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

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

Integrated Control in Tokamaks using Nonlinear Robust Techniques and Actuator Sharing Strategies

Tokamaks are devices whose final purpose is obtaining energy by means of nuclear fusion reactions. To achieve such purpose, a gas is injected into the tokamak\u27s torus-shaped chamber and heated up to extremely high temperatures, giving birth to a plasma. When the necessary conditions of temperature, density, and confinement time are achieved, virtually inexhaustible energy can be produced in a tokamak. The main contribution of this dissertation is the development of integrated control strategies for tokamak plasmas. The development of integrated control architectures is necessary for tokamaks to become efficient and commercially competitive power plants. Because a tokamak plasma is a highly nonlinear, coupled dynamical system, the great diversity of complex control problems that coexist in a tokamak are indeed closely interrelated. However, this variety of control problems must be tackled by means of a limited number of actuators. A functional design for integrated tokamak-control architectures should employ multi-input multi-output controllers to simultaneously regulate as many plasma variables as possible with the available actuators. Supervisory and exception handling systems that monitor the plasma state arise as a necessity to ensure a safe tokamak-operation. Finally, actuator sharing and management capabilities should also exist in order to utilize the available actuators in an optimal way. Various control problems are tackled in this dissertation, including kinetic, magnetic, and instability control problems. Control-oriented, physics-based models that characterize some specific aspects of the plasma dynamics have been employed to develop new control-oriented simulation codes and integrated-control solutions that employ nonlinear, robust control techniques and optimization-based actuator-management strategies. Some of those control solutions have been experimentally tested in the DIII-D tokamak

Strategies for Optimal Control of the Current and Rotation Profiles in the DIII-D Tokamak

The tokamak is currently the most promising device for realizing commercially-viable fusion energy production. The device uses magnetic fields to confine a circulating ring of hydrogen in the plasma state, i.e. a cloud of hydrogen ions and electrons. When sufficiently heated the hydrogen ions can overcome the electrostatic forces and fuse together, providing an overwhelmingly abundant energy source. However, stable, high-performance operation of a tokamak requires several plasma control problems to be handled simultaneously. Moreover, the complex physics which governs the tokamak plasma evolution must be studied and understood to make correct choices in controller design. In this thesis, two key control issues are studied intensely, namely the optimization and control of the plasma current profile and control of the plasma rotation (or flow).In order to maximize performance, it is preferable that tokamaks achieve advanced scenarios (AT) characterized by good plasma confinement, improved magnetohydrodynamic stability, and a largely non-inductively driven plasma current. A key element to the development of AT scenarios is the optimization of the spatial distribution of the current profile. Also, research has shown that the plasma rotation can stabilize the tokamak plasma against degradations in the desired MHD equilibrium.In this thesis, new model-based control approaches for the current profile and rotation profile are developed to allow experimental exploration of advanced tokamak scenarios. Methods for separate control of both the current profile and rotation are developed. The advanced model-based control methods presented in this thesis have contributed to theory of tokamak profile control and in some cases they have been successfully validated experimentally in the DIII-D tokamak

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

Plasma Edge Kinetic-MHD Modeling in Tokamaks Using Kepler Workflow for Code Coupling, Data Management and Visualization

A new predictive computer simulation tool targeting the development of the H-mode pedestal at the plasma edge in tokamaks and the triggering and dynamics of edge localized modes (ELMs) is presented in this report. This tool brings together, in a coordinated and effective manner, several first-principles physics simulation codes, stability analysis packages, and data processing and visualization tools. A Kepler workflow is used in order to carry out an edge plasma simulation that loosely couples the kinetic code, XGC0, with an ideal MHD linear stability analysis code, ELITE, and an extended MHD initial value code such as M3D or NIMROD. XGC0 includes the neoclassical ion-electron-neutral dynamics needed to simulate pedestal growth near the separatrix. The Kepler workflow processes the XGC0 simulation results into simple images that can be selected and displayed via the Dashboard, a monitoring tool implemented in AJAX allowing the scientist to track computational resources, examine running and archived jobs, and view key physics data, all within a standard Web browser. The XGC0 simulation is monitored for the conditions needed to trigger an ELM crash by periodically assessing the edge plasma pressure and current density profiles using the ELITE code. If an ELM crash is triggered, the Kepler workflow launches the M3D code on a moderate-size Opteron cluster to simulate the nonlinear ELM crash and to compute the relaxation of plasma profiles after the crash. This process is monitored through periodic outputs of plasma fluid quantities that are automatically visualized with AVS/Express and may be displayed on the Dashboard. Finally, the Kepler workflow archives all data outputs and processed images using HPSS, as well as provenance information about the software and hardware used to create the simulation. The complete process of preparing, executing and monitoring a coupled-code simulation of the edge pressure pedestal buildup and the ELM cycle using the Kepler scientific workflow system is described in this paper

Model-based Control of the Current Density Profile in the Experimental Advanced Superconducting Tokamak (EAST)

As worldwide energy consumption increases, the world is facing the possibility of an energy shortage problem. While several approaches have been proposed to slow down this process, which include the improvement of the combustion efficiency of fossil fuels and the introduction of nuclear energy and renewable energy, such as solar, wind, and geothermal energy, a replacement for fossil fuels will eventually be needed. The energy that comes from a nuclear reaction, which includes nuclear fission and nuclear fusion, has a high energy production density (rate of energy produced divided by the area of the land needed to produce it) and produces no air pollution or greenhouse gases, which makes it a strong and attractive candidate. Compared with nuclear fission, the radioactive waste from nuclear fusion can be more easily disposed, the reactants in a nuclear fusion reaction are abundantly available in nature, and nuclear fusion poses no risk of a nuclear accident. For all these reasons, nuclear fusion is a potential solution for the energy shortage problem. However, there are many challenges that need to be conquered to achieve nuclear fusion. The primary challenge is to confine the hot reactants, whose temperatures are about one hundred million degrees Kelvin. At these temperatures, the reactants are in the plasma state and have enough kinetic energy to overcome the repelling electrostatic forces and fuse. One of the most promising approaches to confine the fusion plasma is magnetic confinement, where magnetic fields are used to confine the plasma through the Lorentz force. The tokamak is one of the fusion devices that exploit magnetic confinement. To demonstrate the viability of a nuclear fusion power plant, the International Thermonuclear Experimental Reactor (ITER) tokamak project is aimed at producing 500 megawatts power with 50 megawatts of input power, which will make it the first tokamak with net energy output. To be able to obtain the desired fusion gain, the ITER tokamak will need to operate at a temperature and a pressure so high that the plasma has a good chance of becoming unstable and difficult to confine. To address this issue, extensive research has been conducted on different fusion tokamaks around the world to find high performance operating scenarios characterized by a high fusion gain, good plasma confinement, plasma stability, and a dominant self-generated plasma current with the goal of developing candidate scenarios for ITER. The shape of the toroidal current density profile, or the safety factor profile ($q$-profile), impacts steady-state operation, magnetohydrodynamic (MHD) stability, and plasma performance. The plasma $\beta$, which is the ratio of the kinetic pressure of the plasma to the magnetic pressure (pressure exerted on plasma by the magnetic field), acts as an important economic factor in fusion power generation. Therefore, active control of the toroidal current density profile and plasma $\beta$ is one path towards advanced scenarios. This dissertation focuses on developing control solutions for regulating the current density profile, and to some extent the normalized plasma $\beta$ (denoted as $\beta_N$), on the Experimental Advanced Superconducting Tokamak (EAST) located at the Institute of Plasma Physics, Chinese Academy of Sciences (ASIPP), in Hefei, China. Towards this goal, a control-oriented, physics-based model has been developed for the current density profile evolution in EAST in response to available heating and current-drive (H\&CD) systems. The feasibility of reconstructing the internal plasma states, which may be crucial for feedback control, from measurements at the magnetic axis and at the plasma edge has been studied by using experimental data and exploiting the response model. Target scenarios (characterized by desired $q$-profile and $\beta_N$) have been developed by following a model-based finite-time optimization approach. Feedback controllers ranging from simpler Proportional-Integral-Derivative (PID) controllers to more complex model-based optimal controllers, derived from Linear-Quadratic-Regulator (LQR), $H_\infty$, and Model Predictive Control (MPC) theories, have been synthesized to counteract deviations from the desired target scenario. The overall control solution has been implemented in the Plasma Control System (PCS) and closed-loop $q$-profile regulation has been demonstrated for the first time ever in EAST in disturbance rejection and target tracking experiments

MHD stability and disruptions in the SPARC tokamak

SPARC is being designed to operate with a normalized beta of beta(N) = 1.0, a normalized density of n(G) = 0.37 and a safety factor of q(95) approximate to 3.4, providing a comfortable margin to their respective disruption limits. Further, a low beta poloidal beta(p) = 0.19 at the safety factor q = 2 surface reduces the drive for neoclassical tearing modes, which together with a frozen-in classically stable current profile might allow access to a robustly tearing-free operating space. Although the inherent stability is expected to reduce the frequency of disruptions, the disruption loading is comparable to and in some cases higher than that of ITER. The machine is being designed to withstand the predicted unmitigated axisymmetric halo current forces up to 50 MN and similarly large loads from eddy currents forced to flow poloidally in the vacuum vessel. Runaway electron (RE) simulations using GO+CODE show high flattop-to-RE current conversions in the absence of seed losses, although NIMROD modelling predicts losses of similar to 80 %; self-consistent modelling is ongoing. A passive RE mitigation coil designed to drive stochastic RE losses is being considered and COMSOL modelling predicts peak normalized fields at the plasma of order 10(-2) that rises linearly with a change in the plasma current. Massive material injection is planned to reduce the disruption loading. A data-driven approach to predict an oncoming disruption and trigger mitigation is discussed

Model-based Optimization and Feedback Control of the Current Density Profile Evolution in NSTX-U

Unlike nuclear fission in present nuclear power plants, where energy is generated by splitting heavy atoms like uranium, nuclear fusion generates energy by fusing light nuclei like hydrogen isotopes under high-temperature and high-pressure conditions, at which the reactants (hydrogen isotopes) separate from their electrons and form an ionized gas called plasma, which is considered as the fourth state of matter. Contrary to fission, fusion provides more energy density, poses almost no risk of a catastrophic nuclear accident, and produces mostly short-term, low-level radioactive waste.The main difficulty in maintaining fusion reactions is the development of a device that can confine the hot plasma for sufficiently long time while preventing it from hitting the walls of the confining device. Among several techniques, magnetic confinement appears as the most promising approach. In particular, the tokamak device is a toroidal device surrounded by large magnetic coils responsible for the magnetic fields that confine the plasma. A spherical tokamak, or a spherical torus (ST), is a variation of the conventional tokamak concept. Compared to a standard tokamak, the ST device extrapolates to a more compact, potentially lower-cost reactor with higher efficiency of confinement. Nuclear fusion research is a highly challenging, multidisciplinary field seeking contributions from both plasma physics and multiple engineering areas. As an application of plasma control engineering, this dissertation mainly explores methods to control the current density profile evolution within the National Spherical Torus eXperiment-Upgrade (NSTX-U), which is a substantial upgrade based on the NSTX device, which is located in Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ. Active control of the toroidal current density profile is among those plasma control milestones that the NSTX-U program must achieve to realize its next-step operational goals, which are characterized by high-performance, long-pulse, MHD-stable plasma operation with neutral beam heating. Therefore, the aim of this work is to develop model-based, feedforward and feedback controllers that can enable time regulation of the current density profile in NSTX-U by actuating the total plasma current, electron density, and the powers of the individual neutral beam injectors.Motivated by the coupled, nonlinear, multivariable, distributed-parameter plasma dynamics, the first step towards control design is the development of a physics-based, control-oriented model for the current profile evolution in NSTX-U in response to non-inductive current drives and heating systems. Numerical simulations of the proposed control-oriented model show qualitative agreement with the high-fidelity physics code TRANSP. The next step is to utilize the proposed control-oriented model to design an open-loop actuator trajectory optimizer. Given a desired operating state, the optimizer produces the actuator trajectories that can steer the plasma to such state. The objective of the feedforward control design is to provide a more systematic approach to advanced scenario planning in NSTX-U since the development of such scenarios is conventionally carried out experimentally by modifying the tokamak’s actuator trajectories and analyzing the resulting plasma evolution.Finally, the proposed control-oriented model is embedded in feedback control schemes based on optimal control and Model Predictive Control (MPC) approaches. Integrators are added to the standard Linear Quadratic Gaussian (LQG) and MPC formulations to provide robustness against various modeling uncertainties and external disturbances. The effectiveness of the proposed feedback controllers in regulating the current density profile in NSTX-U is demonstrated in closed-loop nonlinear simulations. Moreover, the optimal feedback control algorithm has been implemented successfully in closed-loop control simulations within TRANSP through the recently developed Expert routine