Effect of symmetry-breaking on ballooning modes in quasi-symmetric stellarators

The impact of degraded symmetry on global ballooning stability is examined in the quasi-poloidally symmetric QPS, the quasi- helically symmetric HSX, and an axisymmetric configuration. In the ray tracing method, global ballooning mode stability is calculated by following rays in the eigenvalue space determined by the results of local, infinite-$n$ ballooning theory. The eigenvalue is a function of the flux coordinate $q$ (the safety factor), the field line label $alpha$, and the ballooning parameter, $\theta_{k}$. For each of the different magnetic configurations, the impact of breaking the symmetry (or degrading the quasi-symmetry) on ballooning modes is examined. For the HSX configurartion, three cases are examined: the standard quasi-helically symmetric case, a mirror case, and a hill case. The mirror and hill cases represent degraded symmetry configurations for the HSX experiment. The weak global shear in HSX results in modes which only weakly depend on the ballooning parameter. For QPS, the standard quasi-poloidally symmetric case and a degraded symmertry case are examined. In all of the non-axisymmetric cases studied, the unstable modes are localized in the field- line label, $\alpha$. The results for these cases will be presented.