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Flux Coordinates and Magnetic Field Structure

A Guide to a Fundamental Tool of Plasma Theory

  • Book
  • © 1991

Overview

Authors:
  1. William Denis D’haeseleer

    1. School of Engineering, Katholieke Universiteit Leuven, Leuven, Belgium
      The NET Team, Max-Planck-Institut für Plasmaphysik, Garching bei München, Fed. Rep. of Germany

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  2. William Nicholas Guy Hitchon

    1. Department of Electrical and Computer Engineering, University of Wisconsin-Madison, Madison, USA

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  3. James D. Callen

    1. Departments of Nuclear Engineering & Engineering Physics and Physics, University of Wisconsin-Madison, Madison, USA

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  4. J. Leon Shohet

    1. Department of Electrical and Computer Engineering, University of Wisconsin-Madison, Madison, USA

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Part of the book series: Scientific Computation (SCIENTCOMP)

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Table of contents (14 chapters)

  1. Front Matter

    Pages I-XII
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  2. Introduction and Overview

    1. Introduction and Overview

      • William Denis D’haeseleer, William Nicholas Guy Hitchon, James D. Callen, J. Leon Shohet
      Pages 1-3

  3. Fundamental Concepts

    1. Front Matter

      Pages 5-6
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    2. Vector Algebra and Analysis in Curvilinear Coordinates

      • William Denis D’haeseleer, William Nicholas Guy Hitchon, James D. Callen, J. Leon Shohet
      Pages 7-39

    3. Tensorial Objects

      • William Denis D’haeseleer, William Nicholas Guy Hitchon, James D. Callen, J. Leon Shohet
      Pages 40-54

    4. Magnetic-Field-Structure-Related Concepts

      • William Denis D’haeseleer, William Nicholas Guy Hitchon, James D. Callen, J. Leon Shohet
      Pages 55-96

  4. Flux Coordinates

    1. Front Matter

      Pages 97-99
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    2. The Clebsch-Type Coordinate Systems

      • William Denis D’haeseleer, William Nicholas Guy Hitchon, James D. Callen, J. Leon Shohet
      Pages 100-115

    3. Toroidal Flux Coordinates

      • William Denis D’haeseleer, William Nicholas Guy Hitchon, James D. Callen, J. Leon Shohet
      Pages 116-155

    4. Conversion from Clebsch Coordinates to Toroidal Flux Coordinates

      • William Denis D’haeseleer, William Nicholas Guy Hitchon, James D. Callen, J. Leon Shohet
      Pages 156-159

    5. Establishment of the Flux-Coordinate Transformation; A Summary

      • William Denis D’haeseleer, William Nicholas Guy Hitchon, James D. Callen, J. Leon Shohet
      Pages 160-164

    6. Canonical Coordinates or “Generalized Magnetic Coordinates”

      • William Denis D’haeseleer, William Nicholas Guy Hitchon, James D. Callen, J. Leon Shohet
      Pages 165-175

  5. Selected Topics

    1. Front Matter

      Pages 177-178
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    2. “Proper” Toroidal Coordinates

      • William Denis D’haeseleer, William Nicholas Guy Hitchon, James D. Callen, J. Leon Shohet
      Pages 179-185

    3. The Dynamic Equilibrium of an Ideal Tokamak Plasma

      • William Denis D’haeseleer, William Nicholas Guy Hitchon, James D. Callen, J. Leon Shohet
      Pages 186-200

    4. The Relationship Between ∫dl/B and dV/dΨtor

      • William Denis D’haeseleer, William Nicholas Guy Hitchon, James D. Callen, J. Leon Shohet
      Pages 201-203

    5. Transformation Properties of Vector and Tensor Components

      • William Denis D’haeseleer, William Nicholas Guy Hitchon, James D. Callen, J. Leon Shohet
      Pages 204-210

    6. Alternative Derivations of the Divergence Formula

      • William Denis D’haeseleer, William Nicholas Guy Hitchon, James D. Callen, J. Leon Shohet
      Pages 211-214

  6. Back Matter

    Pages 215-241
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Keywords

About this book

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.

Authors and Affiliations

  • School of Engineering, Katholieke Universiteit Leuven, Leuven, Belgium

    William Denis D’haeseleer

  • The NET Team, Max-Planck-Institut für Plasmaphysik, Garching bei München, Fed. Rep. of Germany

    William Denis D’haeseleer

  • Department of Electrical and Computer Engineering, University of Wisconsin-Madison, Madison, USA

    William Nicholas Guy Hitchon, J. Leon Shohet

  • Departments of Nuclear Engineering & Engineering Physics and Physics, University of Wisconsin-Madison, Madison, USA

    James D. Callen

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