Axisymmetric Magnetic Control Design in Tokamaks Using Perturbed Equilibrium Plasma Response Modeling

A model of linearized tokamak plasma response to variations in external toroidal currents is developed for purposes of axisymmetric control analysis. The plasma model is based on free-boundary equilibria with perturbations in the poloidal field coils. Plasma response to currents in arbitrary passive conductors such as the vacuum vessel is approximated by mapping their effect to equivalent poloidal field coil currents. Ideal magnetohydrodynamic flux conservation is satisfied approximately by allowing total plasma current and current-density profile to vary. The resulting flux-conserving plasma response model including vacuum vessel effects is used along with multivariable control system techniques to design high-performance axisymmetric control systems for the Alcator C-Mod tokamak to stabilize the vertical instability and to provide stable shape control.