Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-26T17:45:24.319Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonlinear theory of large-mode-number ballooning modes in fully toroidal geometry

Published online by Cambridge University Press:  13 March 2009

J. P. Mondt  and
J. Weiland
J. P. Mondt
Affiliation:
Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, New Mexico 87545, USA
J. Weiland
Affiliation:
Institute for Electromagnetic Field Theory, Chalmers University of Technology, S-41296 Göteborg, Sweden
Get access Rights & Permissions [Opens in a new window]

Abstract

A nonlinear model equation describing ballooning modes for β of the order of the inverse aspect ratio and including magnetic shear is derived. For the special case of circular concentric flux surfaces, we obtain an approximate dispersion relation, including finite Larmor radius effects, and show the possibility of explosive instability in the nonlinear regime. The results are shown to remain valid in the presence of a low-density hot-ion constituent.

Type
Research Article
Information
Journal of Plasma Physics , Volume 34 , Issue 1 , August 1985 , pp. 143 - 161
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

Clarke, J. F. & Sigmar, D. J. 1977 Phys. Rev. Lett. 38, 70.CrossRefGoogle Scholar
Connor, J. W., Hastie, R. J., Martin, T. J. & Turner, M. F. 1982 Proceedings of 3rd Joint Varenna-Grenable International Symposium on Heating in Toroidal Plasmas Brussels, vol. 1, p. 65.Google Scholar
Connor, J. W., Hastie, R. J. & Taylor, J. B. 1978 Phys. Rev. Lett. 40, 396.CrossRefGoogle Scholar
Connor, J. W., Hastie, R. J. & Taylor, J. B. 1979 Proc. Royal Soc. A 365, 1.Google Scholar
Coppi, B. & Rosenbluth, M. N. 1965 Proceedings of 2nd International Conference on Plasma Physics and Controlled Fusion, Culham. IAEA.Google Scholar
Coppi, B. 1977 Phys. Rev. Lett. 39, 939.CrossRefGoogle Scholar
Coppi, B., Filreis, J. & Pegoraro, F. 1979 a Ann. Phys. 121, 1.CrossRefGoogle Scholar
Coppi, B., Ferreira, A., Mark, J. W. K. & Ramos, J. J. 1979 b Nucl. Fusion, 19, 715.CrossRefGoogle Scholar
Coppi, B. & Pegoraro, F. 1979 Comm. Plasma Phys. Cont. Fusion, 5, 131.Google Scholar
Coppi, B., Ferreira, A. & Ramos, J. J. 1980 Phys. Rev. Lett. 44, 990.CrossRefGoogle Scholar
Davydova, T. A., Pavlenko, V. P., Taranov, V. B. & Shamrai, K. P. 1978 Plasma Phys. 20, 373.CrossRefGoogle Scholar
Dewar, R. L., Manickam, J., Grimm, R. C. & Chance, M. S. 1981 Nucl. Fusion, 21, 493.CrossRefGoogle Scholar
Dobrott, D., Nelson, D. B., Greene, J. M., Glasser, A. H., Chance, M. S. & Frieman, E. A. 1977 Phys. Rev. Lett. 39, 943.CrossRefGoogle Scholar
Frieman, E. A., Rewoldt, G., Tang, W. M. & Glasser, A. H. 1980 Phys. Fluids, 23, 1750.CrossRefGoogle Scholar
Furth, H. P., Killeen, J. & Rosenbluth, M. N. 1963 Phys. Fluids, 6, 459.CrossRefGoogle Scholar
Furth, H. P., Killeen, J., Rosenbluth, M. N. & Coppi, B. 1965 Proceedings of 2nd International Conference of Plasma Physics and Controlled Fusion, Culham, vol. 1, p. 103. IAEA.Google Scholar
Greene, J. M. & Chance, M. S. 1981 Nucl. Fusion, 21, 453.CrossRefGoogle Scholar
Hasegawa, A., MacLennan, C. G. & Kodama, Y. 1979 Phys. Fluids, 22, 2122.CrossRefGoogle Scholar
Hinton, F. L. & Horton, C. W. 1971 Phys. Fluids, 14, 116.CrossRefGoogle Scholar
Hirshman, S. P. & Jardin, S. C. 1979 Phys. Fluids, 22, 731.CrossRefGoogle Scholar
Horton, W., Estes, R. D. & Biskamp, D. 1980 Plasma Phys. 22, 663.CrossRefGoogle Scholar
Itoh, K., Inoue-Itoh, S. & Tuda, T. 1981 J. Phys. Soc. Japan, 50, 655.CrossRefGoogle Scholar
Kadomtsev, B. B. 1965 Plasma Turbulence. Academic.Google Scholar
Lortz, D. & Nuehrenberg, J. 1978 Phys. Lett. 68A, 49.CrossRefGoogle Scholar
Mercier, C. 1960 Nucl. Fusion, 1, 47.CrossRefGoogle Scholar
Mercier, C. 1979 Proceedings of 7th International Conference on Plasma Physics and Controlled Fusion, Innsbruck, vol. 1, p. 701. IAEA.Google Scholar
Mikhailovskii, A. B. 1978 Soviet J. Plasma Phys. 4, 683.Google Scholar
Moore, R. W. & Bhadra, D. K. 1982 General Atomic Preprint GA A 16603.Google Scholar
Mondt, J. P. 1981 Phys. Fluids, 24, 1279.CrossRefGoogle Scholar
Pegoraro, F. & Schep, T. J. 1981 Phys. Fluids, 24, 478.CrossRefGoogle Scholar
Rosenbluth, M. N., Tsai, S. T., Van Dam, J. W. & Engquist, M. G. 1983 Phys. Rev. Lett. 51, 1967.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, 638.CrossRefGoogle Scholar
Tang, W. M., Connor, J. W. & Hastie, R. J. 1980 Nucl. Fusion, 20, 1439.CrossRefGoogle Scholar
Tang, W. M., Connor, J. W. & White, R. B. 1981 Nucl. Fusion, 21, 891.CrossRefGoogle Scholar
Taylor, J. B. 1977 Proceedings of 6th International Conference on Plasma Physics and Controlled Fusion, Berchtesgaden, vol. 2, p. 323. IAEA.Google Scholar
Todd, A. M. M., Chance, M. S., Greene, J. M., Grimm, R. C., Johnson, J. L. & Manickam, J. 1977 Phys. Rev. Lett. 38, 826.CrossRefGoogle Scholar
Tsang, K. T. & Sigmar, D. J. 1981 Nucl. Fusion, 21, 1227.CrossRefGoogle Scholar
Weiland, J., Sanuki, H. & Liu, C. S. 1981 Phys. Fluids, 24, 93.CrossRefGoogle Scholar
Weiland, J. 1981 Physica Scripta, 23, 802.CrossRefGoogle Scholar
Weiland, J. & Mondt, J. P. 1982 Phys. Rev. Lett. 48, 23.CrossRefGoogle Scholar
Weiland, J. & Wilhelmsson, H. 1977 Coherent Nonlinear Interaction of Waves in Plasma. Pergamon.Google Scholar