AGNI: An ideal MHD stability solver and optimizer for magnetic confinement fusion devices

Finite‑n ideal magnetohydrodynamic (MHD) stability imposes a primary constraint on magnetic confinement devices with significant plasma current, encompassing tokamaks, stellarators, and mirror hybrids. Although axisymmetric stability codes emerged in the late 1970s, no open‑source solver currently treats finite‑n ideal MHD for both stellarators and tokamaks while remaining compatible with gradient‑based optimization workflows essential to contemporary stellarator design.

We present AGNI (Analysis of Global Normal modes in Ideal MHD), an open‑source, GPU‑accelerated stability code that is differentiable end‑to‑end. AGNI discretizes the linearized ideal‑MHD equations with summation‑by‑parts differentiation matrices, separating spatial derivatives of the perturbation variables from equilibrium quantities. This structure permits efficient reverse‑mode automatic differentiation of eigenvalues with respect to equilibrium parameters, providing analytic gradients to optimization algorithms at minimal cost.

Benchmark studies show quantitative agreement with TERPSICHORE for various stellarator configurations and simple analytical tests with axisymmetric systems.