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Resistive tearing-mode instability in a current sheet with equilibrium viscous stagnation-point flow

Published online by Cambridge University Press:  13 March 2009

T. D. Phan  and
B. U.Ö. Sonnerup
T. D. Phan
Affiliation:
Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire 03755, U.S.A.
B. U.Ö. Sonnerup
Affiliation:
Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire 03755, U.S.A.
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Abstract

An analysis is presented of linear stability against tearing modes of a current sheet formed between two oppositely magnetized plasmas forced towards each other in two-dimensional steady stagnation-point flow. The velocity vector in this flow is confined to planes perpendicular to the reversing component of the magnetic field. The unperturbed state is an exact resistive and viscous equilibrium in which the resistive diffusion outwards from the current sheet is exactly balanced by the inward motion associated with the stagnation-point flow. Thus the behaviour of the tearing mode can be examined even when the resistive diffusion time is comparable to or smaller than the growth time of the instability. The linear ordinary differential equation describing the mode structure is integrated numerically. For large Lundquist number S and viscous Reynolds number Re the Furth-Killeen-Rosenbluth scaling of the growth rate is recovered with excellent accuracy. The influence of the stagnation-point flow on the tearing mode is as follows: (i) long-wavelength perturbations are stabilized so that the unstable regime falls between a short-wavelength and a long-wavelength marginal state; (ii) for sufficiently low Lundquist number (S < 12.25) the current sheet is completely stable to tearing-mode perturbations; (iii) the presence of high viscosity reduces the growth rate of the tearing instability. This effect is more important at small wavelength. Finally, application of the results from this study to the problem of solar-wind plasma flow past the earth's magnetosphere is briefly discussed.

Type
Research Article
Information
Journal of Plasma Physics , Volume 46 , Issue 3 , December 1991 , pp. 407 - 421
Copyright
Copyright © Cambridge University Press 1991

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References

REFERENCES

Besser, B. P., Biernat, H. K. & Rijnbeek, R. P. 1990 Planet. Space Sci. 38, 411.CrossRefGoogle Scholar
Bulanov, S. V., Syrovatsky, S. I. & Sakai, J. 1978 JETP Lett. 28, 177.Google Scholar
Chen, X. L. & Morrison, P. J. 1990 Phys. Fluids B 2, 495.CrossRefGoogle Scholar
Cross, M. A. & Van Hoven, G. 1971 Phys. Rev. A4, 2347.CrossRefGoogle Scholar
Dobrott, D., Prager, S. C. & Taylor, J. B. 1977 Phys. Fluids 20, 1850.CrossRefGoogle Scholar
Einaudi, G. & Rubini, E. 1986 Phys. Fluids 29, 2563.CrossRefGoogle Scholar
Einaudi, G. & Rubini, F. 1989 Phys. Fluids B 1, 2224.CrossRefGoogle Scholar
Forbes, T. G. & Priest, E. R. 1987 Rev. Geophys. 25, 1583.CrossRefGoogle Scholar
Furth, H. P., Killeen, J. & Rosenbluth, M. N. 1963 Phys. Fluids 6, 459.CrossRefGoogle Scholar
Killeen, J. & Shestakov, A. I. 1978 Phys. Fluids 21, 1746.CrossRefGoogle Scholar
Laval, G., Pellat, R. & Vuillemin, M. 1966 Proceedings of the Conference on Plasma Physics and Controlled Nuclear Fusion, p. 259. International Atomic Energy Agency.Google Scholar
Lee, L. C. & Fu, Z. F. 1986 J. Geophys. Res. 91, 3311.CrossRefGoogle Scholar
Ofman, L., Chen, X. L. & Morrison, P. J. 1991 Phys. Fluids B 3, 1364.CrossRefGoogle Scholar
Parker, E. N. 1973 J. Plasma Phys. 9, 49.CrossRefGoogle Scholar
Phan, T. D. & Sonnerup, B. U. Ö. 1990 J. Plasma Phys. 44, 525.CrossRefGoogle Scholar
Pudovkin, M. I. & Semenov, V. S. 1977 a Ann. Geophys. 33, 423.Google Scholar
Pudovkin, M. I. & Semenov, V. S. 1977 b Ann. Geophys. 33, 429.Google Scholar
Sckopke, N., Paschmann, G., Haerendel, G., Sonnerup, B. U. Ö., Bame, S. J., Forbes, T. G., Hones, E. W. & Russell, C. T. 1981 J. Geophys. Res. 86, 2099.CrossRefGoogle Scholar
Sonnerup, B. U. Ö. 1979 Solar System Plasma Physics, vol. III (ed. Lanzerotti, L. T., Kennel, C. F. & Parker, E. N.), p. 46. North-Holland.Google Scholar
Sonnerup, B. U. Ö. 1980 Dynamics of the Magnetosphere (ed. Akasofu, S. I.), p. 77. Reidel.Google Scholar
Sonnerup, B. U. Ö. & Priest, E. R. 1975 J. Plasma Phys. 14, 283.CrossRefGoogle Scholar
Sonnerup, B. U. Ö. & Sakai, J.-I. 1981 EOS Trans. AGU 62, 353.Google Scholar
Vasyliunas, V. M. 1975 Rev. Geophys. Space Phys. 13, 303.CrossRefGoogle Scholar
Wesson, J. 1966 Nucl. Fusion 16, 130.CrossRefGoogle Scholar