Fractal MHD wind in the solar atmosphere

Abstract

In this study, we analyzed the fundamental concepts of solar physics based on the product-like fractal measure concept introduced by Li and Ostoja-Starzewski in their attempt to explore anisotropic fractal elastic media and electromagnetic fields. We constructed the magnetohydrodynamic equations in fractal dimensions. We used these equations to analyze solar activities in particular the quiescent prominence based on Kippenhahn and Schlüter model and the solar wind. Many features were raised which are in agreement with observations. In particular, it was revealed the presence of long tails due to the fractal structure of quiescent prominence surrounding the central absorption region. For particular values of the fractal dimension, the system tends toward the isothermal state. The fractal MHD equations were used to study the solar wind based on Parker's model. The fractal model is characterized by a supersonic solar wind's velocity which is greater than the velocity obtained in the Parker's model. This provides an alternative answer to the question of why, in spherical symmetry, the solar wind must quite frequently become supersonic. Further consequences were discussed in some details.