On slowly evolving Grad‐Shafranov equilibria

Abstract

A method is developed for analyzing the slow, purely kinematic evolution of magnetohydrostatic Grad‐Shafranov equilibria, recovered by reconstruction from data taken by a single spacecraft as it traverses a quasi‐static, two‐dimensional, magnetic field/plasma structure in space, such as a flux transfer event at the magnetopause. The evolution is caused by the presence of small plasma velocities in the reconstruction plane, in which a velocity component perpendicular to the field moves and deforms the field lines. The method is developed in a general form that allows for plasma compressibility but is then specialized to a simpler version, in which the velocity field is assumed to be divergence free, at least in the vicinity of the spacecraft path through the structure. Benchmarking and application of the simpler version to Cluster data are presented in a companion paper by Hasegawa et al. (2010). Potential applications include, not only flux transfer events, but also other slowly evolving elongated structures in which dissipation can be neglected, including flux ropes and magnetic clouds in the solar wind.