Study of the fractality in a magnetohydrodynamic shell model forced by solar wind fluctuations

Abstract

Abstract. The description of the relationship between interplanetary plasma and geomagnetic activity requires complex models. Drastically reducing the ambition of describing this detailed complex interaction and, if we are interested only in the fractality properties of the time series of its characteristic parameters, a magnetohydrodynamic (MHD) shell model forced using solar wind data might provide a possible novel approach. In this paper we study the relation between the activity of the magnetic energy dissipation rate obtained in one such model, which may describe geomagnetic activity, and the fractal dimension of the forcing. In different shell model simulations, the forcing is provided by the solution of a Langevin equation where a white noise is implemented. This forcing, however, has been shown to be unsuitable for describing the solar wind action on the model. Thus, we propose to consider the fluctuations of the product between the velocity and the magnetic field solar wind data as the noise in the Langevin equation, the solution of which provides the forcing in the magnetic field equation. We compare the fractal dimension of the magnetic energy dissipation rate obtained, of the magnetic forcing term, and of the fluctuations of v⋅bz, with the activity of the magnetic energy dissipation rate. We examine the dependence of these fractal dimensions on the solar cycle. We show that all measures of activity have a peak near solar maximum. Moreover, both the fractal dimension computed for the fluctuations of v⋅bz time series and the fractal dimension of the magnetic forcing have a minimum near solar maximum. This suggests that the complexity of the noise term in the Langevin equation may have a strong effect on the activity of the magnetic energy dissipation rate.

Non-standard magnetohydrodynamics equations and their implications in sunspots

“…A possible strategy in this direction would develop the Hamiltonian structure of dissipative plasma models; this is a matter that deserves future investigations. It may be interesting to extend in a future work the Parker dynamo waves recently obtained numerically in a standard MHD system [122] and different physical processes forced by solar wind fluctuations [123]. Moreover, the application of Noether's first and second theorems to explore conservation laws in NS-MHD and plasmas dynamics is essential.…”

Complex Network Study of Solar Magnetograms

“…In the last several decades, new strategies based on the study of complexity have been developed to study plasma systems. For instance, fractal and multifractal analyses have been carried out for turbulence in laboratory plasmas [ 3 , 4 ], geomagnetic activity [ 5 , 6 , 7 , 8 , 9 , 10 ], and solar wind dynamics [ 11 , 12 , 13 ]. From the perspective of self-organized criticality, sandpile models have been used to model the energy release from the Sun by means of solar flares [ 14 ] and geomagnetic activity [ 15 ].…”

Applying the Horizontal Visibility Graph Method to Study Irreversibility of Electromagnetic Turbulence in Non-Thermal Plasmas

“…Regardless the nature of the distribution function (thermal or non-thermal), plasmas show a self-organized critical behavior [ 28 ], allowing for the introduction of concepts from complex systems to study this criticality. Those methods are applied both in data sets and models [ 29 , 30 , 31 , 32 ]. Some authors have suggested that the change of fractals and multifractals indexes could be associated with dissipative events or related to the solar cycle, proposing a relation between multifractality and physical processes in plasmas, among them solar cycle, Sun–Earth system, or theoretical models of plasmas [ 29 , 33 ].…”