Modeling Multifractality of the Solar Wind

Abstract

The question of multifractality is of great importance because it allows us to investigate interplanetary hydromagnetic turbulence. The multifractal spectrum has been investigated with Voyager (magnetic field) data in the outer heliosphere and with Helios (plasma) data in the inner heliosphere. We use the Grassberger and Procaccia method that allows calculation of the generalized dimensions of the solar wind attractor in the phase space directly from the cleaned experimental signal. We analyze time series of plasma parameters of the low-speed streams of the solar wind measured in situ by Helios in the inner heliosphere. The resulting spectrum of dimensions shows a multifractal structure of the solar wind attractor. In order to quantify that multifractality, we use a simple analytical model of the dynamical system. Namely, we consider the generalized self-similar baker’s map with two parameters describing uniform compression and natural invariant measure on the attractor of the system. The action of this map exhibits stretching and folding properties leading to sensitive dependence on initial conditions. The obtained solar wind singularity spectrum is consistent with that for the multifractal measure on the weighted baker’s map.