Axisymmetric n = 0 growth rate modeling in Alcator C-Mod and SPARC: rigid versus non-rigid-body approaches

Abstract Accurate prediction of the n = 0 axisymmetric growth rate ( γ ) is critical for controlled tokamak operation. Conventional rigid linearized displacement models treat plasma as rigid, but this linearization neglects essential perturbed dynamics for vertical growth rate analysis. We found that the rigid perturbed model systematically underestimates γ by two-fold in flat-top and operational transition periods on Alcator C-Mod and SPARC. To investigate this we use a non-rigid plasma response model with a magnetic equilibrium-free-boundary Grad–Shafranov evolution linearized framework that self-consistently captures plasma deformation and current redistribution. Analysis of 165 Alcator C-Mod H-mode discharges confirms higher γ predictions from the non-rigid perturbed model during current flat-top, particularly at high elongation ( κ LCFS ) at the last closed flux surface and internal inductance ( ℓ i ). Sensitivity studies identify plasma current density distribution as the dominant driver. Further, active feedback simulations show that even with thick passive walls, non-rigid effects can dominate, doubling the predicted γ compared with rigid perturbation during vertical kick pacing events.