Fractal approach to the description of the auroral region
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Fractal Approach to the Description of the Auroral Region A. A. Chernyshova, M. M. Mogilevskya, and B. V. Kozelovb a
Space Research Institute, Russian Academy of Sciences, Profsoyuznaya ul. 84/32, Moscow, 117997 Russia b Polar Geophysical Institute, Kola Science Center, Russian Academy of Sciences, Akademgorodok 26a, Apatity, Murmansk oblast, 184209 Russia email: [email protected] Received July 18, 2012; in final form, December 6, 2012
Abstract—The plasma of the auroral region, where energetic particles precipitate from the magnetosphere into the ionosphere, is highly inhomogeneous and nonstationary. In this case, traditional methods of classical plasma physics turn out to be inapplicable. In order to correctly describe the dynamic regimes, transition pro cesses, fluctuations, and selfsimilar scalings in this region, nonlinear dynamics methods based of the con cepts of fractal geometry and percolation theory can be used. In this work, the fractal geometry and percola tion theory are used to describe the spatial structure of the ionospheric conductivity. The topological proper ties, fractal dimensions, and connective indices characterizing the structure of the Pedersen and Hall conductivities on the nightside auroral zone are investigated theoretically. The restrictions imposed on the fractal estimates by the condition of ionospheric current percolation are analyzed. It is shown that the fluc tuation scalings of the electric fields and auroral glow observed in the auroral zone fit well the restrictions imposed by the critical condition on the percolation of the Pedersen current. Thus, it is demonstrated that the fractal approach is a promising and convenient method for studying the properties of the ionosphere. DOI: 10.1134/S1063780X13060020
1. INTRODUCTION Polar auroras are possibly the most beautiful and mysterious optical phenomenon in the atmosphere of our planet. In all historical periods, people tried to explain the origin and dynamics of polar auroras using different approaches. At present, it is well known that the polar aurora is the glow of the atmospheric gas at altitudes of 100–200 km caused by the complex of processes occurring in the magnetospheric–iono spheric plasma. The region where the polar aurora is observed is conventionally called the auroral region, and the processes of the magnetosphere–ionosphere interaction occur most actively just in this region. In fact, the inhomogeneities and instabilities of different kinds arising in the magnetospheric plasma at different altitudes are projected onto the auroral zone of the ionosphere by means of fieldaligned inward and out ward currents and, thus, carry the properties of the magnetosphere into the ionosphere. In other words, the polar aurora reflects multiple processes occurring in the magnetosphere–ionosphere system [1–5]. Substantial progress in studying polar auroras and the auroral zone of the ionosphere was achieved in the second half of the past century due to direct measure ments performed on artificial satellites a
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