Magnetohydrodynamic Equilibrium and Stability of Stellarators

Magnetohydrodynamic Equilibrium and Stability of Stellarators
Author: F. Bauer
Publisher: Springer Science & Business Media
Total Pages: 203
Release: 2012-12-06
Genre: Science
ISBN: 1461252407

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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 . . . .

Comparison of Two-dimensional and Three-dimensional MHD Equilibrium and Stability Codes

Comparison of Two-dimensional and Three-dimensional MHD Equilibrium and Stability Codes
Author:
Publisher:
Total Pages:
Release: 1986
Genre:
ISBN:

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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.

Comparison of Two-dimensional and Three-dimensional MHD Equilibrium and Stability Codes

Comparison of Two-dimensional and Three-dimensional MHD Equilibrium and Stability Codes
Author:
Publisher:
Total Pages:
Release: 1986
Genre:
ISBN:

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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.

Energy

Energy
Author:
Publisher:
Total Pages: 580
Release: 1981
Genre: Fuel
ISBN:

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Magnetohydrodynamic Processes in Solar Plasmas

Magnetohydrodynamic Processes in Solar Plasmas
Author: Abhishek Kumar Srivastava
Publisher: Elsevier
Total Pages: 472
Release: 2024-05-31
Genre: Science
ISBN: 0323956653

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Magnetohydrodynamic Processes in The Solar Plasma provides comprehensive and up-to-date theory and practice of the fundamentals of heliospheric research and the Sun’s basic plasma processes, covering the dynamics of the solar interior to its exterior in the framework of magnetohydrodynamics. The book covers novel aspects of solar and heliospheric physics, astrophysics and space science, and fundamentals of the fluids and plasmas. Topics covered include key phenomena in the solar interior such as magnetism, dynamo physics, and helioseismology; dynamics and plasma processes in its exterior including fluid processes such as waves, shocks, instabilities, reconnection, and dynamics in the partially ionized plasma; and physics and science related to coronal heating, solar wind, and eruptive phenomena. The content has been developed to specifically cover fundamental physics-related descriptions and up-to-date developments of the scientific research related to these significant topics. The book therefore provides the entire fundamental and front-line research aspects of solar and heliospheric plasma processes, mainly in the context of solar plasma, however, the content also has larger implications for the astrophysical plasma, and laboratory plasma, fluid dynamics, and associated basic theories. It also includes additional supplementary content such as key instruments and experimental techniques in the form of appendices, boxed-off key information highlighting the most fundamental and key aspects, and worked examples with additional question sets.Magnetohydrodynamic Processes in The Solar Plasma covers both the fundamentals of the topics included as well as up-to-date and future developments in this research field, forming an essential, foundational reference for researchers, academics, and advanced students, in the field of solar physics and astrophysics, as well as neighboring disciplines. Applies fundamental solar science and research in magnetohydrodynamic processes to practice, and uses in teaching and research Covers the latest developments in solar plasma processes in terms of both theoretical and fundamental aspects. Includes the large cohort of plasma processes (e.g., waves, shocks, instabilities, reconnection, heating, magnetism, seismology) significant for the diverse scales of the plasmas and fluids. Provides detailed physical and mathematical descriptions of the theories in each chapter, along with scientific details, which will enhance understanding of basic phenomena and aid in applying the practical content to current research

Plasma Physics

Plasma Physics
Author: Peter Andrew Sturrock
Publisher: Cambridge University Press
Total Pages: 352
Release: 1994-06-02
Genre: Science
ISBN: 9780521448109

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Plasma Physics presents an authoritative and wide-ranging pedagogic study of the 'fourth' state of matter. The constituents of the plasma state are influenced by electric and magnetic fields, and in turn also produce electric and magnetic fields. This fact leads to a rich array of properties of the plasma state. A basic knowledge of mathematics and physics is preferable to appreciate fully this text. The author uses examples throughout, many taken from astrophysical phenomena, to explain concepts. In addition, problem sets at the end of each chapter will serve to reinforce key points.

Finite Element Methods in Linear Ideal Magnetohydrodynamics

Finite Element Methods in Linear Ideal Magnetohydrodynamics
Author: Ralf Gruber
Publisher: Springer Science & Business Media
Total Pages: 190
Release: 2012-12-06
Genre: Science
ISBN: 3642867081

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For more than ten years we have been working with the ideal linear MHD equations used to study the stability of thermonuc1ear plasmas. Even though the equations are simple and the problem is mathematically well formulated, the numerical problems were much harder to solve than anticipated. Already in the one-dimensional cylindrical case, what we called "spectral pollution" appeared. We were able to eliminate it by our "ecological solution". This solution was applied to the two-dimensional axisymmetric toroidal geometry. Even though the spectrum was unpolluted the precision was not good enough. Too many mesh points were necessary to obtain the demanded precision. Our solution was what we called the "finite hybrid elements". These elements are efficient and cheap. They have also proved their power when applied to calculating equilibrium solutions and will certainly penetrate into other domains in physics and engineering. During all these years, many colleagues have contributed to the construc tion, testing and using of our stability code ERATO. We would like to thank them here. Some ofthem gave partial contributions to the book. Among them we mention Dr. Kurt Appert, Marie-Christine Festeau-Barrioz, Roberto Iacono, Marie-Alix Secretan, Sandro Semenzato, Dr. Jan Vac1avik, Laurent Villard and Peter Merkel who kindly agreed to write Chap. 6. Special thanks go to Hans Saurenmann who drew most of the figures, to Dr

Fusion Energy Update

Fusion Energy Update
Author:
Publisher:
Total Pages: 160
Release: 1986
Genre: Controlled fusion
ISBN:

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