Abstract
As a step in solving the so-called resonance problems, a method of formal expansion in the neighbourhood of an arbitrarily shaped toroidal magnetic surface is developed. Sufficient conditions for the existence of all coefficients of the power-series expansion of equilibrium quantities with respect to the volume contained between each magnetic surface and the prescribed one are presented for arbitrarily prescribed distributions of pressure and rotational transform ratio and for the surface harmonic with an arbitrary weight on the initially prescribed magnetic surface. It is suggested that the conditions should usually also be necessary in the case of asymmetry. The conditions are written in terms of similar functions appearing in the well-known condition of local stability. A possibility that non-existence of equilibrium without symmetry may occur in a certain case is suggested. Relations between the existence theorems previously proposed by several authors and our results are discussed to be consistent except for the foregoing case. Convergence of the formal solutions has, however, not yet been examined.
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