 was that it did not include effects due to the magnetic field component parallel to the current direction, i.e., the guide field. Guide field effects, however, are of paramount importance because zero-guide-field current sheets rarely exist in reality, and the presence of even the smallest guide fields significantly alter ensuing dynamics, e.g., in guide field reconnection 31 , 32 .…”

Bifurcated Current Sheet Observed on the Boundary of Kelvin-Helmholtz Vortices

“…On the other hand, bifurcated current sheets observed in Earth's magnetotail are often not necessarily associated with fast flows (Asano et al, 2003). Numerous studies have been put forth to understand the formation of such bifurcated magnetotail current-sheets, attributing its cause to flapping of the current sheet (Sergeev et al, 2003), magnetic turbulence (Greco et al, 2002), Kelvin-Helmholtz instability (Nakagawa and Nishida, 1989;Yoon, Drake and Lui, 1996), Ion-ion kink instability (Karimabadi et al, 2003), temperature anisotropy (Sitnov et al, 2004;Zelenyi et al, 2004) or relaxation processes of a disequilibrated current sheet, in particular, during current sheet thinning or quasi-steady compression (Schindler and Hesse, 2008;Jiang and Lu, 2021;Yoon et al, 2021).…”