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We demonstrate a fast adjoint-based method to optimize tokamak andstellarator equilibria against a pressure-driven instability known as theinfinite-$n$ ideal ballooning mode. We present three finite-$\beta$ (the ratioof thermal to magnetic pressure) equilibria: one tokamak equilibrium and twostellarator equilibria that are unstable against the ballooning mode. Using theself-adjoint property of ideal MHD, we construct a technique to rapidlycalculate the change in the growth rate, a measure of ideal ballooninginstability. Using the~\texttt{SIMSOPT} framework, we then implement our fastadjoint gradient-based optimizer to minimize the growth rate and find stableequilibria for each of the three initially unstable equilibria.

An adjoint-based method for optimizing MHD equilibria against the infinite-n, ideal ballooning mode