Fractal multi-scale nature of solar/stellar magnetic field

TL;DR

This paper reviews how the concept of fractal and multi-fractal organization helps in understanding complex phenomena in solar and stellar magnetic fields, including energy release, turbulence, and dynamo processes.

Contribution

It summarizes recent applications of multi-fractal analysis in solar and stellar magnetism, highlighting new insights into magnetic turbulence and dynamo mechanisms.

Findings

Multi-fractality characterizes burst-like energy release events.

Fractal analysis aids in understanding turbulent magnetic diffusivity.

Multi-fractality provides insights into the dual nature of solar dynamo.

Abstract

An abstract mathematical concept of fractal organization of certain complex objects received significant attention in astrophysics during last decades. The concept evolved into a broad field including multi-fractality and intermittency, percolation theory, self-organized criticality, theory of catastrophes, etc. Such a strong mathematical and physical approach provide new possibilities for exploring various aspects of astrophysics. In particular, in the solar and stellar magnetism, multi-fractal properties of magnetized plasma turned to be useful for understanding burst-like dynamics of energy release events, conditions for turbulent dynamo action, nature of turbulent magnetic diffusivity, and even the dual nature of solar dynamo. In this review, I will briefly outline how the ideas of multi-fractality are used to explore the above mentioned aspects of solar magnetism.