On the relevance of fractal diffusion to auroral backscatter

An analytical approach to non-conventional diffusive transport in auroral ionospheric turbulence is presented. Radar observations suggest that the probability density function (PDF) for plasma irregularities is non-Gaussian and exhibits stretched exponential decaying tails. In order to model these observations, we propose a transport model for the PDF based on a fractional Fokker-Planck equation that includes both non-local and non-Gaussian features. A closed form expression for the autocorrelation function (ACF) is derived and shown to reproduce some of the characteristic features of auroral backscatter, suggesting non-Gaussian, and non-Markovian statistics. The analysis of correlation in radar signals provides a quantitative measure of memory of the turbulent ionospheric plasma. The primary goal of the present work is to predict the shape of coherent scatter radar Doppler spectra.