One-dimensional simulations of nonlinear burn control in ITER

Actively controlling the plasma temperature and density in future reactor-grade tokamaks will be a formidable challenge due to the multi-dimensional, coupled, and nonlinear characteristics of the burning-plasma dynamics. In ITER, the actuator systems that will be useful for temperature–density control (also known as burn control) include neutral beam injection, ion and electron cyclotron heating, pellet injection, and gas puffing. In this work, a nonlinear, model-based, burn-control algorithm is proposed. A model-based approach is attractive because it directly incorporates the complex plasma dynamics into the burn-control algorithm. Using Lyapunov techniques, the burn-control algorithm is synthesized from a control-oriented plasma model that is zero-dimensional (0-D). The reduced dimensionality of this plasma model renders the burn-control design more feasible. Nonetheless, this 0-D plasma model still captures the nonlinear response of the plasma energy and density to deuterium–tritium (D–T) fusion, radiation, auxiliary heating, external fueling, and other phenomena. More importantly, the control objective is indeed 0-D since the primary goal of a burn controller is usually to regulate volume-averaged properties of the plasma (e.g., overall fusion power $P_f$ or fusion gain $Q$). This makes 0-D models appropriate for control synthesis. However, the assessment of the effect of the proposed 0-D burn-control algorithms on the spatio-temporal dynamics of the plasma is a critical step of the control-design process. This work presents a one-dimensional (1-D) plasma model that is used in closed-loop simulations. The presented simulation study demonstrates how the spatial profiles of the D–T fuel density, the fusion-born alpha-particle density, the ion energy density, and the electron energy density evolve temporally under 0-D burn control. By testing 0-D controllers in 1-D simulations, the effectiveness of 0-D burn-control techniques can be investigated before implementation in actual tokamaks. Through investigations of this kind, control issues can be identified and addressed, enabling iterative improvement of the burn-control designs.