Plasma Shape and Current Density Profile Control in Advanced Tokamak Operating Scenarios

The need for new sources of energy is expected to become a critical problem within the next few decades. Nuclear fusion has sufficient energy density to potentially supply the world population with its increasing energy demands. The tokamak is a magnetic confinement device used to achieve controlled fusion reactions. Experimental fusion technology has now reached a level where tokamaks are able to produce about as much energy as is expended in heating the fusion fuel. The next step towards the realization of a nuclear fusion tokamak power plant is ITER, which will be capable of exploring advanced tokamak (AT) modes, characterized by a high fusion gain and plasma stability. The extreme requirements of the advanced modes motivates researchers to improve the modeling of the plasma response as well as the design of feedback controllers. This dissertation focuses on several magnetic and kinetic control problems, including the plasma current, position and shape control, and data-driven and first-principles-driven modeling and control of plasma current density profile and the normalized plasma pressure ratio βN.The plasma is confined within the vacuum vessel by an external electromagnetic field, produced primarily by toroidal and poloidal field coils. The outermost closed plasma surface or plasma boundary is referred to as the shape of the plasma. A central characteristic of AT plasma regimes is an extreme elongated shape. The equilibrium among the electromagnetic forces acting on an elongated plasma is unstable. Moreover, the tokamak performance is improved if the plasma is located in close proximity to the torus wall, which guarantees an efficient use of available volume. As a consequence, feedback control of the plasma position and shape is necessary. In this dissertation, an H∞-based, multi-input-multi-output (MIMO) controller for the National Spherical Torus Experiment (NSTX) is developed, which is used to control the plasma position, shape, and X-point position.Setting up a suitable toroidal current profile is related to both the stability and performance of the plasma. The requirements of ITER motivate the research on plasma current profile control. Currently, physics-based control-oriented modeling techniques of the current profile evolution can be separated into two major classes: data-driven and first-principles-driven. In this dissertation, a two-timescale linear dynamic data-driven model of the rotational transform profile and βN is identified based on experimental data from the DIII-D tokamak. A mixed-sensitivity H∞ controller is developed and tested during DIII-D high-confinement (H-mode) experiments by using the heating and current drive (H&CD) systems to regulate the plasma rotational transform profile and βN around particular target values close to the reference state used for system identification. The preliminary experimental results show good progress towards routine current profile control in DIII-D. As an alternative, a nonlinear dynamic first-principles-driven model is obtained by converting the physics-based model that describes the current profile evolution in H-mode DIII-D discharges into a form suitable for control design. The obtained control-oriented model is validated by comparing the model prediction to experimental data. An H∞ control design problem is formulated to synthesize a stabilizing feedback controller, with the goal of developing a closed-loop controller to drive the current profile in DIII-D to a desirable target evolution. Simulations show that the controller is capable of regulating the system around the target rotational transform profile in the presence of disturbances. When compared to a previously designed data-driven model-based controller, the proposed first-principles-driven model-based controller shows potential for improving the control performance

Nonlinear Burn Condition and Kinetic Profile Control in Tokamak Fusion Reactors

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

Physics-model-based Optimization and Feedback Control of the Current Profile Dynamics in Fusion Tokamak Reactors

As the demand for energy continues to increase, the need to develop alternative energy sources to complement (and one day replace) conventional fossil fuels is becoming increasingly important. One such energy source is nuclear fusion, which has the potential to provide a clean source of energy and possesses an abundant fuel supply. However, due to the technological difficulty in creating the conditions necessary for controlled fusion to occur, nuclear fusion is not yet commercially viable. The tokamak is a device that utilizes magnetic fields to confine the reactants, which are in the plasma state, and it is one of the most promising devices capable of achieving controlled fusion. The ITER tokamak project is the next phase of tokamak development and will be the first tokamak reactor to explore the burning plasma (one with a significant amount of fusion reactions) operating regime.In order for ITER to meet its demanding goals, extensive research has been conducted to develop advanced tokamak operating scenarios characterized by a high fusion gain, good plasma confinement, magnetohydrodynamic stability, and a significant fraction of noninductively driven plasma current to maximize the plasma performance and potentially enable steady-state operation. As the dynamics of the tokamak plasma magnetic and kinetic states are highly coupled, distributed, nonlinear systems that exhibit many instabilities, it is extremely difficult to robustly achieve advanced operating scenarios. Therefore, active control of the plasma dynamics has significant potential to improve the ability to access advanced operating regimes. One of the key plasma properties investigated in the development of advanced scenarios is the plasma current profile because of its intimate relationship to plasma energy/particle transport and to plasma stability limits that are approached by increasing the plasma pressure. The plasma density and temperature profiles are also important parameters due to their close relationship to the amount of generated fusion power, to the total plasma stored energy, and to the amount of noninductive current drive. In tokamaks, the current and electron temperature profiles are coupled through resistive diffusion, noninductive current drive, and plasma energy/particle transport. As a result, integrated algorithms for current profile and electron temperature profile control will be necessary to maintain plasma stability, optimize plasma performance, and respond to changing power demand in ITER, and eventually a commercial, power producing tokamak reactor.In this work, model-based feedforward and feedback algorithms are developed to control the plasma current profile and thermal state dynamics with the goal of improving the ability to achieve robust tokamak operation. A first-principles-driven (FPD), physics-based approach is employed to develop models of the plasma response to the available actuators, which provides the freedom to handle the trade-off between the physics accuracy and the tractability for control design of the models. A numerical optimization algorithm to synthesize feedforward trajectories for the tokamak actuators that steer the plasma through the tokamak operating space to achieve a predefined target scenario (characterized by a desired current profile and total stored energy), subject to the plasma dynamics (described by the developed physics-based model), actuator constraints, and plasma state constraints, is developed. Additionally, robust feedback control algorithms for current profile, combined current profile + total stored energy, and simultaneous current profile + electron temperature profile control are synthesized for various tokamaks by embedding a FPD model into the control design process.Examples of the performance of the controllers in simulations (DIII-D, ITER, and TCV tokamaks) and DIII-D experiments are presented to illustrate the potential and versatility of the employed control methodology. The DIII-D experimental tests demonstrate the potential physics-model-based profile control has to provide a systematic approach for the development and robust sustainment of advanced scenarios. The ITER simulations demonstrate the ability to drive the current profile to a stationary target while simultaneously modulating the amount of fusion power that is generated. Finally, the TCV simulations demonstrate the ability to drive the current and electron temperature profiles to a self consistent target, as well as to maintain the current profile in a stationary condition while simultaneously modulating the electron temperature profile between equilibrium points