Influence of Geometry and Topology on Helicity

  1. Michael R. Brown,
  2. Richard C. Canfield and
  3. Alexei A. Pevtsov
  1. Jason Cantarella,
  2. Dennis Deturck,
  3. Herman Gluck and
  4. Mikhail Teytel

Published Online: 19 MAR 2013

DOI: 10.1029/GM111p0017

Magnetic Helicity in Space and Laboratory Plasmas

Magnetic Helicity in Space and Laboratory Plasmas

How to Cite

Cantarella, J., Deturck, D., Gluck, H. and Teytel, M. (1999) Influence of Geometry and Topology on Helicity, in Magnetic Helicity in Space and Laboratory Plasmas (eds M. R. Brown, R. C. Canfield and A. A. Pevtsov), American Geophysical Union, Washington, D. C.. doi: 10.1029/GM111p0017

Author Information

  1. Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104

Publication History

  1. Published Online: 19 MAR 2013
  2. Published Print: 1 JAN 1999

ISBN Information

Print ISBN: 9780875900940

Online ISBN: 9781118664476

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Keywords:

  • Magnetic reconnection;
  • Particles (Nuclear physics)-Helicity;
  • Plasma (Ionized gases);
  • Plasma astrophysics

Summary

This chapter contains sections titled:

  • Two Fundamental Problems

  • Hellcity and Writhing Number

  • Relation between Helicity and Writhing Number

  • How the Geometry of the Domain Influences Helicity

  • Magnetic Fields and Helicity

  • A General Point of View

  • The Modified Biot-Savart Operator

  • Spectral Methods

  • Connection with the Curl Operator

  • Explicit Computation of Energy-Minimizing Vector Fields

  • The Isoperimetric Problem

  • First Variation Formulas

  • Constraints on Any Optimal Domain

  • The Search for Optimal Domains

  • Appendix. The Hodge Decomposition Theorem