The basic roles of several of the principal modulations of plasma boundary shape on MHD equilibria are investigated. The appropriate combination of the principal helical modulations for elimination of the bumpy field component in the realization of the quasi-axisymmetric (QAS) and quasi-helically symmetric (QHS) configurations is explained by considering the variation of the areas of the magnetic surface cross-sections. A triangular modulation is utilized effectively to form a magnetic well by shifting the magnetic axis outward compared with the centre of mass of the magnetic surface cross-section. The spatialization of the magnetic axis or the bumpy modulations of the plasma boundary are rather important for reducing the toroidicity in the magnetic field, which can lead to QHS configurations. Some stellarator magnetic configurations at present in the design stage or in existing experimental devices are discussed from the point of view of plasma boundary modulations. On the basis of these main findings about plasma boundary modulations, examples of the essential approach to QAS and QHS configurations are demonstrated step by step. The possibility of a quasi-bumpy (or poloidally) symmetric (QBS) configuration is also mentioned.
Free-plasma-boundary solver for axisymmetric ideal MHD equilibria with flow