The 3D topology and interaction of complex magnetic flux systems

In order to understand the topology of complex flux systems we analyse in detail the rich structural properties of the magnetic field created in turn by two or three balanced or unbalanced flux sources. Passing through each three-dimensional magnetic null point (where the field vanishes) is an isolated spine field line and a flux surface known as a Fan. The fans form separatrix surfaces which separate the volume into topologically distinct regions and generally intersect each other in separator field lines linking pairs of null points. Furthermore, the fan of one null can terminate at the spine of another null, whilst the spine terminates either at a source or at infinity. The skeleton of complex three-dimensional magnetic fields therefore comprises the magnetic null points and a network of spine curves and separatrix fan surfaces. The skeletons due to three sources are classified and found to be surprisingly complex. For example, a new discovery is that a configuration with a separator map be produced by only three sources.