On the feasibility of model-based feedback control of vertical instability growth rate using out-vessel coils in ARC-like scenarios
In this work, we propose a model-based feedback controller that regulates the vertical instability growth rate ($γ_{gr}$) of a high-elongation, double-null tokamak directly, using only out-vessel poloidal field (PF) coils. High elongation raises the achievable plasma current and fusion performance but makes the plasma vertically unstable, and in a fusion power plant the in-vessel coils that present devices rely on for stabilization may be absent, leaving only distant out-vessel circuits. The controller couples a machine learning surrogate of non-rigid, profile agnostic vertical instability metric to a constrained quadratic program: the surrogate supplies real-time $γ_{gr}$ estimates and, via automatic differentiation, the actuator sensitivities, while the program allocates coil voltages to track a target growth rate, maintain double-null divertor balance, and respect electromechanical limits. We tested this method on the ARC~V3A power plant design configuration across 24 closed-loop simulations spanning equilibrium variations, actuator degradations, and transient disturbances. We achieved full or marginal success in 83\% of these cases (full in 50\%, marginal in a further 33\%) and lose control in the remaining 17\%; the failures map the boundary of out-vessel controllability (occurring at the highest growth rates) and under actuator limits. The controller does not regulate boundary shape explicitly: separatrix geometry follows indirectly from growth rate and flux balance control and would require a separate shape control layer for sustained scenario evolution.