Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-06T07:45:40.303Z Has data issue: false hasContentIssue false
  • English
  • Français

Parametric instability driven by density modulation in velocity space

Published online by Cambridge University Press:  13 March 2009

D. Sherwell  and
R. A. Cairns
D. Sherwell
Affiliation:
Atomic Energy Board, Private Bag X256, Pretoria, South Africa
R. A. Cairns
Affiliation:
Department of Applied Mathematics, University of St Andrews, Fife, Scotland
Get access Rights & Permissions [Opens in a new window]

Abstract

Any ion distribution f;i =(θ—ώit) is an exact solution of the Vlasov equation for a uniformly magnetized plasma. Here θ is the phase angle in velocity space and ώi is the Larmor frequency. Then fi rotates rigidly in velocity space with frequency ώ;i about an axis along a magnetic field line. If fi has anisotropy in the perpendicular velocity plane of the form fi(V, t) = fi(V) [1+A cos 2(θ— ώit)], then it represents a density modulation of frequency 2ώ;i which is confined to velocity space. This non-Maxwellian distribution is an oscillating source of free energy (a pump) which may stimulate certain ion Bernstein modes, their frequencies being near harmonics of Ωi. We here investigate the linear kinetic theory of the system. Linearization implies the parametric approximation of a strong constant pump. Application of the theory may be found in the earth's bow shock.

Type
Research Article
Information
Journal of Plasma Physics , Volume 24 , Issue 1 , August 1980 , pp. 25 - 37
Copyright
Copyright © Cambridge University Press 1980

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

Auer, P. L., Kilb, R. W. & Crevier, W. F. 1971 J. Geophys. Res. 76, 2927.CrossRefGoogle Scholar
Biskamp, D. 1973 Nucl. Fusion, 13, 719.CrossRefGoogle Scholar
Chodura, R. 1975 Nucl. Fusion, 15, 55.CrossRefGoogle Scholar
Coppi, B., Rosenbluth, M. N. & Sudan, P. N. 1969 Ann. Phys. 55, 207.Google Scholar
Formisano, V., Hedgecock, P. C., Moreno, G., Sear, J. & Bollea, D. 1971 Planet. Space Sci. 19, 1519.CrossRefGoogle Scholar
Formisano, V. & Hedgecock, P. C. 1973 J. Geophys. Res. 78, 6522.Google Scholar
Fredricks, R. W. 1968 J. Plasma Phys. 2, 365.Google Scholar
Fredricks, R. W., Crook, G. M., Kennel, C. F., Green, I. M., Scarf, F. L., Coleman, P. J. & Russel, C. T. 1970 J. Geophys. Res. 75, 3751.Google Scholar
Greenstadt, E. W. 1974 Solar Wind Thres. Los Angeles: University of California Press.Google Scholar
Harris, E. G. 1961 J. Nuclear Energy, C, Plasma Phys. 2, 138.CrossRefGoogle Scholar
Harris, E. G. 1970 Physics of Hot Plasmas, p. 145. Oliver and Boyd.CrossRefGoogle Scholar
Morse, D. L. 1976 J. Geophys. Res. 81, 6126.Google Scholar
Montgomery, D., Ashridge, J. R. & Bame, S. J. 1970 J. Geophys. Res. 75, 1217.CrossRefGoogle Scholar
Nishikawa, K. & Liu, C. S. 1976 Advances in Plasma Physics, vol. 6 (ed. Simon, A. and Thompson, W. B.). Intersciece.Google Scholar
Puri, S., Leuterer, F. & Tutter, M. 1973 J. Plasma Phys. 9, 89.Google Scholar
Rosenbluth, M. N., Coppi, B. & Sudan, P. N. 1969 Ann. Phys. 55, 248.CrossRefGoogle Scholar
Schumacher, N. 1968 Proceedings of 3rd International Conference on Plasma Physics and Controlled Nuclear Fusion Research, Novosibirsk, vol. 1, p. 93. IAEA.Google Scholar
Sherwell, D. & Cairns, R. A. 1977 J. Plasma Phys. 17, 265.CrossRefGoogle Scholar
Weiland, J. & Wilhelmsson, H. 1977 Coherent Nonlinear Interaction of Waves in Plasmas. Pergamon.Google Scholar