Hostname: page-component-7dd5485656-wjfd9 Total loading time: 0 Render date: 2025-10-30T19:24:38.009Z Has data issue: false hasContentIssue false
  • English
  • Français

Helicity injection and relaxation in a solar-coronal magnetic loop with a free surface

Published online by Cambridge University Press:  13 March 2009

P. K. Browning
P. K. Browning
Affiliation:
Department of Pure and Applied Physics, UMIST, PO Box 88, Manchester M60 1QD, U.K.
Get access Rights & Permissions [Opens in a new window]

Abstract

A solar-coronal magnetic loop is rooted in the photosphere, where motions shuffle the footpoints of the field, generating currents in the corona. The dissipation of these currents provides a possible mechanism for heating the solar corona. A theory is described based on a generalization of Taylor's hypothesis, predicting that as the loop is twisted up, it relaxes towards a minimum-energy state V × B = μB. The footpoint motions inject helicity as well as energy, and the evolution is determined through a helicity-injection equation. The loop is modelled as a straight magnetic-flux tube, with twisting motions at the ends, confined by a constant external pressure at the curved surface, which is a free boundary. The problem of the loop evolution in response to given footpoint motions is solved, and an interesting example of multiple equilibria arises. The heating rate is calculated for an almost-potential loop. The model may also be regarded as representing a laboratory experiment: in particular, a simple idealization of a spheromak, with the footpoint motions replaced by an applied voltage.

Information

Type
Research Article
Information
Journal of Plasma Physics , Volume 40 , Issue 2 , October 1988 , pp. 263 - 280
Copyright
Copyright © Cambridge University Press 1988

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

Berger, M. A. 1984 Geophys. Astrophys. Fluid Dyn. 30, 79.CrossRefGoogle Scholar
Bevir, M. & Gray, J. W. 1980 Proceedings of RFP Theory Workshop; Los Alamos Report LA 8944-LC, p. 176.Google Scholar
Birn, J. & Schindler, K. 1981 Solar Flare Magnetohydrodynamics (ed. Priest, E. R.), chap. 6. Gordon and Breach.Google Scholar
Bodin, H. A. B. & Newton, A. A. 1980 Nucl. Fusion, 20, 1255.CrossRefGoogle Scholar
Browning, P. K. 1984 Inhomogeneous magnetic fields in the solar atmosphere. Ph.D. thesis, University of St Andrews, Scotland.Google Scholar
Browning, P. K. 1987 Proceedings of IOP Plasma Physics Conference, St Andrews, Scotland: Plasma. Phys. 30, 2.Google Scholar
Browning, P. K. & Priest, E. R. 1983 Astrophys. J. 266, 848.Google Scholar
Browning, P. K. & Priest, E. R. 1986 Astron. Astrophys. 159, 129.Google Scholar
Browning, P. K., Sakurai, T. & Priest, E. R. 1986 Astron. Astrophys. 158, 217.Google Scholar
Bruhns, H. 1986 Plasma Phys. 28, 1389.Google Scholar
Chiuderi, C. 1981 Solar Phenomena in Stars and Stellar systems (ed. Bonnet, R. M. & Dupree, A. K.), p. 269. Reidel.CrossRefGoogle Scholar
Dixon, A., Berger, M., Browning, P. K. & Priest, E. R. 1987 A generalization of the Woltjer minimum-energy principle (Preprint.)Google Scholar
Dixon, A., Browning, P. K. & Priest, E. R. 1987 Geophys. Astrophys. Fluid Dyn. 40, 293.CrossRefGoogle Scholar
Faber, V., White, A. B. & Wing, G. M. 1982 J. Math. Phys. 23, 1524.CrossRefGoogle Scholar
Hamciri, E. & Bhattacharjee, A. 1987 Phys. Fluids 30, 1743.CrossRefGoogle Scholar
Hart, G. W., Janos, A., Meyerhofer, D. D. & Yamada, M. 1986 Phys. Fluids, 29, 1994.CrossRefGoogle Scholar
Heyvaerts, J. 1985 Unstable Current Systems and Instabilities in Astrophysics. IAU Symposium 107 (ed. Kundu, M. R. & Holman, G. D.), p. 95. Reidel.Google Scholar
Heyvaerts, J. & Priest, E. R. 1984 Astron. Astrophys. 137, 63.Google Scholar
Ionson, J. A. 1986 Solar Physics, 100, 213.Google Scholar
Jarboe, T. R., Henins, I., Hoida, H. W., Linford, R. K., Marshall, J., Platts, D. A. & Sherwood, A. R. 1980 Phys. Rev. Lett. 45, 1264.CrossRefGoogle Scholar
Jarboe, T. R., Henins, I., Sherwood, A. R., Barnes, C. W. & Hoida, H. W. 1983 Phys. Rev. Lett. 51, 39.CrossRefGoogle Scholar
Parker, E. N. 1972 Astrophys. J. 74, 499.Google Scholar
Parker, E. N. 1979 Cosmical Magnetic Fields, Chap. 9. Oxford University Press.Google Scholar
Parker, E. N. 1983 a Astrophys. J. 264, 635.CrossRefGoogle Scholar
Parker, E. N. 1983 b Astrophys. J. 264, 642.Google Scholar
Parker, E. N. 1987 Physics Today, 40, No. 7, p. 36.Google Scholar
Priest, E. R. 1982 Solar Magnetohydrodynamics, Chap. 6. Reidel.CrossRefGoogle Scholar
Reiman, A. 1981 Phys. Fluids, 24, 956.CrossRefGoogle Scholar
Sakurai, T. & Levine, R. H. 1981 Astrophys. J. 277, 404.Google Scholar
Schoenberg, K. F., Moses, R. W. & Hagenson, R. L. 1984 Phys. Fluids, 25, 107.Google Scholar
Steinolfson, R. S. 1986 Coronal and Prominence Plasmas (ed. Poland, A.), NASA CP 2442, 475.Google Scholar
Steinolfson, R. S. & Tajima, T. 1987 Energy build-up in coronal magnetic flux tubes (Preprint.)Google Scholar
Taylor, J. B. 1974 Phys. Rev. Lett. 33, 1139.CrossRefGoogle Scholar
Taylor, J. B. 1975 Plasma Physics and Controlled Nuclear Fusion Research, vol. 1 p. 161. IAEA.Google Scholar
Taylor, J. B. 1976 Pulsed High Beta Plasmas (ed. Evans, D. E.), p. 59. Pergamon.Google Scholar
Taylor, J. B. 1986 Rev. Mod. Phys. 58, 741.CrossRefGoogle Scholar
Ting, A. G., Matthaeus, W. H. & Montgomery, D. 1986 Phys. Fluids, 29, 326.CrossRefGoogle Scholar
Turner, W. C., Goldenbaum, G. C., Granneman, E. H. A., Hammer, J. H., Hartman, C. W., Prono, D. S. & Taska, J. 1983 Phys. Fluids, 26, 1965Google Scholar
Vekstein, G. E. 1987 Soviet J. Plasma Phys. 13, 262Google Scholar