Multiply connected source and null pairs

The magnetic fields within the solar atmosphere have a complex topology owing to the fragmentary nature with which they thread the solar surface. The topologies of the potential magnetic fields containing only a few (up to four) point photospheric sources have been classified. For small numbers of sources determining the connectivity of source pairs is equivalent to counting the number of flux domains. As the numbers of sources increase this, however, is no longer the case. Instead, a pair of connected sources can have more than one distinct flux domain linking them. We call these multiply connected source pairs. Pairs of nulls connected by more than one separator are called multiply connected null pairs. Multiply connected source and null pairs go hand-in-hand such that two separators connecting the same pair of nulls immediately implies multiple flux domains linking the same source pair and vice versa. It is found that multiply connected source pairs are common not only in fairly complex potential magnetic fields but more interestingly in the resistive-MHD evolution of both simple and complex magnetic fields. Magnetic energy release is often significant around separators. Thus fields with multiply connected source pairs, which naturally have more separators, (i) have more sites for intense energy release and (ii) are likely to release energy more quickly than other magnetic fields. Moreover, the combination of multiply connected source and null pairs can give rise to a situation where flux is reconnected repeatedly between two flux domains.