A note on two‐dimensional asymptotic magnetotail equilibria

Abstract

In order to understand, on the fluid level, the structure, the time evolution, and the stability of current sheets, such as the magnetotail plasma sheet in Earth's magnetosphere, one has to consider magnetic field configurations that are in magnetohydrodynamic (MHD) force equilibrium. Any reasonable MHD current sheet model has to be two‐dimensional, at least in an asymptotic sense (Bz/Bx) = ε « 1. The necessary two‐dimensionality is described by a rather arbitrary function fnof;(x). We utilize the free function fnof'(x) to construct two‐dimensional magnetotail equilibria that are “equivalent” to current sheets in empirical three‐dimensional models. We obtain a class of asymptotic magnetotail equilibria ordered with respect to the magnetic disturbance index Kp. For low Kp values the two‐dimensional MHD equilibria reflect some of the realistic, observation based, aspects of three‐dimensional models. For high Kp values the three‐dimensional models do not fit the asymptotic MHD equilibria, which is indicative of their inconsistency with the assumed pressure function. This, in turn, implies that high magnetic activity levels of the real magnetosphere might be ruled by thermodynamic conditions different from local thermodynamic equilibrium.