Magnetic Winding: Theory and Applications (in Helicities in Geophysics, Astrophysics and Beyond)

Magnetic winding is a renormalization of magnetic helicity that provides a direct measure of field line topology. Despite its close connection to magnetic helicity, magnetic winding can provide different and important infor- mation about field line topology that is not clear from an analysis of magnetic helicity alone. In this chapter, we introduce magnetic winding from a theoretical perspective, with a keen eye on its role in understanding magnetic helicity and field line topology. We also provide practical applications of magnetic winding, highlighting that it can be used as an important measure for understanding the evolution of active regions in solar observations