Equilibrium calculations for helical axis stellarators

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Abstract
An average method based on a vacuum flux coordinate system is presented. This average method permits the study of helical axis stellarators with toroidally dominated shifts. An ordering is introduced, and to lowest order the toroidally averaged equilibrium equations are reduced to a Grad–Shafranov equation. Also, to lowest order, a Poisson‐type equation is obtained for the toroidally varying corrections to the equilibrium. By including these corrections, systems that are toroidally dominated, but with significant helical distortion to the equilibrium, may be studied. Numerical solutions of the average method equations are shown to agree well with three‐dimensional calculations.