A necessary condition for omnigenity in stellarators

Abstract

A lower bound for the total variation Bmax/Bminof the field strength B on a toroidal vacuum magnetic surface with finite twist (rotational transform) of the field is given as a necessary (not sufficient) condition for the field lines to be geodesics on it. If such a surface existed, it would be omnigenous with respect to the local gradient-B and centrifugal guiding-centre drift approximation, which means that the normal components of these drift velocities would be zero. It is found that the lower bound on Bmax/Bmindepends on the maximum of – (r/B) ∂B/∂r within the surface. Hereris the distance from the origin of the torus. The lower bound is large if this maximum is small, and vice versa. For some more recent stellarator configurations the condition is found to be satisfied at outer magnetic surfaces. It is obtained without the use of expansion techniques, under the assumption that there is a nested system of magnetic surfaces within the omnigenous one.