Study of auroral ionosphere using percolation theory and fractal geometry

In this work, values of the fractal dimension and the connectivity index characterizing the structure of Hall conductivities on the night side of the auroral ionosphere are derived in general form. Restrictions imposed on fractal structure of the ionospheric conductivity are analyzed in terms of the percolation of the ionospheric Hall currents. It is shown that the structure of ionospheric Hall conductivities can be described as asymptotically path-connected fractal. This result is supported by analysis of typical structure observed in auroral electron precipitation which are also the main source of ionization on the night side of the ionosphere. It is demonstrated that crossing the precipitation region in the direction perpendicular to the multiple arcs system, one should observe the structure of the precipitation which looks like a generalized Cantor set.