Study of fractal features of magnetized plasma through an MHD shell model

Abstract

A magnetohydrodynamic (MHD) shell model is used to describe the dissipative events which take place in magnetized plasmas. A scatter plot box-counting fractal dimension D is calculated for the time series of the magnetic energy dissipation rate obtained in the MHD shell model, and the correlation between D and the energy dissipation rate is analyzed. We show that, depending on the values of the viscosity and the diffusivity, the fractal dimension and the occurrence of bursts exhibit correlations similar to those observed in previous studies.