Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-25T05:33:09.867Z Has data issue: false hasContentIssue false
  • English
  • Français

On the maximum rate of magnetic-field reconnexion for Petschek's mechanism

Published online by Cambridge University Press:  13 March 2009

B. Roberts†  and
E. R. Priest
B. Roberts†
Affiliation:
Department of Applied Mathematics, The University of St Andrews, Scotland
E. R. Priest
Affiliation:
Department of Applied Mathematics, The University of St Andrews, Scotland
Get access Rights & Permissions [Opens in a new window]

Abstract

The standard model for fast magnetic-field reconnexion (Petschek 1964) is qualitatively valid, despite numerous criticisms of its quantitative details. It contains four slow magnetohydrodynamic shock waves, which radiate from a central diffusion region. On the basis of Petschek's rough analysis, it is generally stated that, for large values of the magnetic Reynolds number Rm, reconnexion can occur at a rate no faster than a fraction π/(4 log Rm) of the Alfvén speed. Alternative models of the region outside that of diffusion have been put forward by Yeh & Axford (1970), whose general solutions Vasyliusnas (1975) proved invalid, and by Sonnerup (1970), whose model is mathematically useful, but of limited practical applicability. But their results suggest that reconnexion can occur at any rate whatsoever, with the diffusion-region dimensions responding accordingly. The present paper analyses the external region for Petschek's mechanism in greater detail than hitherto, with the object of deciding whether or not there is a maximum rate. The inclinations of the shock waves are calculated as a function of the fluid speed ve at large distances, which is taken as a measure of the reconnexion rate. It is found that, in agreement with Petschek's rough analysis, there is indeed an upper limit on the allowable rate of magnetic-field reconnexion. Its variation with Rm is calculated, and it is shown, for log10 Rm ≫1, to be approximately 20% of Petschek's value. Typical values are 0·10vAe for Rm = 10·2 and 0·02vAe for Rm = 106. (vAe is the Alfvén speed at large distances from the diffusion region.)

Type
Research Article
Information
Journal of Plasma Physics , Volume 14 , Issue 3 , December 1975 , pp. 417 - 431
Copyright
Copyright © Cambridge University Press 1975

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.)

References

REFERENCES

Axford, W. I. 1967 Space Sci. Rev. 7, 149.CrossRefGoogle Scholar
Copson, E. T. 1935 Theory of Functions of a Complex Variable. Oxford University Press.Google Scholar
Dungey, J. W. 1953 Phil. Mag. 44, 725.CrossRefGoogle Scholar
Gradshteyn, I. S. & Ryzhik, I. M. 1965 Table of Integrals, Series and Products. Academic.Google Scholar
Muskhelishvili, N. I. 1953 Singular Integral Equations. Noordhoff.Google Scholar
Parker, E. N., 1963 Astrophys. J. Suppl. (77) 8, 177.CrossRefGoogle Scholar
Petschek, H. E. 1964 AAS-NASA Symp. on the Phys. of Solar Flares (ed. Hess, W. N.). NASA SP-50, 425.Google Scholar
Priest, E. R. 1972 Mon. Not. B. astron. Soc. 159, 389.CrossRefGoogle Scholar
Priest, E. R. 1973 Astrophys. J. 181, 227.CrossRefGoogle Scholar
Priest, E. R. & Cowley, S. W. H. 1975 J. Plasma. Phys. 14, 271.CrossRefGoogle Scholar
Sonnerup, B. U. O. 1970 J. Plasma Phys. 4, 161.CrossRefGoogle Scholar
Sonnerup, B. U. O. 1972 NASA Symp. on High Energy Phenomena on the Sun, Greenbelt, Maryland.Google Scholar
Sweet, P. A. 1958 Nuovo Cimento, Suppl. (10) 8, 188.CrossRefGoogle Scholar
Sweet, P. A. & Green, R. M. 1967 Astrophys. J. 147, 1153.Google Scholar
Vasyliunas, V. M. 1975 Rev. Geophys. and Space Phys. 13, 303.CrossRefGoogle Scholar
Whittaker, E. T. & Watson, G. N. 1962 A Course of Modern Analysis. Cambridge University Press.Google Scholar
Yeh, T. & Axford, W. I. 1970 J. Plasma Phys. 4, 207.CrossRefGoogle Scholar