Nonlinear Burn Condition and Kinetic Profile Control in Tokamak Fusion Reactors

Abstract

One of the most promising devices for realizing power production through nuclear fusion is the tokamak. In order to maximize performance, it is preferable that tokamaks achieve operating scenarios characterized by good plasma confinement, improved magnetohydrodynamic stability, and a largely non-inductively driven plasma current. Such scenarios could enable steady-state reactor operation with high fusion gain, the ratio of fusion power produced to the external heating power needed to sustain reactions. There are many experimental tokamaks around the world, each exploring different facets of plasma physics and fusion technology. These experiments have reached the point where the power released from fusion is nearly equal to the power input required to heat the plasma. The next experimental step is ITER, which aims to reach a fusion gain exceeding ten for short pulses, and to sustain a gain of five for longer pulses (around 1000 s). In order for ITER to be a success, several challenging control engineering problems must be addressed.Among these challenges is to precisely regulate the plasma density and temperature, or burn condition. Due to the nonlinear and coupled dynamics of the system, modulation of the burn condition (either during ramp-up/shut-down or in response to changing power demands) without a well designed control scheme could result in undesirable transient performance. Feedback control will also be necessary for responding to unexpected changes in plasma confinement, impurity content, or other parameters, which could significantly alter the burn condition during operation. Furthermore, although stable operating points exist for most confinement scalings, certain conditions can lead to thermal instabilities. Such instabilities can either lead to quenching or a thermal excursion in which the system moves to a higher temperature equilibrium point. In any of these situations, disruptive plasma instabilities could be triggered, stopping operation and potentially causing damage to the confinement vessel.In this work, the problem of burn condition control is addressed through the design of a nonlinear control law guaranteeing stability of desired equilibria. Multiple actuation methods, including auxiliary heating, isotopic fueling, and impurity injection, are used to ensure the burn condition is regulated even when actuators saturate. An adaptive control scheme is used to handle model uncertainty, and an online optimization scheme is proposed to ensure that the plasma is driven to an operating point that minimizes an arbitrary cost function. Due to the possible limited availability of diagnostic systems in ITER and future reactors, an output feedback control scheme is also proposed that combines the nonlinear controller with an observer that estimates the states of the burning plasma system based on available measurements. Finally, the control scheme is tested using the integrated modeling code METIS.The control of spatial profiles of parameters, including current, density, and temperature, is also an important challenge in fusion research, due to their effect on MHD stability, non-inductive current drive, and fusion power. In this work, the problem of kinetic profile control in burning plasmas is addressed through a nonlinear boundary feedback control law designed using a technique called backstepping. A novel implementation of the backstepping technique is used that enables the use of both boundary and interior actuation. The backstepping technique is then applied to the problem of current profile control in both low-confinement and high-confinement mode discharges in the DIII-D tokamak based on a first-principles-driven model of the current profile evolution. Both designs are demonstrated in simulations and experimental tests