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Linear stability analysis of a class of solutions of the filament model for a stationary field electron ring accelerator

Published online by Cambridge University Press:  13 March 2009

Techien Chen  and
J. B. Ehrman
Techien Chen
Affiliation:
Physics Department, University of Saskatchewan, Saskatoon, Canada
J. B. Ehrman
Affiliation:
Department of Applied Mathematics, University of Western Ontario, London, Canada
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Abstract

The stability of two of the short time scale solutions obtained in the filament model for a stationary field electron ring accelerator is studied by means of a linearized perturbation on the electron and ion distribution functions. The Vlasov equations for the electrons and ions are coupled. The coupling of these equations results in a Fredholm integral equation which can be converted into an infinite system of linear equations. A stability criterion is then obtained from the zeros of the truncated determinants of the coefficients of the infinite system. One of the equilibrium solutions, for which the ion density in phase space is a monotonic non-increasing function of the unperturbed ion Hamiltonian, is entirely stable. The other solution, for which this monotonicity does not hold, may be unstable, but turns out to be stable provided that both the non-monotonicity parameter ∈ and the ratio of the ion period to the electron period are not too large. In the nonmonotonic case, the ion density in physical space also does not drop off to zero monotonically from the centre of the ring. For the unstable cases, the instability is driven by a ‘spike’ in the phase-space ion density located at the maximum value of the unperturbed ion Hamiltonian.

Type
Research Article
Information
Journal of Plasma Physics , Volume 16 , Issue 1 , August 1976 , pp. 17 - 36
Copyright
Copyright © Cambridge University Press 1976

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References

REFERENCES

Bernstein, I. B., Greene, J. M. & Kruskal, M. D. 1957 Phys. Rev. 108, 546.CrossRefGoogle Scholar
Bernstein, I. B. 1961 Radiation and Waves in Plasmas (ed. Mitchner, M.) p. 19. Stanford University Press.Google Scholar
Buneman, .O. 1961 Plasma Physics (ed. Drummond, J. E.) pp. 202–223. McGraw-Hill.Google Scholar
Davidson, R. C. & Lawson, J. D. 1972 Particle Accel. 4, 1.Google Scholar
Davidson, R. C. & Mahajan, S. M. 1972 Particle Accel. 4, 53.Google Scholar
Davidson, R. C., Mahajan, S. M. & Schwartz, M. J. 1974 Phys. Fluids, 17, 1287.Google Scholar
de Packh, D. C. 1962 J. Electronics and Control, 13, 417.Google Scholar
De Packh, D. C. 1969 Proposal for Electron Ring Accelerator Studies. Naval Research Laboratory, Washington D.C.Google Scholar
De Packh, D. C. 1970 Drag Forces on a Moving Charge Ring. Naval Research Laboratory, Washington D.C.Google Scholar
Drummond, J. E., Gerwin, R. A. & Springer, B. G. 1961 Plasma Phys. 2, 98.Google Scholar
Ehrman, J. B. 1960 Phys. Fluids, 3, 303.Google Scholar
Ehrman, J. B. 1966 Plasma Phys. 8, 377.Google Scholar
Ehrman, J. B. 1974 J. Plasma Phys. 12, 233.Google Scholar
Goldman, M. V. & Berk, H. L. 1971 Phys. Fluids, 14, 801.Google Scholar
Landau, R. W. & Neill, V. K. 1966 Phys. Fluids, 9, 2412.Google Scholar
Nielsen, C. E., Sessler, A. M. & Symon, K. R. 1959 International Conference on High Energy Accelerators and Instrumentation, p. 239, CERN, Geneva.Google Scholar
Nocentini, A., Berk, H. L. & Sudan, R. N. 1968 J. Plasma Phys. 2, 311.CrossRefGoogle Scholar