Zur Mehrwertigkeit des skalaren magnetischen Potentials beim hydromagnetischen Stabilitätsproblem eines Plasmas

Abstract

BERNSTEIN, FRIEMAN, KRUSKAL and KULSRUD have found a variational principle (energy principle) which provides a necessary and sufficient condition for the stability of a plasma configuration surrounded by a vacuum and an external conductor. In this energy principle the perturbed magnetic field in the vacuum is derived from a vector potential. In the present investigation the energy principle is formulated with the help of a magnetic scalar potential instead of the vector potential, which simplifies the application of the principle. The many-valued character of the scalar potential assures that this description is equivalent to that using the vector potential. The nature of this many-valuedness is thoroughly investigated.