Two-dimensional self-similar plasma equilibria

Abstract

Force-free plasma equilibria are expected to form in the solar corona, while in-situ spacecraft observations have shown that force-free equilibria are formed in the planetary magnetotails. In this paper, we develop fluid models of two-dimensional axially symmetric force-free equilibria and discuss similar slab equilibria. The group theory approach is used to find the symmetry groups and reduce the Grad-Shafranov equation with exponential and power law nonlinearities to ordinary differential equations for the self-similar (automodel) solutions that we analyze analytically and numerically. Force-free equilibria of the developed class have a magnetotail-type configuration with magnetic field lines stretched in the radial direction and represent nonlinear force-free equilibria, because rot B=α(r) B with α(r)≠const. Making use of the same symmetry groups, we generalize the developed force-free equilibria by including a finite plasma pressure gradient and compare different equilibria of the developed class. These models can be useful for describing the structure and stability of current sheets observed in planetary magnetotails and formed in the solar atmosphere.

Comparison of the Flank Magnetopause at Near‐Earth and Lunar Distances: MMS and ARTEMIS Observations

“…The current sheet thickness weakly evolves with radial distance and remains comparable to the gyroradius of thermal magnetospheric ions (and larger than the gyroradius of thermal magnetosheath ions). Therefore, we can conclude that the nightside magnetopause current sheet profile does not fundamentally/ significantly changes with the radial distance, but self-similarly changing (by preserving an almost constant thickness) in response to the magnetic field and current density decay (see the 2-D model of such self-similar C-type current sheets in Hilmer & Voigt, 1987;Lukin et al, 2018). Despite that the magnetopause in different Journal of Geophysical Research: Space Physics 10.1029/2020JA028406 regions separates magnetosheath and magnetospheric domains (plasma sheet, lobes, and cusp) with different plasma and magnetic field properties, the magnetopause current sheet can always be described by C-type or S-type sheets.…”

Plasma Sheet Boundary Layer in Jupiter's Magnetodisk as Observed by Juno

“…We then investigate the distributions of electron fluxes and wave intensity in the plane consisting of the radial and north‐south directions. This plane illustrates the 2‐D configuration of magnetic field lines that are almost azimuthally symmetric (to a zero‐order approximation) around the planet (see, e.g., simple models by Goertz, 1976; Lukin et al., 2018; Vasko et al., 2013). The radial coordinate, R / R J , acts as a proxy of distance to the planet; that is, as R decreases, plasma fluxes (within the plasma sheet) are expected to increase (Bagenal et al., 2016; Frank & Paterson, 2004).…”

Force‐Free Current Sheets in the Jovian Magnetodisk: The Key Role of Electron Field‐Aligned Anisotropy

“…The main current density flows along the y ‐axis, transversely to magnetic field lines. (b) 3D configuration of the magnetic field line in the current sheet with $${B}_{y}^{2}/8\pi $$ gradients playing the role of P gradients (see discussion on the $$P\to {B}_{y}^{2}$$ transition in Syrovatskii, 1981; Lukin et al., 2018). The dashed curve illustrates the field line projection to the xy plane.…”