• Auroral arcs;
  • magnetic stress release;
  • S-shaped

[1] An analytical model is presented for auroral arcs as the result of a fast release of magnetic shear stresses. The shear stresses are set up by a longitudinal convection that is driven by pressure forces in the outer magnetosphere against the frictional forces exerted in the lower ionosphere. A distorted-dipole geometry is employed allowing for high plasma beta near the equator. Steep ledges in the radial pressure distribution, extending along the direction of convection, are invoked as the sources of the auroral current sheets. The differential magnetic energy content of these narrow current sheets is released within a few Alfvén transit times by the decoupling of the magnetospheric plasma and field from the ionosphere, owing to the existence of field-aligned potential drops in the auroral acceleration region, and converted into kinetic energy of the primary auroral particles. A well-known current-voltage relation is employed for the formulation of the energy conversion process. This scenario has two important consequences. (1) The loss of magnetic energy creates a concomitant decrease of internal energy of the generator plasma and results in a progression of pressure ledge and auroral current sheet into the more highly stressed magnetic field region. This is the reason for the observed proper motion of auroral arcs with respect to the plasma frame. (2) Plasma and field undergo a rapid stress relief motion along the arc with large but mostly reversible displacements. The net displacement, equivalent to a small S-shaped contribution to the essentially U-shaped potential distribution above the auroral arc, is consistent with the transit of the field lines through the progressing current sheet. This scenario is cast into a set of simple relations expressing the key parameters of auroral arcs, such as width, energy flux, potential drop, and proper motion. The main ingredient herein is an auxiliary magnetic perturbation field into which the main properties of the large-scale current system are condensed. It corresponds to about twice the transverse magnetic perturbation field near the arc and thus to the total shear stresses. Two free parameters are the relative magnitude of the pressure jump at the ledge in the source plasma and the plasma beta. Matching the quantitative results of the relations for the arc properties with observed values suggests pressure jumps of order 10% and beta values between 1 and 5.