BIFURCATIONS OF MAGNETIC TOPOLOGY BY THE CREATION OR ANNIHILATION OF NULL POINTS

Linear null points of a magnetic field may come together and coalesce at a second-order null, or vice versa a second-order null may form and split, giving birth to a pair of linear nulls. Such local bifurcation s lead to global changes of magnetic topology and in some cases releas e of magnetic energy. In two dimensions the null points are of X or O type and the flux function is a Hamiltonian; the magnetic held may und ergo saddle-centre, pitchfork or degenerate resonant bifurcations. In three dimensions the null points and their creation or annihilation by bifurcations are considerably more complex. The nulls possess a skele ton consisting of a spine curve and a fan surface and are of radial-ty pe (proper or improper) or spiral-type the type of null and the inclin ation of spine and fan depend on the magnitudes of the current compone nts along and normal to the spine. In cylindrically symmetric fields a comprehensive treatment is given of the various types of saddle-node, Hopf and saddle-node-Hopf bifurcations. In fully three-dimensional si tuations examples are given of saddle-node and degenerate bifurcations ; in which generically two nulls are created or destroyed and are join ed by a separator field line, which is the intersection of the two fan s. Furthermore, global bifurcations can create chaotic field lines tha t could perhaps trigger energy release in, for example, solar flares.