UC San Diego

Tokamaks can excite kink modes that can lock or nearly lock to the vacuum vessel wall, and whose rotation frequencies and growth rates vary in time but are generally inversely proportional to the magnetic flux diffusion time of the vacuum vessel wall. This magnetohydrodynamic (MHD) instability is pressure limiting in tokamaks and is called the Resistive Wall Mode (RWM). Future tokamaks that are expected to operate as fusion reactors will be required to maximize plasma pressure in order to maximize fusion performance. The DIII-D tokamak is equipped with electromagnetic control coils, both inside and outside of its vacuum vessel, which create magnetic fields that are small by comparison to the machine’s equilibrium field but are able to dynamically counteract the RWM. Presently for RWM feedback, DIII-D uses its interior control coils using a classical proportional gain only controller to achieve high plasma pressure. Future advanced tokamak designs will not likely have the luxury of interior control coils and a proportional gain algorithm is not expected to be effective with external control coils. The computer code VALEN was designed to calculate the performance of an MHD feedback control system in an arbitrary geometry. VALEN models the perturbed magnetic field from a single MHD instability and its interaction with surrounding conducting structures using a finite element approach. A linear quadratic gaussian (LQG) control, or ℋ₂ optimal control, algorithm based on the VALEN model for RWM feedback was developed for use with DIII-D’s external control coil set. The algorithm is implemented on a platform that combines a graphics processing unit (GPU) for real-time control computation with low latency digital input/output control hardware and operates in parallel with the DIII-D Plasma Control System (PCS). Simulations and experiments showed that modern control techniques performed better, using 77% less current, than classical techniques when using coils external to the vacuum vessel for RWM feedback. RWM feedback based on VALEN outperformed a classical control algorithm using external coils to suppress the normalized plasma response to a rotating n=1 perturbation applied by internal coils over a range of frequencies. This study describes the design, development and testing of the GPU based control hardware and algorithm along with its performance during experiment and simulation.