Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-27T14:29:24.006Z Has data issue: false hasContentIssue false
  • English
  • Français

Wall stabilization in a collisionless bumpy theta-pinch

Published online by Cambridge University Press:  13 March 2009

George Vahala  and
Linda Vahala
George Vahala
Affiliation:
Department of Physics, College of William and Mary, Williamsburg, Virginia23185
Linda Vahala
Affiliation:
Department of Physics, College of William and Mary, Williamsburg, Virginia23185
Get access Rights & Permissions [Opens in a new window]

Abstract

Finite wavelength guiding centre plasma stability of the bumpy θ-pinch is examined by a normal mode analysis. It is shown that previous bumpy θ-pinch calculations are recoverable as special cases of this analysis. The ideal magnetohydrodynamic and guiding centre plasma growth rates are compared for various pressure anisotropies and for various wavenumbers of the field line bumpiness. The well-posedness conditions on the guiding centre plasma equations are shown to give upper and lower bounds on the permissible pressure anisotropy which corresponds to the Aifvén continuum staying on the stable side of the spectrum and to the particle mirror force not having a singularity. It is also found that the higher azimuthal m ≥ 2 modes have growth rates larger than the m = 1 mode.

Type
Research Article
Information
Journal of Plasma Physics , Volume 18 , Issue 2 , October 1977 , pp. 317 - 337
Copyright
Copyright © Cambridge University Press 1977

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

Berkowitz, J., Grad, H. & Rubin, H. 1958 Proc. U.N. International Conf. on Peaceful uses Atomic Energy, vol. 31, p. 171. Columbia University Press.Google Scholar
Cayton, T. E. 1976 Ph.D. thesis, College of William and Mary.Google Scholar
Cayton, T. E. & Vahala, G. 1976 Phys. Fluids, 19, 590.Google Scholar
Chew, G. F., Goldberger, M. L. & Low, F. E. 1955 Los Alamos Lecture Notes LA-2055.Google Scholar
Dandl, R. A., Dory, R. A., Eason, H. O., Guest, G. E., Harris, E. G., Haste, G. R., Hedrick, C. L., Ikegami, H., Jaeger, E. F., Lazer, N. H., Luton, J. N., McAlees, D. G., McNell, D. H. & Nelson, D. B. 1975 Oak Ridge National Laboratory ORNL-TM-4941.Google Scholar
Ellis, W. R., Jahoda, F. C., Kristal, R., Quinn, W. E., Ribe, F. L., Sawyer, G. A. & Siemon, R. E. 1974 Nucl. Fusion, 14, 841.Google Scholar
Freidberg, J. P. 1972 Phys. Fluids, 15, 1102.Google Scholar
Freidberg, J. P. & Marder, B. M. 1973 Phys. Fluids, 16, 247.CrossRefGoogle Scholar
Freideberg, J. P., Marder, B. M. & Weitzner, H. 1974 Nucl. Fusion, 14, 809.Google Scholar
Grad, H. 1956 AEC Report TID-7503, p. 495.Google Scholar
Grad, H. 1961 Proc. Symposium on Electromagnetics and Fluid Dynamics of Gaseous Plasmas, p. 37. Polytechnic Institute of Brooklyn.Google Scholar
Grad, H. 1966 Phys. Fluids, 9, 498.CrossRefGoogle Scholar
Grad, H. 1967 Proc. Symposium in Applied Mathematics of American Math. Soc. vol. 18, p. 162. Rhode Island.Google Scholar
Grad, H. & Weitzner, H. 1969 Phys. Fluids, 12, 1725.Google Scholar
Haas, F. & Wesson, J. 1967 Phys. Fluids, 10, 2245.Google Scholar
Kadish, A. 1966 Phys. Fluids, 9, 514.CrossRefGoogle Scholar
Kulsrud, R. M. 1962 Phys. Fluids, 5, 192.Google Scholar
Kulsrud, R. M. 1964 Advanced Plasma Theory, p. 64. Academic.Google Scholar
Northrop, T. G. & Whiteman, K. J. 1964 Phys. Rev. Lett., 12, 639.CrossRefGoogle Scholar
Rosenbluth, M. N., Johnson, J. L., Greene, J. M. & Weimer, K. E. 1969 Phys. Fluids, 12, 726.CrossRefGoogle Scholar
Schmidt, M. J. 1976 Ph.D. thesis, College of William and Mary.Google Scholar
Schmidt, M. J. & Vahala, G. 1976 Plasma Physics, 18, 499.CrossRefGoogle Scholar
Weitzner, H. 1971 Phys. Fluids, 14, 658.CrossRefGoogle Scholar
Weitzner, H. 1973 Phys. Fluids, 16, 237.CrossRefGoogle Scholar
Weitzner, H. 1976 Phys. Fluids, 19, 420.Google Scholar