Representations for vacuum potentials in stellarators

A set of vacuum potentials which has proved to be of practical use for toroidal stellarators is given by several representations: recursively by integration and by an algorithmic formula generator written in REDUCE, nonrecursively by complex loop integrals and by generating functions followed by a general explicit algebraic representation. Test examples include a collection of formulae for harmonics of low orders, a simple approximate magnetic surface invariant in special cases and a demonstration of the suppression of magnetic islands by resonant fields. (orig.)