DETERMINATION OF 2-DIMENSIONAL MAGNETOSTATIC EQUILIBRIA AND ANALOGOUS EULER FLOWS

The equivalence of the method of magnetic relaxation to a variational problem with an infinity of constraints is established. This variational problem is solved in principle and approximations to the exact solution are compared to results obtained by numerical relaxation of fields with a single stationary elliptic point. In the case of a finite energy field of the above topology extending to infinity, we show that the minimum energy state is the one in which all field lines are concentric circles and that this state is topologically accessible from the original one. This state is used as a reference state for understanding the relaxation of fields constrained by finite boundaries. We then consider the relaxation of fields containing saddle points and confirm the tendency of the saddle points to collapse and form two Y-points. An infinite family of local equilibrium solutions each describing a Y-point is provided.