Axisymmetric n = 0 Growth Rate Modeling in Alcator C-Mod and SPARC: Rigid vs. Non-Rigid Body Approaches

Accurate prediction of $n=0$ axisymmetric growth rate ($\gamma$) is critical for controlled tokamak operation. Conventional rigid linearized displacement model treat plasma as rigid, but this linearization neglect essential perturbed dynamics for vertical growth rate analysis. We found that, the rigid perturbed model systematically underestimate $\gamma$ by two-fold in flat-top and operational transitions period on Alcator C-Mod and SPARC. To investigate, we use non-rigid plasma response model using MEQ-FGEL framework that self-consistently captures plasma deformation and current redistribution. Analysis of 165 Alcator C-Mod H-mode discharges confirms higher $\gamma$ predictions from non-rigid perturbed model during current flat-top, particularly at high elongation ($\kappa_{\text{\rm LCFS}}$) at the last closed flux surface and internal inductance ($\ell_i$). Sensitivity studies identify plasma current density distribution as dominant driver. Further, active feedback simulations show that even with thick passive walls, non-rigid effects can dominate, doubling the predicted $\gamma$ compared to rigid perturbation during vertical kick pacing event.