The two-dimensional nonlinear evolution of the ionization-driven adiabatic auroral arc instability has been studied for the first time. We find: (1) the adiabatic auroral arc instability can fully develop on time scales of tens to hundreds of seconds and on spatial scales of tens to hundreds of kilometers, (2) the evolution of this instability leads to nonlinear ''hook-shaped'' conductivity structures, (3) this instability can lead to parallel current filamentation over a wide range of scale sizes from k&Lgr;01 where k is the wavenumber and &Lgr;0 is the initial arc width perpendicular to the geomagnetic field, and (4) the k-spectra of the density, electric field, and parallel current develop into inverse power laws in agreement with satellite observations. Comparison with mesoscale auroral phenomenology and current filamentation structures is made. ¿ American Geophysical Union 1992