Plasma equilibrium equation for a stellarator of arbitrary aspect ratio

In reducing the three-dimensional plasma equilibrium equations for a stellarator to two-dimensional form (a single scalar equation or a system of vector equations), the aspect ratio A is usually considered to be large and an expansion is performed in A−1. In this paper a two-dimensional scalar equation is derived for plasma equilibrium, with accurate allowance for toroidality and without expansion in A−1, so that it can also be used to describe compact small-aspect-ratio stellarators, e.g. systems of the stellatron type. The analysis is performed by the method of inversion of variables, and the result is a complete three-dimensional description of the equilibrium configuration.