Reduced magnetohydrodynamics with electron inertia in pseudodipole coordinates

Abstract

We study the altitude-dependent structuring of field-aligned currents by driven Alfvén waves in an expanding auroral flux tube. The model uses the reduced magnetohydrodynamics (RMHD) long-thin ordering assumptions along with electron inertia. We derive a magnetic tension operator consistent with energy conservation in the expanding geometry. We compare uniform density with a prescribed profile containing a dense ionospheric end and a low-density upper region. The simulations produce localized current concentrations near the lower boundary and filamentary structures at greater heights. Broad structures remain visible in the magnetic and velocity stream functions while their perpendicular derivatives reveal finer magnetic field, velocity, and current structure. With the nonuniform density profile, the run with additional upper boundary reflection shows finer current structure and greater numerical dissipation. Spectral diagnostics show forward nonlinear energy transfer and altitude-dependent power-law-like intervals without a broad constant-flux range. The narrowest current concentrations span only a few grid cells, so their physical widths remain unresolved.