Nonlinear Local Control of the Safety-Factor-Profile Gradient at Moving Spatial Locations in Tokamak Plasmas*

Tokamaks are toroidal devices that confine a very hot plasma (hydrogenic ionized gas) by using strong magnetic fields. When the kinetic energy is high, positively charged nuclei in the plasma can overcome the Coulombic forces of repulsion and fuse to form a heavier nucleus. A tremendous amount of energy is released during this reaction. The pitch of the magnetic field in a tokamak, measured by the safety factor profile q, plays a crucial role in ensuring the magnetohydrodynamic (MHD) stability of the tokamak plasma. MHD instabilities like the Neoclassical Tearing Mode (NTM), which can deteriorate or even terminate plasma confinement, can appear at regions in the tokamak where the safety factor profile assumes a rational value. Since the safety factor profile is a continuous function of location in the tokamak, rational values at specific locations are inevitable. Controlling the gradient of the safety factor profile at these locations can prevent or mitigate the effect of MHD instabilities. In this work, a one-dimensional model that approximates the safety factor gradient dynamics at one of the locations where the safety factor q achieves a rational value is developed. A controller based on feedback linearization of this model is designed to track a target gradient value in the steady-state scenario. The effectiveness of this controller is demonstrated in nonlinear numerical simulations powered by the Control Oriented Transport SIMulator (COTSIM) for a DIII-D tokamak scenario.