Evolution of Solar Magnetic Arcades. I. Ideal MHD Evolution under Footpoint Shearing

Abstract

The ideal MHD evolution of a single magnetic arcade undergoing footpoint motions in a two-dimensional Cartesian geometry is investigated using numerical simulation. Also, force-free states of the same arcade are constructed with the use of a magnetofrictional method, which is formulated di †erently from those used in previous studies. In MHD simulations, no instability or nonequilibrium is found to the value of shear 100 times as large as the footpoint separation in the potential Ðeld. The evolutionary sequence is composed of three distinct phases. The Ðrst phase is characterized by the increase of the toroidal Ðeld strength and the second phase by a sort of self-similar expansion. In the third phase, the formation and growth of a central current layer are conspicuous. With increasing shear, the maximum current density increases, the width of the current layer decreases, and the feet of the current layer, which bifurcates above the bottom boundary, get closer to each other. The Ðeld lines in the current layer tend to thread the bottom boundary nearly horizontally for a large shear. From our results, it is inductively inferred that the magnetic arcade in a two-dimensional Cartesian geometry approaches an open Ðeld as the shear increases indeÐnitely.