Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-17T16:25:43.677Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulent disruptions from the Strauss equations

Published online by Cambridge University Press:  13 March 2009

Jill P. Dahlburg ,
David Montgomery  and
William H. Matthaeus
Jill P. Dahlburg
Affiliation:
Department of Physics, College of William and Mary, Williamsburg, VA 23185
David Montgomery
Affiliation:
Department of Physics, College of William and Mary, Williamsburg, VA 23185
William H. Matthaeus
Affiliation:
Bartol Research Foundation, University of Delaware, Newark, DE 19716
Get access Rights & Permissions [Opens in a new window]

Abstract

The Strauss equations of reduced resistive magnetohydrodynamics are solved pseudo-spectrally, inside a cylinder of square cross-section. Conducting, free-slip, boundary conditions are imposed at the boundaries normal to the direction of the imposed d.c. magnetic field and net current, and periodic boundary conditions are imposed in the third direction. The emphasis is on the development of disruptions. Initial conditions are not analytical equilibria, and are characterized by wide-band noise perturbations in many Fourier modes. Typical spatial resolution is 32 × 32 × 16. At this resolution, the code takes approximately 0·7 seconds per time step on a CRAY-1 computer. Lundquist numbers are limited by the need to resolve the small-scale turbulence which develops. Disruptions are characterized by (i) a burst of kinetic fluid activity which is roughly equipartitioned with the magnetic fluctuations at the small scales, but which involves overall kinetic energies which are much less than the magnetic energies; (ii) a helical ‘m = l, n = 1’ current filament which develops out of the wide-band turbulent noise and wraps itself around the magnetic axis; and (iii) relatively mild disturbances of the magnetic field lines, at least at these low values of Lundquist number (S ≃ 100). The results are compared with those from similar codes which solve the linearized Strauss equations.

Type
Research Article
Information
Journal of Plasma Physics , Volume 34 , Issue 1 , August 1985 , pp. 1 - 46
Copyright
Copyright © Cambridge University Press 1985

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

Aydemir, A. Y. & Barnes, D. C. 1984 a J. Comp. Phys. 53, 100.CrossRefGoogle Scholar
Aydemir, A. Y. & Barnes, D. C. 1984 b Phys. Rev. Lett. 52, 930.CrossRefGoogle Scholar
Bateman, G. 1978 MHD Instabilities. MIT Press.Google Scholar
Biskamp, D. & Welter, H. 1983 Proceedings of 9th International Conference on Plasma Physics and Controlled Fusion, vol. 3, p. 373. IAEA.Google Scholar
Caramana, E. J., Nebel, R. A. & Schnack, D. D. 1983 Phys. Fluids, 26, 1305.CrossRefGoogle Scholar
Carreras, B. A., Hicks, H. R., Holmes, J. A. & Waddell, B. V. 1980 Phys. Fluids, 23, 1811.CrossRefGoogle Scholar
Carreras, B. A. (ed.) 1981 Proceedings of U.S.–Japan Workshop on 3-d MHD Studies for Toroidal Devices. Oak Ridge National Laboratory, Report CONF-8110101.Google Scholar
Carreras, B. A., Hicks, H. R. & Lee, D. K. 1981 Phys. Fluids, 24, 66.CrossRefGoogle Scholar
Cooley, J. W., Lewis, P. A. & Welch, P. D. 1970 J. Sound Vib. 12, 315.CrossRefGoogle Scholar
Dahlquist, G., Bjorck, A. & Anderson, N. 1974 Numerical Methods. Prentice-Hall.Google Scholar
Dnestrovskii, Y. N., Lysenko, S. E. & Smith, R. 1977 Soviet J. Plasma Phys. 3, 9.Google Scholar
Fyfe, D., Joyce, G. & Montgomery, D. 1977 a J. Plasma Phys. 17, 317.CrossRefGoogle Scholar
Fyfe, D. & Montgomery, D. 1976 J. Plasma Phys. 16, 181.CrossRefGoogle Scholar
Fyfe, D., Montgomery, D. & Joyce, G. 1977 b J. Plasma Phys. 17, 369.CrossRefGoogle Scholar
Fox, D. A. & Orszag, S. A. 1973 J. Comp. Phys. 11, 612.CrossRefGoogle Scholar
Gottlieb, D. & Orszag, S. A. 1977 Numerical Analysis of Spectral Methods: Theory and Applications. Society for Industrial and Applied Mathematics.CrossRefGoogle Scholar
Hicks, H. R., Carreras, B. A., Garcia, L. & Holmes, J. A. 1984 Oak Ridge National Laboratory preprint ORNL/TM-9127.Google Scholar
Hicks, H. R., Carreras, B., Holmes, J. A., Lee, D. K. & Waddell, B. V. 1981 J. Comp.Phys. 44, 46.CrossRefGoogle Scholar
Hossain, M. 1983 Ph.D. dissertation, College of William and Mary.Google Scholar
Hussaini, M. Y., Streett, C. L. & Zang, T. A. 1983 ICASE NASA Contractor Report 172248. Hampton, VA: ICASE, NASA-Langley Research Center.Google Scholar
Izzo, R., Monticello, D. A., Strauss, H. R., Park, W., Manickam, J., Grimm, R. C. & DeLucia, J. 1983 Phys. Fluids, 26, 3066.CrossRefGoogle Scholar
Kraichnan, R. H. 1965 Phys. Fluids, 8, 1385.CrossRefGoogle Scholar
Matthaeus, W. H. & Montgomery, D. 1981 J. Plasma Phys. 25, 11.CrossRefGoogle Scholar
Montgomery, D. 1981 Proceedings of U. S.–Japan Workshop on 3-d MHD Studies for Toroidal Devices (ed. Carreras, B. A.), p. 32. Oak Ridge National Laboratory Report CONF-8110101.Google Scholar
Montgomery, D. 1982 Physica Scripta, T2/1, 83.CrossRefGoogle Scholar
Orszag, S. A. 1972 Stud. Appl. Math. 51, 253.CrossRefGoogle Scholar
Phillips, N. A. 1959 The Atmosphere and the Sea in Motion, p. 501. Rockerfeller Institute Press.Google Scholar
Potter, D. 1973 Computational Physics. Wiley.Google Scholar
Roache, P. J. 1972 Computational Fluid Dynamics. Hermosa.Google Scholar
Salu, Y. & Knorr, G. 1975 J. Comp. Phys. 17, 68.CrossRefGoogle Scholar
Schnack, D. & Killeen, J. 1980 J. Comp. Phys. 35, 110.CrossRefGoogle Scholar
Schnack, D. D., Baxter, D. C. & Caramana, E. J. 1984 J. Comp. Phys. 55, 485.CrossRefGoogle Scholar
Shebalin, J. V., Matthaeus, W. H. & Montgomery, D. 1983 J. Plasma Phys. 29, 525.CrossRefGoogle Scholar
Strauss, H. R. 1976 Phys. Fluids, 19, 134.CrossRefGoogle Scholar
Strauss, H. R., Park, W., Monticello, D. A., White, R. B., Jardin, S. C., Chance, M. S., Todd, A. M. M. & Glasser, A. H. 1980 Nucl. Fusion, 20, 628.CrossRefGoogle Scholar
Strauss, H. R., Park, W., Monticello, D., Izzo, R., White, R., McGuire, K., Manickam, J. & Goldston, R. 1983 Report PPPL-2023. Princeton Plasma Physics Laboratory.Google Scholar
Sykes, A. & Wesson, J. A. 1976 Phys. Rev. Lett. 37, 140.CrossRefGoogle Scholar
Temperton, C. 1983 J. Comp. Phys. 52, 1.CrossRefGoogle Scholar
Waddell, B. V., Rosenbluth, M. N., Monticello, D. A. & White, R. B. 1976 Nucl. Fusion, 16, 528.CrossRefGoogle Scholar
Waddell, B. V., Carreras, B., Hicks, H. R. & Holmes, J. A. 1979 Phys. Fluids, 22, 896.CrossRefGoogle Scholar
Wakatani, M., Shirai, H., Zushi, H., Kaneko, H., Motojima, O., Obiki, T., Iiyoshi, A. & Uo, K. 1983 Nucl. Fusion, 23, 1669.CrossRefGoogle Scholar