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Infinite contraction in force-free magnetic field evolution in cylindrical geometry

Published online by Cambridge University Press:  13 March 2009

Peter A. Watterson
Peter A. Watterson
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
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Abstract

This paper provides a new formulation of the resistive force-free evolution of cylindrically symmetric magnetic fields subject to purely radial motions. It is shown analytically that the evolution bounded by a perfect conductor ceases to exist after a finite time if the initial field has total axial flux of opposite sign to the field on the axis of symmetry. A numerical solution indicates that the evolution ceases to exist owing to the unlimited contraction of the field profile producing a line of infinite current density. The asymptotic form of this ‘blow-up’ is identified as the particular self-similar contraction for which the field direction is exactly reversed in the limit of large radius. Possible applications to solar flares and the reversed-field pinch are discussed.

Type
Research Article
Information
Journal of Plasma Physics , Volume 35 , Issue 2 , April 1986 , pp. 273 - 293
Copyright
Copyright © Cambridge University Press 1986

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References

REFERENCES

Boström, R. 1973 Astrophys. Space Sci. 22, 353.Google Scholar
Low, B. C. 1973 a Astrophys. J. 181, 209.CrossRefGoogle Scholar
Low, B. C. 1973 b Astrophys. J. 184, 917.CrossRefGoogle Scholar
Low, B. C. 1980 J. Plasma Phys. 24, 181.Google Scholar
Low, B. C. 1982 Phys. Fluids, 25, 402.Google Scholar
Lundquist, S. 1950 Arkiv Fysik Band 2, no. 35, 361.Google Scholar
Reid, J. & Laing, E. W. 1979 a J. Plasma Phys. 21, 501.Google Scholar
Reid, J. & Laing, E. W. 1979 b J. Plasma Phys. 22, 193.Google Scholar
Robinson, D. C. 1971 Plasma Phys. 13, 439.Google Scholar
Rust, D. M. 1968 Structure and Development of Solar Active Regions (ed. Kiepenheuer, K. O.), IAU Symposium, no. 35, p. 77.Google Scholar
Švestka, Z. 1981 Solar Flare Magnetohydrodynamics (ed. Priest, E. R.), p. 47. Gordon & Breach.Google Scholar
Watterson, P. A. 1985 Ph.D. Thesis, University of Cambridge.Google Scholar