Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-26T03:56:35.587Z Has data issue: false hasContentIssue false
  • English
  • Français

Drift-kinetic stability analysis of z–pinches

Published online by Cambridge University Press:  13 March 2009

Hans O. Åkerstedt
Hans O. Åkerstedt
Affiliation:
Department of Technology, Uppsala University, Box 534, S-75121 Uppsala, Sweden
Get access Rights & Permissions [Opens in a new window]

Abstract

From the Vlasov-fluid model, a set of approximate stability equations describing the stability of a cylindrically symmetric z–pinch is derived. The equations are derived in the limit of small gyroradius and include kinetic effects such as finite Larmor radius, particle drifts and resonant particles. In the limit of zero Larmor radius and short wavelengths, we apply the equations to the internal m = 0 and m = 1 modes. If the drift term mωD + kVD is neglected in the resonant denominators, we find stability criteria that are more optimistic than the corresponding stability criteria for perpendicular MHD. The neglect of the drift term is, however, not justified for the m = 1 mode, where mωD needs to be retained in order to preserve the property that this approximate model should have the same point of marginal stability as the exact Vlasov-fluid model. Retaining the drift terms, growth rates have been calculated for the m = 1 mode, for a constant-current-density equilibrium and for the Bennett equilibrium. For the Bennett profile, we obtain, when compared with perpendicular MHD, a substantial reduction in growth rate γ/γMHD ≈ 0·2.

Type
Research Article
Information
Journal of Plasma Physics , Volume 41 , Issue 1 , February 1989 , pp. 45 - 59
Copyright
Copyright © Cambridge University Press 1989

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

Ågren, O. 1987 Uppsala Univ. Rep.; to be published in Plasma Phys. Contr. Nucl. Fusion Res.Google Scholar
Ågren, O. 1988 Uppsala Univ. Rep. UPTEC-8815R.Google Scholar
Åkerstedt, H. O. 1988 Physica Scripta 37, 117.CrossRefGoogle Scholar
Berk, H. L., Van Dam, J. W., Rosenbluth, M. N. & Spong, D. A. 1983 Phys. Fluids, 26, 201.CrossRefGoogle Scholar
Eriksson, G. 1985 Uppsala Univ. Rep. UPTEC-8568R.Google Scholar
Eriksson, G. 1987 Physica Scripta, 35, 851.CrossRefGoogle Scholar
Faghihi, M. 1987 Physica Scripta, 35, 674.CrossRefGoogle Scholar
Faghihi, M. and Scheffel, J. 1987 J. Plasma Phys. 38, 495.CrossRefGoogle Scholar
Freidberg, J. P. 1972 Phys. Fluids, 15, 1102.CrossRefGoogle Scholar
Freidberg, J. P. 1982 Rev. Mod. Phys. 54, 801.CrossRefGoogle Scholar
Haines, M. 1982 Proceedings of 1982 International Conference on Plasma Physics; Physica Scripta, T2: 2, 380.Google Scholar
Langer, R. E. 1932 Trans. Am. Math. Soc. 33, 23.CrossRefGoogle Scholar
Scheffel, J. & Faghihi, M. 1987 Royal Institute of Technology, Stockholm Rep. TRITA-PFU-87–09.Google Scholar
Schwartzmeir, J. L. & Seyler, C. E. 1984 Phys. Fluids, 27, 2151.CrossRefGoogle Scholar
Seyler, C. E. & Lewis, H. R. 1982 J. Plasma Phys. 27, 37.CrossRefGoogle Scholar
Spies, G. 1987 Royal Institute of Technology, Stockholm Rep. TRITA-PFU-87–07.Google Scholar
Spies, G. & Faghihi, M. 1987 Phys. Fluids, 30, 1724.CrossRefGoogle Scholar