A database of omnigenous stellarator equilibria including umbilic-torus-like designs and their applications with DESC

Omnigenity is a favorable property of a toroidal magnetic field that ensures trapped particle confinement. Since omnigenity is a superset of quasisymmtry, in theory, the design space of omnigenous configurations will be larger than that of quasi-symmetric configurations. To better understand this design space, we generate a database of 50k omnigenous equilibria generated using the DESC optimizer. In the first part of this poster, we find interesting trends in stability, coil complexity, and degree of omnigenity with respect to the shape parameters of the plasma, such as magnetic axis torsion, number of field periods, elongation, and aspect ratio. We choose equilibria for each type of omnigenity: toroidal, poloidal, and helical. Using DESC, we then perform multiobjective MHD and kinetic stability optimization to find omnigenous equilibria with enhanced Mercier, ballooning, and kinetic ballooning stability.

In the second part, we present a small subset of this database comprises umbilic-torus-like equilibria; equilibria with a single closed, continuous sharp edge that goes around multiple times toroidally and behaves like an X-point. This causes the iota to be a low-order rational number on the boundary, which can be useful for generating resonant divertor concepts.