Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-29T12:22:30.207Z Has data issue: false hasContentIssue false
  • English
  • Français

Large-scale disruptions in a current-carrying magnetofluid

Published online by Cambridge University Press:  13 March 2009

Jill P. Dahlburg ,
David Montgomery ,
Gary D. Doolen  and
William H. Matthaeus
Jill P. Dahlburg
Affiliation:
Department of Physics, College of William and Mary, Williamsburg, VA 23185
David Montgomery
Affiliation:
Dartmouth College, Department of Physics and Astronomy, Hanover, NH 03755
Gary D. Doolen
Affiliation:
Los Alamos National Laboratory, Los Alamos, NM 87545
William H. Matthaeus
Affiliation:
Bartol Research Foundation, University of Delaware, Newark, DE 19716
Get access Rights & Permissions [Opens in a new window]

Abstract

A pseudo-spectral three-dimensional Strauss-equations code is used to describe internal disruptions in a strongly magnetized, electrically-conducting fluid, with and without an externally applied, axial electric field. Rigid conducting walls form a square (x, y) boundary, and periodic boundary conditions are assumed in the axial (z) direction. Typical resolution is 64 × 64 × 32 and the maximum Lundquist number is approximately 400. The dynamics are dominated by a helical current filament which wraps itself around the axis of the cylinder; parts of this filament can sometimes become strongly negative. The ratio of turbulent kinetic energy to total poloidal magnetic energy rises from very small values to values of the order of a few hundredths, and executes ‘bounces’ as a function of time in the absence of the external electric field. In the presence of the external electric field, the first bounce is by far the largest, then the plasma settles into a non-uniform quasi-steady state characterized by a poloidal fluid velocity flow. At the large scales, this flow has the shape of a pair of counter-rotating bean-shaped vortices. The subsequent development of this fluid flow depends strongly upon whether or not a viscous term is added to the equation of motion. Inclusion of viscosity tends to damp the flow and leads to pronounced subsequent bounces suggestive of sawtooth oscillations, though the first bounce remains substantially the largest. By means of a three-mode (Lorenz-like) truncation of the Strauss equations, the evolution of the largest spatial scales alone may be examined. Some time-dependent solutions of the low-order truncation system suggest qualitative agreement with fully resolved solutions of the Strauss equations, while other solutions exhibit interesting dynamical-systems behaviour which is thus far unparalleled in the fully-resolved simulation results.

Type
Research Article
Information
Journal of Plasma Physics , Volume 35 , Issue 1 , February 1986 , pp. 1 - 42
Copyright
Copyright © Cambridge University Press 1986

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

Bender, C. M. & Orszag, S. A. 1978 Advanced Mathematical Methods for Scientists and Engineers. McGraw-Hill.Google Scholar
Biskamp, D. & Welter, H. 1983 Proceedings of 9th International Conference on Plasma Physics and Controlled Fusion, Baltimore, vol. 2, p. 373. IAEA.Google Scholar
Braginskii, S. I. 1965 Reviews of Plasma Physics (ed. Leontovich, M. A.), vol. 1. Consultant's Bureau.Google Scholar
Curry, J. H., Herring, J. R., Loncaric, J. & Orszag, S. A. 1984 J. Fluid Mech. 147, 1.CrossRefGoogle Scholar
Dahlburg, J. P. 1985 Ph.D. dissertation. College of William and Mary.Google Scholar
Dahlburg, J. P., Montgomery, D. & Matthaeus, W. H. 1984 Bullx. Am. Phys. Soc. Ser. II, 29, 1239.Google Scholar
Dahlburg, J. P., Montgomery, D. & Matthaeus, W. H. 1985 a J. Plasma Phys. 34, 1.CrossRefGoogle Scholar
Dahlburg, J. P., Montgomery, D., Matthaeus, W. H. & Doolen, G. D. 1985 b Proceedings of 1985 Sherwood Meeting on Theoretical Aspects of Controlled Thermonuclear Research, Madison. U.S. Department of Energy.Google Scholar
Dnestrovskii, Y. N., Lysenko, S. E. & Smith, R. 1977 Soviet J. Plasma Phys. 3, 9.Google Scholar
Dubois, M. A., Pecquet, A. L. & Reverdin, C. 1983 Nucl. Fusion, 23, 147.CrossRefGoogle Scholar
Eastwood, J. W. & Hopcraft, K. I. 1985 J. Comp. Phys. 60, 549.CrossRefGoogle Scholar
Fox, D. G. & Orszag, S. A. 1973 J. Comp. Phys. 11, 612.CrossRefGoogle Scholar
Fyfe, D. & Montgomery, D. 1976 J. Plasma Phys. 16, 181.CrossRefGoogle Scholar
Gottlieb, D. & Orszag, S. A. 1977 Numerical Analysis of Spectral Methods: Theory and Applications. Society for Industrial and Applied Mathematics, Philadelphia.CrossRefGoogle Scholar
Gottlieb, D., Hussaini, M. Y. & Orszag, S. A. 1984 Spectral Methods for Partial Differential Equations (ed. Voight, R. G., Gottlieb, D. and Hussaini, M. Y.) Society for Industrial and Applied Mathematics, Philadelphia.Google Scholar
Jahns, G. L., Soler, M., Waddell, B. V., Callen, J. D. & Hicks, B. R. 1978 Nucl. Fusion, 18, 609.CrossRefGoogle Scholar
Kadomtsev, B. B. 1975 Soviet J. Plasma Phys. 1, 389.Google Scholar
Kadomtsev, B. B. 1984 Plasma Phys. Contr. Fusion, 26, 217.CrossRefGoogle Scholar
Kreiss, H. & Oliger, J. 1973 Methods for the Approximate Solution of Time Dependent Problems: Global Atmospheric Research Programme Publication Series No. 10. World Meterological Organization, Geneva.Google Scholar
Lichtenberg, A. J. 1984 Nucl. Fusion, 24, 1277.CrossRefGoogle Scholar
Lorenz, E. N. 1963 J. Atmos. Sci. 20, 130.2.0.CO;2>CrossRefGoogle Scholar
Maschke, E. K. & Saramito, B. 1982 Physica Scripta, T2/2, 410.CrossRefGoogle Scholar
Montgomery, D. 1982 Physica Scripta, T2/1, 83.CrossRefGoogle Scholar
Sauthoff, N. R., Von Goeler, S., Eames, D. R. & Stodiek, W. 1979 Proceedings of Symposium on Current Disruptions in Toroidal Devices (ed. Lackner, K. and Zehrfeld, H. P.). IPP 3/51. IAEA, Garching.Google Scholar
Schmalz, R. F. 1983 Computer Phys. Comm. 30, 139.CrossRefGoogle Scholar
Strauss, H. R. 1976 Phys. Fluids, 19, 134.CrossRefGoogle Scholar
Sykes, A. & Wesson, J. A. 1976 Phys. Rev. Lett. 37, 140.CrossRefGoogle Scholar
Tang, C.-M. 1977 Ph.D. thesis. Massachusetts Institute of Technology.Google Scholar
Von Goeler, S., Stodiek, W. & Sauthoff, N. 1974 Phys. Rev. Lett. 33, 1201.CrossRefGoogle Scholar
Waddell, B. V., Rosenbluth, M. N., Monticello, D. A. & White, R. B. 1976 Nucl. Fusion, 16, 528.CrossRefGoogle Scholar