The topological properties of magnetic helicity

The relation between helicity integrals and field structure is investigated in detail. Magnetic helicity is related to the morphology of closed field structures. Helicity is described in terms of the internal structure of a flux tube and the external relations between flux tubes. The concepts of twist number and writhing number are introduced from the mathematical biology literature to describe the contributions to helicity from twist about the axis of a flux tube and from the structure of the axes themselves. The helicity of open field configurations not bounded by magnetic surfaces is discussed, and a measure of the propagation of topological structures across open boundaries is given.