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Turbulent relaxation of a confined magnetofluid to a force-free state

Published online by Cambridge University Press:  13 March 2009

Jill P. Dahlburg ,
David Montgomery ,
Gary D. Doolen  and
Leaf Turner
Jill P. Dahlburg
Affiliation:
U.S. Naval Research Laboratory, Washington, DC 20375
David Montgomery
Affiliation:
Dartmouth College, Hanover, NH 03755
Gary D. Doolen
Affiliation:
Los Alamos National Laboratory, University of California, Los Alamos, NM 87545
Leaf Turner
Affiliation:
Los Alamos National Laboratory, University of California, Los Alamos, NM 87545
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Abstract

Three-dimensional, pseudo-spectral computation is used to follow the evolution of a resistive, incompressible magnetofluid. The magnetofluid is confined by rigid, free-slip, perfectly-conducting square boundaries in the x, y directions (‘poloidal’ boundaries), and periodic boundary conditions are assumed in the z direction (‘toroidal’ direction). A constant, uniform d.c. magnetic field B0 is assumed in the z direction and a non-uniform current density j flows along it initially. Starting from a non-equilibrium hollow current profile, the evolution is followed for several tens of Alfvén transit times. Considerable small-scale turbulence develops, which causes energy to decay more rapidly than magnetic helicity. The average toroidal magnetic field at the (x, y) boundary reverses sign spontaneously. The near spatial constancy of the ratio jB/(jB) ≡ cos θ, in the relaxed state at late times, suggests that the state is nearly force-free. However, the ratio j. B/B2 ≡ α is considerably less uniform than is cos θ suggesting more residual disorder than a pure minimum-energy state would display.

Type
Research Article
Information
Journal of Plasma Physics , Volume 37 , Issue 2 , April 1987 , pp. 299 - 321
Copyright
Copyright © Cambridge University Press 1987

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References

REFERENCES

Aydemir, A. Y. & Barnes, D. C. 1983 J. Comp. Phys. 53, 100.CrossRefGoogle Scholar
Aydemir, A. Y. & Barnes, D. C. 1984 Phys. Rev. Lett. 52, 930.CrossRefGoogle Scholar
Aydemir, A. Y., Barnes, D. C., Caramana, E. J., Mirin, A. A., Nebel, R. A., Schnack, D. D. & Sgro, A. G. 1985 Phys. Fluids, 28, 898.CrossRefGoogle Scholar
Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.Google Scholar
Bretherton, F. & Haidvogel, D. 1976 J. Fluid Mech. 78, 129.CrossRefGoogle Scholar
Dahlburg, J. P. 1985 Ph.D. dissertation, College of William and Mary.Google Scholar
Dahlburg, J. P., Montgomery, D. & Matthaeus, W. H. 1985 J. Plasma Phys. 34, 1.CrossRefGoogle Scholar
Dahlburg, J. P., Montgomery, D., Doolen, G. D. & Matthaeus, W. H. 1986 a J. Plasma Phys. 35, 1.CrossRefGoogle Scholar
Dahlburg, J. P., Montgomery, D., Doolen, G. D. & Turner, L. 1986 b Phys. Rev. Lett. 57, 428.CrossRefGoogle Scholar
Evans, D. E. (ED.) 1976 Pulsed High-Beta Plasmas. Pergamon.Google Scholar
Frisch, U., Pouquet, A., Leorat, J. & Mazure, A. 1975 J. Fluid Mech. 68, 769.CrossRefGoogle Scholar
Fyfe, D. & Montgomery, D. 1976 J. Plasma Phys. 16, 181.CrossRefGoogle Scholar
Fyfe, D., Joyce, G. & Montgomery, D. 1977 a J. Plasma Phys. 17, 317.CrossRefGoogle Scholar
Fyfe, D., Montgomery, D. & Joyce, G. 1977 b J. Plasma Phys. 17, 369.CrossRefGoogle Scholar
Horiuchi, R. & Sato, T. 1985 Phys. Rev. Lett. 55, 211.CrossRefGoogle Scholar
Hutchinson, I. H., Malacarne, M., Noonan, P. & Brotherton-Ratcliffe, D. 1984 Nucl. Fusion, 24, 59.CrossRefGoogle Scholar
Kraichnan, R. H. & Montgomery, D. 1980 Rep. Prog. Phys. 43, 547.CrossRefGoogle Scholar
Matthaeus, W. H. & Montgomery, D. 1980 Ann. N.Y. Acad. Sci. 357, 203.CrossRefGoogle Scholar
Monin, A. F. & Yaglom, A. M. 1965 Statistical Fluid Mechanics: Mechanics of Turbulence, vol. 2. MIT Press.Google Scholar
Montgomery, D., Turner, L. & Vahala, G. 1978 Phys. Fluids, 21, 757.CrossRefGoogle Scholar
Priest, E. R. 1986 Solar System Magnetic Fields. Reidel.Google Scholar
Riyopoulos, S., Bondeson, A. & Montgomery, D. 1982 Phys. Fluids, 25, 107.CrossRefGoogle Scholar
Rusbridge, M. G. 1969 a Plasma Phys. 11, 35.CrossRefGoogle Scholar
Rusbridge, M. G. 1969 b Plasma Phys. 11, 73.CrossRefGoogle Scholar
Rusbridge, M. G. 1977 Plasma Phys. 19, 499.CrossRefGoogle Scholar
Rusbridge, M. G. 1980 a Plasma Phys. 22, 331.CrossRefGoogle Scholar
Rusbridge, M. G. 1980 b Proceedings of Reversed Field Pinch Theory Workshop (ed. Lewis, H. R.). Los Alamos National Laboratory.Google Scholar
Schnack, D. D., Caramana, E. J. & Nebel, R. A. 1985 Phys. Fluids, 28, 321.CrossRefGoogle Scholar
Shebalin, J. V., Matthaeus, W. H. & Montgomery, D. 1983 J. Plasma Phys. 29, 525.CrossRefGoogle Scholar
Sykes, A. & Wesson, J. A. 1977 Proceedings of 8th European Conference on Controlled Fusion and Plasma Physics, Prague, p. 80. Czechoslovak Academy of Sciences.Google Scholar
Taylor, J. B. 1974 a Phys. Rev. Lett. 33, 1139.CrossRefGoogle Scholar
Taylor, J. B. 1974 b Proceedings of 5th International Conference on Plasma Physics and Controlled Fusion, Tokyo, vol. 1, p. 161. IAEA.Google Scholar
Taylor, J. B. 1976 Pulsed High-Beta Plasmas (ed. D. E. Evans), pp. 59–67.Google Scholar
Taylor, J. B. 1986 Revs. Mod. Phys. 58, 741.CrossRefGoogle Scholar
Temperton, C. 1983 J. Comp. Phys. 52, 1.CrossRefGoogle Scholar
Ting, A., Matthaeus, W. H. & Montgomery, D. 1986 Phys. Fluids. 29, 3261.CrossRefGoogle Scholar
Turner, L. & Christiansen, J. 1981 Phys. Fluids, 24, 893.CrossRefGoogle Scholar
Turner, L. 1983 Ann. Phys. (NY), 149, 58.CrossRefGoogle Scholar
Werley, K. A., Nebel, R. A. & Wurden, G. A. 1985 Phys. Fluids, 28, 1450.CrossRefGoogle Scholar
Woltjer, L. 1958 Proc. Nat. Acad. Sci. USA, 44, 489.CrossRefGoogle Scholar
Woltjer, L. 1959 Astrophys. J. 130, 400.CrossRefGoogle Scholar
Woltjer, L. 1960 Revs. Mod. Phys. 32, 914.CrossRefGoogle Scholar