A mathematical model of the structure and evolution of small‐scale discrete auroral arcs

Abstract

A three‐dimensional fluid model which includes the dispersive effect of electron inertia is used to study the nonlinear macroscopic plasma dynamics of small‐scale discrete auroral arcs within the auroral acceleration zone and ionosphere. The motion of the Alfven wave source relative to the magnetospheric and ionospheric plasma forms an oblique Alfven wave which is reflected from the topside ionosphere by the negative density gradient. The superposition of the incident and reflected wave can be described by a steady state analytic solution of the model equations with the appropriate boundary conditions. This two‐dimensional discrete auroral arc equilibrium provides a simple explanation of auroral acceleration associated with the parallel electric field. Three‐dimensional fully nonlinear numerical simulations indicate that the equilibrium arc configuration evolves three‐dimensionally through collisionless tearing and reconnection of the current layer. The instability evolves nonlinearly to produce complex transverse structure that may be the origin of the folds and curls observed to be associated with small‐scale discrete arcs. At late times the plasma becomes turbulent having transverse electric field power spectra that tend toward a universal k −5/3 spectral form.