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Mhd Equilibrium And Stability For Stellarator
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Book Synopsis Magnetohydrodynamic Equilibrium and Stability of Stellarators by : F. Bauer
Download or read book Magnetohydrodynamic Equilibrium and Stability of Stellarators written by F. Bauer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we describe in detail a numerical method to study the equilibrium and stability of a plasma confined by a strong magnetic field in toroidal geometry without two-dimensional symmetry. The principal appli cation is to stellarators, which are currently of interest in thermonuclear fusion research. Our mathematical model is based on the partial differential equations of ideal magnetohydrodynamics. The main contribution is a computer code named BETA that is listed in the final chapter. This work is the natural continuation of an investigation that was presented in an early volume of the Springer Series in Computational Physics (cf. [3]). It has been supported over a period of years by the U.S. Department of Energy under Contract DE-AC02-76ER03077 with New York University. We would like to express our gratitude to Dr. Franz Herrnegger for the assistance he has given us with the preparation of the manuscript. We are especially indebted to Connie Engle for the high quality of the final typescript. New York F. BAUER October 1983 O. BETANCOURT P. GARABEDIAN Contents 1. Introduction 1 2. Synopsis of the Method 3 1. Variational principle 3 2. Coordinate system 6 3. Finite Difference Scheme 8 1. Difference equations ....................... " 8 2. Island structure ............................. 10 3. Accelerated iteration procedure .............. . . .. 12 Nonlinear Stability 15 4. 1. Second minimization . . . . . . . . . . . . . . . . .. . . 15 . . . . . 2. Test functions and convergence studies . . . . . . . .. . . 17 . 3. Comparison with exact solutions ................. 19 5. The Mercier Criterion 22 1. Local mode analysis . . . . . . . . . . . . . . . . .. . . 22 . . . . . 2. Computational method . . . . . . . . . . . . . . . .. . . 23 . . . .
Book Synopsis MHD Equilibrium and Stability for Stellarator by :
Download or read book MHD Equilibrium and Stability for Stellarator written by and published by . This book was released on 1984 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The stellarator equilibrium and stability studies presented in this paper are concentrated in two areas: the improvement of the understanding of high beta torsatrons through the concept of flux control and the study of helical axis configurations.
Book Synopsis Magnetohydrodynamic Equilibrium and Stability of Stellarators by : Felix Bauer
Download or read book Magnetohydrodynamic Equilibrium and Stability of Stellarators written by Felix Bauer and published by Springer. This book was released on 2011-10-30 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we describe in detail a numerical method to study the equilibrium and stability of a plasma confined by a strong magnetic field in toroidal geometry without two-dimensional symmetry. The principal appli cation is to stellarators, which are currently of interest in thermonuclear fusion research. Our mathematical model is based on the partial differential equations of ideal magnetohydrodynamics. The main contribution is a computer code named BETA that is listed in the final chapter. This work is the natural continuation of an investigation that was presented in an early volume of the Springer Series in Computational Physics (cf. [3]). It has been supported over a period of years by the U.S. Department of Energy under Contract DE-AC02-76ER03077 with New York University. We would like to express our gratitude to Dr. Franz Herrnegger for the assistance he has given us with the preparation of the manuscript. We are especially indebted to Connie Engle for the high quality of the final typescript. New York F. BAUER October 1983 O. BETANCOURT P. GARABEDIAN Contents 1. Introduction 1 2. Synopsis of the Method 3 1. Variational principle 3 2. Coordinate system 6 3. Finite Difference Scheme 8 1. Difference equations ....................... " 8 2. Island structure ............................. 10 3. Accelerated iteration procedure .............. . . .. 12 Nonlinear Stability 15 4. 1. Second minimization . . . . . . . . . . . . . . . . .. . . 15 . . . . . 2. Test functions and convergence studies . . . . . . . .. . . 17 . 3. Comparison with exact solutions ................. 19 5. The Mercier Criterion 22 1. Local mode analysis . . . . . . . . . . . . . . . . .. . . 22 . . . . . 2. Computational method . . . . . . . . . . . . . . . .. . . 23 . . . .
Book Synopsis Magnetohydrodynamic Equilibrium and Stability of Stellarators by : Frances Bauer
Download or read book Magnetohydrodynamic Equilibrium and Stability of Stellarators written by Frances Bauer and published by . This book was released on 1984 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stellarator Expansion Methods for MHD Equilibrium and Stability Calculations by :
Download or read book Stellarator Expansion Methods for MHD Equilibrium and Stability Calculations written by and published by . This book was released on 1986 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Comparison of Two-dimensional and Three-dimensional MHD Equilibrium and Stability Codes by :
Download or read book Comparison of Two-dimensional and Three-dimensional MHD Equilibrium and Stability Codes written by and published by . This book was released on 1986 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Stability results obtained with the fully three-dimensional magnetohydrodynamic code BETA, the helically invariant code HERA, and the asymptotic stellarator expansion code STEP agree well for a straight l = 2, M = 5 stellarator model. This good agreement between the BETA and STEP codes persists as toroidal curvature is introduced. This validation provides justification for confidence in work with these models. 20 refs., 11 figs.
Book Synopsis Comparison of Two-dimensional and Three-dimensional MHD Equilibrium and Stability Codes by :
Download or read book Comparison of Two-dimensional and Three-dimensional MHD Equilibrium and Stability Codes written by and published by . This book was released on 1986 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Stability results obtained with the fully three-dimensional magnetohydrodynamic code BETA, the helically invariant code HERA, and the asymptotic stellarator expansion code STEP agree well for a straight l = 2, M = 5 stellarator model. This good agreement between the BETA and STEP codes persists as toroidal curvature is introduced. This validation provides justification for confidence in work with these models. 20 refs., 11 figs.
Download or read book Ideal MHD written by Jeffrey P. Freidberg and published by Cambridge University Press. This book was released on 2014-06-26 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive, self-contained, and clearly written, this book describes the macroscopic equilibrium and stability of high temperature plasmas.
Book Synopsis Comparison of the Calculations of the Stability Properties of a Specific Stellarator Equilibrium with Different MHD Stability Codes by : Y. Nakamura
Download or read book Comparison of the Calculations of the Stability Properties of a Specific Stellarator Equilibrium with Different MHD Stability Codes written by Y. Nakamura and published by . This book was released on 1995 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Extension of Stellarator Approximation in Magnetohydrodynamic Equilibrium and Stability of Toroidal Helical Systems by : Jiro Todoroki
Download or read book Extension of Stellarator Approximation in Magnetohydrodynamic Equilibrium and Stability of Toroidal Helical Systems written by Jiro Todoroki and published by . This book was released on 1989 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis MHD Equilibrium and Stability of the Spheromak by : M. Okabayashi
Download or read book MHD Equilibrium and Stability of the Spheromak written by M. Okabayashi and published by . This book was released on 1979 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Magnetohydrodynamic Stability of Tokamaks by : Hartmut Zohm
Download or read book Magnetohydrodynamic Stability of Tokamaks written by Hartmut Zohm and published by John Wiley & Sons. This book was released on 2015-02-09 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Comparison of the Calculations of the Stability Properties of a Specific Stellarator Equilibrium with Different MHD Stability Codes by :
Download or read book Comparison of the Calculations of the Stability Properties of a Specific Stellarator Equilibrium with Different MHD Stability Codes written by and published by . This book was released on 1995 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: A particular configuration of the LHD stellarator with an unusually flat pressure profile has been chosen to be a test case for comparison of the MHD stability property predictions of different three-dimensional and averaged codes for the purpose of code comparison and validation. In particular, two relatively localized instabilities, the fastest growing modes with toroidal mode number n = 2 and n = 3 were studied using several different codes, with the good agreement that has been found providing justification for the use of any of them for equilibria of the type considered.
Book Synopsis Stellarator and Heliotron Devices by : Masahiro Wakatani
Download or read book Stellarator and Heliotron Devices written by Masahiro Wakatani and published by Oxford University Press, USA. This book was released on 1998 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph describes plasma physics for magnetic confinement of high temperature plasmas in nonaxisymmetric toroidal magnetic fields or stellarators. The techniques are aimed at controlling nuclear fusion for continuous energy production. While the focus is on the nonaxisymmetric toroidal field, or heliotron, developed at Kyoto University, the physics applies equally to other stellarators and axisymmetric tokamaks. The author covers all aspects of magnetic confinement, formation of magnetic surfaces, magnetohydrodynamic equilibrium and stability, single charged particle confinement, neoclassical transport and plasma heating. He also reviews recent experiments and the prospects for the next generation of devices.
Book Synopsis Averaged Equilibrium and Stability in Low-aspect-ratio Stellarators by :
Download or read book Averaged Equilibrium and Stability in Low-aspect-ratio Stellarators written by and published by . This book was released on 1989 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The MHD equilibrium and stability calculations or stellarators are complex because of the intrinsic three-dimensional (3-D) character of these configurations. The stellarators expansion simplifies the equilibrium calculation by reducing it to a two-dimensional (2-D) problem. The classical stellarator expansion includes terms up to order epsilon2, and the vacuum magnetic field is also included up to this order. For large-aspect-ratio configurations, the results of the stellarator expansion agree well with 3-D numerical equilibrium results. But for low-aspect-ratio configurations, these are significant discrepancies with 3-D equilibrium calculations. The main reason for these discrepancies is the approximation in the vacuum field contributions. This problem can be avoided by applying the average method in a vacuum flux coordinate system. In this way, the exact vacuum magnetic field contribution is included and the results agree well with 3-D equilibrium calculations even for low-aspect-ratio configurations. Using the average method in a vacuum flux coordinate system also permit the accurate calculation of local stability properties with the Mercier criterion. The main improvement is in the accurate calculation of the geodesic curvature term. In this paper, we discuss the application of the average method in flux coordinates to the calculation of the Mercier criterion for low-aspect-ratio stellarator configurations. 12 refs., 3 figs.
Book Synopsis MHD Computations for Stellarators by :
Download or read book MHD Computations for Stellarators written by and published by . This book was released on 1985 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Considerable progress has been made in the development of computational techniques for studying the magnetohydrodynamic equilibrium and stability properties of three-dimensional configurations. Several different approaches have evolved to the point where comparison of results determined with different techniques shows good agreement. 55 refs., 7 figs.
Book Synopsis MHD Equilibrium and Stability of the Spheromak by :
Download or read book MHD Equilibrium and Stability of the Spheromak written by and published by . This book was released on 1979 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The MHD stability of spheromak type equilibria from the classical spheromak configuration to the diffuse pinch limit are analyzed numerically. It is found that oblate configurations of ellipticity 0.5 have the optimum stability properties with regard to internal MHD modes and can be stabilized up to an engineering .beta. of 15% (defined with respect to the applied external field strength for equilibrium). Stability to global modes requires that a conducting shell surround the plasma. The location of the shell is dependent on geometry and the current profile, but realistic configurations that are stable to all ideal MHD modes have been found with the shell located at approx. 1.2 minor radii.
