Funktionentheoretische Bestimmung des Aussenfeldes zu einer zweidimensionalen magnetohydrostatischen Konfiguration

Two-dimensional analogues of the torus-like Meyer-Schmidt plasma configurations without interior field are treated by functiontheoretical methods. If the boundary of the doubly connected plasma domain consists of two closed analytic curves, the structure of the exterior magnetic field and its singularities (which determine the currents) can be found by a combination of analytic continuation and conformal mapping. An example is discussed in detail. The problem is essentially equivalent to a problem in hydrodynamics: to find the structure of an incompressible irrotational flow in two dimensions which has a given closed analytic curve as a free streamline.