Introduction to Field Line Helicity

Abstract

Field line helicity measures the net linking of magnetic flux with a single magnetic field line. It offers a finer topological description than the usual global magnetic helicity integral, while still being invariant in an ideal evolution unless there is a flux of helicity through the domain boundary. In this chapter, we explore how to appropriately define field line helicity in different volumes in a way that preserves a meaningful topological interpretation. We also review the time evolution of field line helicity under both boundary motions and magnetic reconnection.Comment: 23 pages, 8 figures, to appear as chapter of AGU book "Helicities in Geophysics, Astrophysics and Beyond", published by Wiley, ISBN 111984168