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this part is supported by two useful appendices on some of the mathematical tools used and the physical units of plasma physics. State-space models, state observers, H control, and process simulations are some of the familiar techniques used by ? the authors to meet the demanding spatial control specifications for these processes; however, the research reported in the monograph is more that just simulation studies and proposals for possible future hypothetical controllers, for the authors have worked with some of the world’s leading existing tokamak facilities. Chapter 5, 8, and 9 respectively, give practical results of implementations of their control schemes on the FTU Tokamak (Italy), the TCV Tokamak (Switzerland), and the JET Tokamak (United Kingdom). Additionally, the authors present simulation results of their ideas for the control of the new tokamak proposed for the ITER project. In conclusion, being very aware that most control engineers will not be conversant with the complexities of tokamak nuclear fusion reactor control, the authors have taken special care to give a useful introduction to the background of nuclear fusion, the science of plasma physics and appropriate models in the first part of the monograph (Chapters 1 to 3). This introduction is followed by six chapters (4 to 9) of control studies. In Chapter 4, the generic control problem is established and then five case study chapters follow.
This book is a complete treatment of work done to resolve the problems of position-, current-, and shape-control of plasma in tokamak-type (toroidal) devices being studied as a potential means of commercial energy production by nuclear fusion. Modelling and control are both detailed, allowing non-expert readers to understand the control problem. Starting from the magneto-hydro-dynamic equations, all the steps needed for the derivation of plasma state-space models are enumerated with frequent recall of the basic concepts of electromagnetics. The control problem is then described, beginning with the control of current and position—vertical and radial—control and progressing to the more challenging shape control. The solutions proposed vary from simple PIDs to more sophisticated MIMO controllers. The second edition of Magnetic Control of Tokamak Plasmas contains numerous updates and a substantial amount of completely new material covering areas such as: • modelling and control of resistive wall modes—the most important non-axisimmetric mode; • the isoflux approach for shape control; • a general approach for the control of limiter plasmas; • the use of inner vessel coils for vertical stabilization; and • significantly enhanced treatment of plasma-shape control at JET, including experimental results and introducing a method implemented for operation in the presence of current saturations. Whenever possible, coverage of the various topics is rounded out with experimental results obtained on currently existing tokamaks. The book also includes a presentation of the typical actuators and sensors used for control purposes in tokamaks. Some mathematical details are given in the appendices for the interested reader. The ideas formulated in this monograph will be of great practical help to control engineers, academic researchers and graduate students working directly with problems related to the control of nuclear fusion. They will also stimulate control researchers interested more generally in the advanced applications of the discipline. Advances in Industrial Control aims to report and encourage the transfer of technology in control engineering. The rapid development of control technology has an impact on all areas of the control discipline. The series offers an opportunity for researchers to present an extended exposition of new work in all aspects of industrial control.
There has been an increase in interest worldwide in fusion research over the last decade and a half due to the recognition that a large number of new, environmentally attractive, sustainable energy sources will be needed to meet ever increasing demand for electrical energy. Based on a series of course notes from graduate courses in plasma physics and fusion energy at MIT, the text begins with an overview of world energy needs, current methods of energy generation, and the potential role that fusion may play in the future. It covers energy issues such as the production of fusion power, power balance, the design of a simple fusion reactor and the basic plasma physics issues faced by the developers of fusion power. This book is suitable for graduate students and researchers working in applied physics and nuclear engineering. A large number of problems accumulated over two decades of teaching are included to aid understanding.
Resulting from ongoing, international research into fusion processes, the International Tokamak Experimental Reactor (ITER) is a major step in the quest for a new energy source.The first graduate-level text to cover the details of ITER, Controlled Fusion and Plasma Physics introduces various aspects and issues of recent fusion research activities through the shortest access path. The distinguished author breaks down the topic by first dealing with fusion and then concentrating on the more complex subject of plasma physics. The book begins with the basics of controlled fusion research, followed by discussions on tokamaks, reversed field pinch (RFP), stellarators, and mirrors. The text then explores ideal magnetohydrodynamic (MHD) instabilities, resistive instabilities, neoclassical tearing mode, resistive wall mode, the Boltzmann equation, the Vlasov equation, and Landau damping. After covering dielectric tensors of cold and hot plasmas, the author discusses the physical mechanisms of wave heating and noninductive current drive. The book concludes with an examination of the challenging issues of plasma transport by turbulence, such as magnetic fluctuation and zonal flow. Controlled Fusion and Plasma Physics clearly and thoroughly promotes intuitive understanding of the developments of the principal fusion programs and the relevant fundamental and advanced plasma physics associated with each program.
Plasma Science and Engineering transforms fundamental scientific research into powerful societal applications, from materials processing and healthcare to forecasting space weather. Plasma Science: Enabling Technology, Sustainability, Security and Exploration discusses the importance of plasma research, identifies important grand challenges for the next decade, and makes recommendations on funding and workforce. This publication will help federal agencies, policymakers, and academic leadership understand the importance of plasma research and make informed decisions about plasma science funding, workforce, and research directions.
TO THE SECOND EDITION In the nine years since this book was first written, rapid progress has been made scientifically in nuclear fusion, space physics, and nonlinear plasma theory. At the same time, the energy shortage on the one hand and the exploration of Jupiter and Saturn on the other have increased the national awareness of the important applications of plasma physics to energy production and to the understanding of our space environment. In magnetic confinement fusion, this period has seen the attainment 13 of a Lawson number nTE of 2 x 10 cm -3 sec in the Alcator tokamaks at MIT; neutral-beam heating of the PL T tokamak at Princeton to KTi = 6. 5 keV; increase of average ß to 3%-5% in tokamaks at Oak Ridge and General Atomic; and the stabilization of mirror-confined plasmas at Livermore, together with injection of ion current to near field-reversal conditions in the 2XIIß device. Invention of the tandem mirror has given magnetic confinement a new and exciting dimension. New ideas have emerged, such as the compact torus, surface-field devices, and the EßT mirror-torus hybrid, and some old ideas, such as the stellarator and the reversed-field pinch, have been revived. Radiofrequency heat ing has become a new star with its promise of dc current drive. Perhaps most importantly, great progress has been made in the understanding of the MHD behavior of toroidal plasmas: tearing modes, magnetic Vll Vlll islands, and disruptions.
During the past century, world-wide energy consumption has risen dramatically, which leads to a quest for new energy sources. Fusion of hydrogen atoms in hot plasmas is an attractive approach to solve the energy problem, with abundant fuel, inherent safety and no long-lived radioactivity. However, one of the limits on plasma performance is due to the various classes of magneto-hydrodynamic instabilities that may occur. The physics and control of these instabilities in modern magnetic confinement fusion devices is the subject of this book. Written by foremost experts, the contributions will provide valuable reference and up-to-date research reviews for "old hands" and newcomers alike.
Assuming no prior knowledge of plasma physics or numerical methods, Computational Methods in Plasma Physics covers the computational mathematics and techniques needed to simulate magnetically confined plasmas in modern magnetic fusion experiments and future magnetic fusion reactors. Largely self-contained, the text presents the basic concepts neces
Control of the Safety Factor Profile in a Tokamak uses Lyapunov techniques to address a challenging problem for which even the simplest physically relevant models are represented by nonlinear, time-dependent, partial differential equations (PDEs). This is because of the spatiotemporal dynamics of transport phenomena (magnetic flux, heat, densities, etc.) in the anisotropic plasma medium. Robustness considerations are ubiquitous in the analysis and control design since direct measurements on the magnetic flux are impossible (its estimation relies on virtual sensors) and large uncertainties remain in the coupling between the plasma particles and the radio-frequency waves (distributed inputs). The Brief begins with a presentation of the reference dynamical model and continues by developing a Lyapunov function for the discretized system (in a polytopic linear-parameter-varying formulation). The limitations of this finite-dimensional approach motivate new developments in the infinite-dimensional framework. The text then tackles the construction of an input-to-state-stability Lyapunov function for the infinite-dimensional system that handles the medium anisotropy and provides a common basis for analytical robustness results. This function is used as a control-Lyapunov function and allows the amplitude and nonlinear shape constraints in the control action to be dealt with. Finally, the Brief addresses important application- and implementation-specific concerns. In particular, the coupling of the PDE and the finite-dimensional subsystem representing the evolution of the boundary condition (magnetic coils) and the introduction of profile-reconstruction delays in the control loop (induced by solving a 2-D inverse problem for computing the magnetic flux) is analyzed. Simulation results are presented for various operation scenarios on Tore Supra (simulated with METIS) and on TCV (simulated with RAPTOR). Control of the Safety Factor Profile in a Tokamak will be of interest to both academic and industrially-based researchers interested in nuclear energy and plasma-containment control systems, and graduate students in nuclear and control engineering.
This book bridges the gap between general plasma physics lectures and the real world problems in MHD stability. In order to support the understanding of concepts and their implication, it refers to real world problems such as toroidal mode coupling or nonlinear evolution in a conceptual and phenomenological approach. Detailed mathematical treatment will involve classical linear stability analysis and an outline of more recent concepts such as the ballooning formalism. The book is based on lectures that the author has given to Master and PhD students in Fusion Plasma Physics. Due its strong link to experimental results in MHD instabilities, the book is also of use to senior researchers in the field, i.e. experimental physicists and engineers in fusion reactor science. The volume is organized in three parts. It starts with an introduction to the MHD equations, a section on toroidal equilibrium (tokamak and stellarator), and on linear stability analysis. Starting from there, the ideal MHD stability of the tokamak configuration will be treated in the second part which is subdivided into current driven and pressure driven MHD. This includes many examples with reference to experimental results for important MHD instabilities such as kinks and their transformation to RWMs, infernal modes, peeling modes, ballooning modes and their relation to ELMs. Finally the coverage is completed by a chapter on resistive stability explaining reconnection and island formation. Again, examples from recent tokamak MHD such as sawteeth, CTMs, NTMs and their relation to disruptions are extensively discussed.