Astron. Astrophys. 361, 743-758 (2000)

The linear force-free field in a spherical shell using a new method to determine the coefficients of the eigenfunction expansion

J.R. Clegg ¹, P.K. Browning ², P. Laurence ³, B.J.I. Bromage ¹ and E. Stredulinsky <sup>4

1</sup> Centre for Astrophysics, University of Central Lancashire, Preston, UK (j.clegg, b.j.i.bromage@uclan.ac.uk)
² Department of Physics, University of Manchester Institute of Science and Technology, Manchester, UK (p.browning@umist.ac.uk)
³ Courant Institute, New York & Università di Roma I, Italia (laurence@courant.nyu.edu)
⁴ University of Wisconsin Richland, Richland Center, USA (estredul@mail.uwc.edu)

Received 26 May 2000 / Accepted 7 August 2000

Abstract

The linear force-free field of a plasma in between spherical shells is found allowing for inhomogeneous boundary conditions. A three-dimensional solution is found by analysis and used as a benchmark to test a solution in terms of an expansion of eigenfunctions where the coefficients are determined by a new method. Alternative methods are also applied in the context of the spherical shell example and used to illustrate some mathematical constraints that can affect their validity. The solution is used to model the solar coronal field in the presence of a large low-latitude coronal hole; SOHO-MDI data provide the inner boundary conditions.

Key words: magnetic fields Magnetohydrodynamics (MHD) plasmas Sun: chromosphere Sun: corona

Send offprint requests to: J.R.Clegg

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Contents

• 1. Introduction
• 2. Bench Mark Solutions
  • 2.1. General field in a spherical shell
  • 2.2. Simplified boundary conditions
• 3. Eigenfunction expansion for the benchmark fields
  • 3.1. Series solution using a scalar parameter
  • 3.2. Eigenfunction Field expansion using the new method of Laurence et al.
  • 3.3. Simplified boundary conditions: Jensen & Chu formulation
• 4. Discussion
• Acknowledgements
• Appendices
  • A: separation of variables
  • B: scalar field eigenfunction analysis
  • C: the determination of zeroes
  • D: integration and orthogonality
• References

© European Southern Observatory (ESO) 2000

Online publication: October 2, 2000
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