Measures of Topological Structure in Magnetic Fields

Abstract

Observers and theorists describing magnetic field structures often use terms such as twisted, kinked, sheared and braided. All these aspects of field structure can be quantified using topological invariants. While topological quantities obey conservation laws in systems with no resistivity and simple boundary conditions, in more general circumstances they can change in time as the physical system evolves. Topological structure is often thought of as a global property of a magnetic system. However, some aspects of structure can be examined in sub-volumes of space. This allows us to examine transport of structure from one region of space to another. We illustrate by examining the transport of magnetic helicity through parts of the sun and heliosphere during the solar cycle.