Use of fractal approach to investigate ionospheric conductivity in the auroral zone

Abstract

Fractal geometry is used to describe the spatial structure of the ionospheric conductivity. Topological values of fractal dimension and connectivity index, characterizing the structure of the Pedersen and Hall conductivities on the nightside of the auroral zone, are analytically obtained. Restrictions imposed on fractal structure of the ionospheric conductivity are analyzed in terms of the percolation of the ionospheric Pedersen and Hall currents. It is shown that the observed scaling for the fluctuations of electric field and for the auroral glow in the auroral region is well within the limitations imposed by the critical condition for percolation of Pedersen currents. The dimension of multiple arc structures corresponds well to fractal estimates of Hall conductivity. Correspondence of theoretical estimates and experimental results indicates validity of the fractal approach to describe processes in the auroral region.