Ebook: Flux Coordinates and Magnetic Field Structure: A Guide to a Fundamental Tool of Plasma Theory

Flux Coordinates and Magnetic Field Structure gives a systematic and rigorous presentation of the mathematical framework and principles underlying the description of magnetically confined fusion plasmas. After a brief treatment of vector algebra in curvilinear coordinate systems the book introduces concepts such as flux surfaces, rotational transforms, and magnetic differential equations. The various specific types of coordinate system are dealt with in detail. Researchers and advanced students in plasma physics, electromagnetics, and mathematical physics will greatly benefit from this useful guide and reference book.

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Flux Coordinates and Magnetic Field Structure gives a systematic and rigorous presentation of the mathematical framework and principles underlying the description of magnetically confined fusion plasmas. After a brief treatment of vector algebra in curvilinear coordinate systems the book introduces concepts such as flux surfaces, rotational transforms, and magnetic differential equations. The various specific types of coordinate system are dealt with in detail. Researchers and advanced students in plasma physics, electromagnetics, and mathematical physics will greatly benefit from this useful guide and reference book.

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Flux Coordinates and Magnetic Field Structure gives a systematic and rigorous presentation of the mathematical framework and principles underlying the description of magnetically confined fusion plasmas. After a brief treatment of vector algebra in curvilinear coordinate systems the book introduces concepts such as flux surfaces, rotational transforms, and magnetic differential equations. The various specific types of coordinate system are dealt with in detail. Researchers and advanced students in plasma physics, electromagnetics, and mathematical physics will greatly benefit from this useful guide and reference book.
Content:
Front Matter....Pages I-XII
Introduction and Overview....Pages 1-3
Front Matter....Pages 5-6
Vector Algebra and Analysis in Curvilinear Coordinates....Pages 7-39
Tensorial Objects....Pages 40-54
Magnetic-Field-Structure-Related Concepts....Pages 55-96
Front Matter....Pages 97-99
The Clebsch-Type Coordinate Systems....Pages 100-115
Toroidal Flux Coordinates....Pages 116-155
Conversion from Clebsch Coordinates to Toroidal Flux Coordinates....Pages 156-159
Establishment of the Flux-Coordinate Transformation; A Summary....Pages 160-164
Canonical Coordinates or “Generalized Magnetic Coordinates”....Pages 165-175
Front Matter....Pages 177-178
“Proper” Toroidal Coordinates....Pages 179-185
The Dynamic Equilibrium of an Ideal Tokamak Plasma....Pages 186-200
The Relationship Between ?dl/B and dV/d? tor ....Pages 201-203
Transformation Properties of Vector and Tensor Components....Pages 204-210
Alternative Derivations of the Divergence Formula....Pages 211-214
Back Matter....Pages 215-241

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Flux Coordinates and Magnetic Field Structure gives a systematic and rigorous presentation of the mathematical framework and principles underlying the description of magnetically confined fusion plasmas. After a brief treatment of vector algebra in curvilinear coordinate systems the book introduces concepts such as flux surfaces, rotational transforms, and magnetic differential equations. The various specific types of coordinate system are dealt with in detail. Researchers and advanced students in plasma physics, electromagnetics, and mathematical physics will greatly benefit from this useful guide and reference book.
Content:
Front Matter....Pages I-XII
Introduction and Overview....Pages 1-3
Front Matter....Pages 5-6
Vector Algebra and Analysis in Curvilinear Coordinates....Pages 7-39
Tensorial Objects....Pages 40-54
Magnetic-Field-Structure-Related Concepts....Pages 55-96
Front Matter....Pages 97-99
The Clebsch-Type Coordinate Systems....Pages 100-115
Toroidal Flux Coordinates....Pages 116-155
Conversion from Clebsch Coordinates to Toroidal Flux Coordinates....Pages 156-159
Establishment of the Flux-Coordinate Transformation; A Summary....Pages 160-164
Canonical Coordinates or “Generalized Magnetic Coordinates”....Pages 165-175
Front Matter....Pages 177-178
“Proper” Toroidal Coordinates....Pages 179-185
The Dynamic Equilibrium of an Ideal Tokamak Plasma....Pages 186-200
The Relationship Between ?dl/B and dV/d? tor ....Pages 201-203
Transformation Properties of Vector and Tensor Components....Pages 204-210
Alternative Derivations of the Divergence Formula....Pages 211-214
Back Matter....Pages 215-241
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