Modeling of active control of external magnetohydrodynamic instabilities

A general circuit formulation of resistive wall mode (RWM) feedback stabilization developed by Boozer [Phys. Plasmas 5, 3350 (1998)] has been used as the basis for the VALEN computer code that calculates the performance of an active control system in arbitrary geometry. The code uses a finite element representation of a thin shell structure in an integral formulation to model arbitrary conducting walls. This is combined with a circuit representation of stable and unstable plasma modes. Benchmark comparisons of VALEN results with large aspect ratio analytic model of the current driven kink mode are in very good agreement. VALEN also models arbitrary sensors, control coils, and the feedback logic connecting these sensors and control coils to provide a complete simulation capability for feedback control of plasma instabilities. VALEN modeling is in good agreement with experimental results on DIII-D [Garofalo et al., Nucl. Fusion 40, 1491 (2000)] and HBT-EP [Cates et al., Phys. Plasmas 7, 3133 (2000)]. VALEN feedback simulations have also been used to evaluate and optimize the sensor/coil configurations for present and planned RWM experiments on DIII-D. These studies have shown a clear advantage for the use of local poloidal field sensors driving a 'mode control' feedback logic control loop and configurations which minimize the control coil coupling to the stabilizing resistive wall