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

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

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

Research Needs for Magnetic Fusion Energy Sciences. Report of the Research Needs Workshop (ReNeW) Bethesda, Maryland, June 8-12, 2009

Nuclear fusion - the process that powers the sun - offers an environmentally benign, intrinsically safe energy source with an abundant supply of low-cost fuel. It is the focus of an international research program, including the ITE R fusion collaboration, which involves seven parties representing half the world's population. The realization of fusion power would change the economics and ecology of energy production as profoundly as petroleum exploitation did two centuries ago. The 21st century finds fusion research in a transformed landscape. The worldwide fusion community broadly agrees that the science has advanced to the point where an aggressive action plan, aimed at the remaining barriers to practical fusion energy, is warranted. At the same time, and largely because of its scientific advance, the program faces new challenges; above all it is challenged to demonstrate the timeliness of its promised benefits. In response to this changed landscape, the Office of Fusion Energy Sciences (OFES ) in the US Department of Energy commissioned a number of community-based studies of the key scientific and technical foci of magnetic fusion research. The Research Needs Workshop (ReNeW) for Magnetic Fusion Energy Sciences is a capstone to these studies. In the context of magnetic fusion energy, ReNeW surveyed the issues identified in previous studies, and used them as a starting point to define and characterize the research activities that the advance of fusion as a practical energy source will require. Thus, ReNeW's task was to identify (1) the scientific and technological research frontiers of the fusion program, and, especially, (2) a set of activities that will most effectively advance those frontiers. (Note that ReNeW was not charged with developing a strategic plan or timeline for the implementation of fusion power.) This Report presents a portfolio of research activities for US research in magnetic fusion for the next two decades. It is intended to provide a strategic framework for realizing practical fusion energy. The portfolio is the product of ten months of fusion-community study and discussion, culminating in a Workshop held in Bethesda, Maryland, from June 8 to June 12, 2009. The Workshop involved some 200 scientists from Universities, National Laboratories and private industry, including several scientists from outside the US. Largely following the Basic Research Needs model established by the Office of Basic Energy Sciences (BES ), the Report presents a collection of discrete research activities, here called 'thrusts.' Each thrust is based on an explicitly identified question, or coherent set of questions, on the frontier of fusion science. It presents a strategy to find the needed answers, combining the necessary intellectual and hardware tools, experimental facilities, and computational resources into an integrated, focused program. The thrusts should be viewed as building blocks for a fusion program plan whose overall structure will be developed by OFES , using whatever additional community input it requests. Part I of the Report reviews the issues identified in previous fusion-community studies, which systematically identified the key research issues and described them in considerable detail. It then considers in some detail the scientific and technical means that can be used to address these is sues. It ends by showing how these various research requirements are organized into a set of eighteen thrusts. Part II presents a detailed and self-contained discussion of each thrust, including the goals, required facilities and tools for each. This Executive Summary focuses on a survey of the ReNeW thrusts. The following brief review of fusion science is intended to provide context for that survey. A more detailed discussion of fusion science can be found in an Appendix to this Summary, entitled 'A Fusion Primer.

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

Designing a Fusion Power Plant with Superconducting Training Magnets

Fusion power has the potential to revolutionise global energy production with a reliable, low CO2 (not zero due to the use of steel, concrete etc. that typically produce CO2 during manufacture), low radioactivity power supply, that is readily available at the point of need. The ITER and SPARC reactors are already under construction, with plans to begin full-power (Qfus ≥ 10) operation in the early 2030s; proving that fusion is a viable energy source. To see wide adoption however, reactors must be made as commercially attractive as possible. Here we present superconducting pilot reactor designs that have been optimised for minimum capital cost using the PROCESS systems code. Key design choices were made using technologies that are either available now or already in development; with concentrated effort these reactors could be built on 2030-2040 timescales. We focus primarily on the reactor from this set with the lowest overall capital cost, our “preferred” reactor: a 100 MW net electricity producing tokamak with REBCO superconducting toroidal field coils and central solenoid and Nb-Ti superconducting poloidal field coils. In addition, we have investigated using ductile, remountable Nb-Ti training coils (named after the training wheels of children’s bicycles) during the commissioning phase of a reactor to remove the risk of brittle failure of the full-power magnets during this stage. Such magnets would operate at lower field, but would enable thorough machine testing. Finally, we investigate and predict how advances in magnet technologies could effect our preferred reactor design and cost, and conclude that the effects of such advances do not justify waiting yet longer before beginning detailed reactor design and construction

A flexible architecture for plasma magnetic control in tokamak reactors

Plasma magnetic control is one of the core engineering issues to be tackled in a fusion device. Over the last years, model based approaches have been proposed to face this issue, proving their effectiveness and allowing to reduce the time span needed for control testing and validation. The first part of this work is intended to give an overview of the subject, from the historical milestones to the underlying physics; the most common techniques for tokamak plasmas electromagnetic modeling and control are also introduced and discussed. After this introduction, a general architecture for plasma magnetic control in tokamaks is proposed. Finally, the proposed solution is applied to the Experimental Advanced Superconducting Tokamak (EAST) tokamak, where a new plasma magnetic control architecture was developed and implemented during the 2016-2018 experimental campaigns, and to the Japan Torus-60 Super Advanced (JT-60SA) device, which is currently under construction in Japan

A flexible architecture for plasma magnetic control in tokamak reactors

Plasma magnetic control is one of the core engineering issues to be tackled in a fusion device. Over the last years, model based approaches have been proposed to face this issue, proving their effectiveness and allowing to reduce the time span needed for control testing and validation. The first part of this work is intended to give an overview of the subject, from the historical milestones to the underlying physics; the most common techniques for tokamak plasmas electromagnetic modeling and control are also introduced and discussed. After this introduction, a general architecture for plasma magnetic control in tokamaks is proposed. Finally, the proposed solution is applied to the Experimental Advanced Superconducting Tokamak (EAST) tokamak, where a new plasma magnetic control architecture was developed and implemented during the 2016-2018 experimental campaigns, and to the Japan Torus-60 Super Advanced (JT-60SA) device, which is currently under construction in Japan

Extremely Shaped Plasmas to Improve the Tokamak Concept

Energy is essential for human existence and our future depends on plentiful and accessible sources of energy. The world population is fast growing and the average energy used per capita increases. One of the greatest challenges for human beings is that of meeting the growing demand for energy in a responsible, equitable and sustainable way. The possibility to obtain energy by "fusing" light atoms addresses these needs. Nuclear fusion reactions are clean, safe and the amount of fuel present on Earth (hydrogen isotopes) is practically inexhaustible and well distributed. Nuclear fusion is a natural process that occurs in all active stars like our Sun. Since the first demonstration of a deuterium fusion reaction (Rutherford 1933), researchers worldwide have tried to replicate this process on Earth by building a thermonuclear fusion reactor. Nevertheless, the challenge posed by the construction of a nuclear fusion reactor is greater than the one presented earlier by the development of a fission reactor. During the IAEA Conference in Geneva in the early 1958, L.A.Artsimovich declared: "Plasma physics is very difficult. Worldwide collaboration is needed for progress" and E.Teller, at the same conference: "Fusion technology is very complex. It is almost impossible to build a fusion reactor in this century". They were right. The extremely high temperature and density necessary to fuse hydrogen isotopes makes it difficult indeed to create a successful fusion reactor. Even though the physics of the fusion reaction appears clear, we are still facing problems on the road towards bulding the "box" that can efficiently confine the hot gas in the state of plasma. The best results so far have been obtained confining a plasma with strong magnetic fields in a toroidal configuration ("tokamak"). The Centre de Recherches en Physique des Plasmas in Switzerland actively studies this promising configuration towards the development of a nuclear fusion reactor. The experimental activity of the Tokamak à Configuration Variable (TCV) mainly focuses on the research of optimized plasma shapes capable of improving the global performance and solve the technological challenges of a tokamak reactor. Several theoretical and experimental results show the importance of the plasma shape in tokamaks. The maximum value of β (an indicator of the confinement efficiency) is for example related to the ratio between the height and the width of the plasma. The plasma shape can also affect the power necessary to access improved confinement regimes, as well as the plasma stability. This thesis reports on a contribution towards the optimization of the tokamak plasma shape. In particular, it describes the theoretical and experimental studies carried out in the TCV tokamak on two innovative plasma shapes: the doublet shaped plasma and the snowflake divertor. Doublet shaped plasmas have been studied in the past by the General Atomics group. Since then, the development of new plasma diagnostics and the discovery of new confinement regimes have given new reasons for interest in this unusual configuration. TCV is the only tokamak worldwide theoretically able to establish and control this configuration. This thesis illustrates new motivations for creating doublet plasmas. The vertical stability of the configuration is studied using a rigid model and the results are compared with those obtained with the KINX MHD stability code. The best strategy for controlling a doublet on TCV is also investigated, and a possible setup of the TCV control system is suggested for the doublet configuration. Analyzing the possible scenarios for doublet creation, the most promising scenario consists of the creation of two independent plasmas, which are subsequently merged to establish a doublet. For this reason, particular attention needs to be devoted to the problem of the plasma start-up. In this thesis, a general analysis of the TCV ohmic and assisted with ECH plasma start-up is presented, and recent attempts to create a doublet plasma are reported. Since the magnetic field reconstruction at the breakdown time is important to better diagnose these plasmas, the entire magnetic system of TCV has been calibrated with an original technique, also described in the manuscript. The last part of this thesis is devoted to the snowflake divertor configuration. This innovative plasma shape has been proposed and theoretically studied by Dr. D.D.Ryutov from the Lawrence Livermore National Laboratory. In Ryutov's articles, this configuration was proposed to alleviate the problems of the plasma-wall interaction and possibly affect the plasma edge stability. The TCV tokamak was the first to report the creation and control of a snowflake configuration, and the candidate was the principal investigator of this work. These results are accordingly discussed in this thesis. Details are provided in particular on the strategy used to establish the configuration. An edge-localized mode (ELM) H-mode regime, supported by electron cyclotron heating, has been successfully established in a snowflake. This regime exhibits 2 to 3 times lower ELM frequency but only a 20%-30% increase in normalized ELM energy (ΔWELM/WP ) compared to an identically-shaped, conventional, single-null, diverted H-mode. Enhanced stability of mid- to high-toroidal-mode-number ideal modes is consistent with the different snowflake ELM phenomenology. Finally, the capability of the snowflake to redistribute the edge power on the additional strike points has been confirmed experimentally and is also reported in this thesis