High-Beta Quasisymmetric Configurations

The space of high-beta, approximately quasiaxisymmetric, large-aspect-ratio stellarator configurations is explored using an inverse coordinate approach and a quadratic polynomial ansatz for the flux function, following the method of Hernandes and Clemente. This approach yields a system of nonlinear ODEs that, when solved, give equilibria exhibiting positive or negative triangularity, cusps, and (in an extreme limit) current singularities. It is shown that a cubic ansatz may also be used, but that polynomials of degree 4 or higher will lead to overdetermination. Connections to bifurcated 3D tokamak equilibria, in particular the saturated state of the n=m=1 internal kink mode, are explored. These bifurcated equilibria are shown to be approximately quasisymmetric in the limit of large aspect ratio.