A Variational Principle for Ideal Magnetohydrodynamics PDF Download
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Author: Edward Detyna
Publisher:
ISBN:
Category : Magnetohydrodynamics
Languages : en
Pages : 19
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Author: Edward Detyna
Publisher:
ISBN:
Category : Magnetohydrodynamics
Languages : en
Pages : 19
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Author: Norman C. Wenger
Publisher:
ISBN:
Category : Magnetohydrodynamics
Languages : en
Pages : 36
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Book Description
Variational principle for calculating velocity profile and electric potential distribution in magnetohydrodynamic channel flow.
Author: Kurt Appert (Physicist, Switzerland)
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: F. Bauer
Publisher: Springer Science & Business Media
ISBN: 1461252407
Category : Science
Languages : en
Pages : 203
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Book Description
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 . . . .
Author: Angel Fierros Palacios
Publisher: Springer Science & Business Media
ISBN: 3211343245
Category : Science
Languages : en
Pages : 426
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Book Description
The book describes Fluid Dynamics, Magnetohydrodynamics, and Classical Thermodynamics as branches of Lagrange’s Analytical Mechanics. The approach presented is markedly different from the treatment given to them in traditional text books. A Hamilton-Type Variational Principle as the proper mathematical technique for the theoretical description of the dynamic state of any fluid is formulated. The scheme is completed proposing a new group of variations regarding the evolution parameter.
Author: Norman C. Wenger
Publisher:
ISBN:
Category :
Languages : en
Pages : 25
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Author: Gary Webb
Publisher: Springer
ISBN: 3319725114
Category : Science
Languages : en
Pages : 306
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Book Description
This text focuses on conservation laws in magnetohydrodynamics, gasdynamics and hydrodynamics. A grasp of new conservation laws is essential in fusion and space plasmas, as well as in geophysical fluid dynamics; they can be used to test numerical codes, or to reveal new aspects of the underlying physics, e.g., by identifying the time history of the fluid elements as an important key to understanding fluid vorticity or in investigating the stability of steady flows. The ten Galilean Lie point symmetries of the fundamental action discussed in this book give rise to the conservation of energy, momentum, angular momentum and center of mass conservation laws via Noether’s first theorem. The advected invariants are related to fluid relabeling symmetries – so-called diffeomorphisms associated with the Lagrangian map – and are obtained by applying the Euler-Poincare approach to Noether’s second theorem. The book discusses several variants of helicity including kinetic helicity, cross helicity, magnetic helicity, Ertels’ theorem and potential vorticity, the Hollman invariant, and the Godbillon Vey invariant. The book develops the non-canonical Hamiltonian approach to MHD using the non-canonical Poisson bracket, while also refining the multisymplectic approach to ideal MHD and obtaining novel nonlocal conservation laws. It also briefly discusses Anco and Bluman’s direct method for deriving conservation laws. A range of examples is used to illustrate topological invariants in MHD and fluid dynamics, including the Hopf invariant, the Calugareanu invariant, the Taylor magnetic helicity reconnection hypothesis for magnetic fields in highly conducting plasmas, and the magnetic helicity of Alfvén simple waves, MHD topological solitons, and the Parker Archimedean spiral magnetic field. The Lagrangian map is used to obtain a class of solutions for incompressible MHD. The Aharonov-Bohm interpretation of magnetic helicity and cross helicity is discussed. In closing, examples of magnetosonic N-waves are used to illustrate the role of the wave number and group velocity concepts for MHD waves. This self-contained and pedagogical guide to the fundamentals will benefit postgraduate-level newcomers and seasoned researchers alike.
Author: Felix Bauer
Publisher: Springer
ISBN: 9781461252412
Category : Science
Languages : en
Pages : 196
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Book Description
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 . . . .
Author: Kurt Appert
Publisher:
ISBN:
Category :
Languages : en
Pages : 10
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Book Description
Author: John M. Greene
Publisher:
ISBN:
Category : Magnetohydrodynamic instabilities
Languages : en
Pages : 23
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Book Description
