Determination of two-dimensional magnetostatic equilibria and analogous Euler flows. (English) Zbl 0765.76095
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.
MSC:
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
| 76M30 | Variational methods applied to problems in fluid mechanics |
Keywords:
saddle points; method of magnetic relaxation; variational problem; single stationary elliptic point; finite energy field; topology; minimum energy stateReferences:
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