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Filament model for a stationary field electron ring accelerator: the generalized Bernstein—Green—Kruskal problem

Published online by Cambridge University Press:  13 March 2009

J. B. Ehrman
J. B. Ehrman
Affiliation:
Department of Applied Mathematics, The University of Western Ontario
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Abstract

The longitudinal behaviour of the electron ion ring in a stationary electron ring accelerator (ERA) is studied by means of a filament model which neglects the radial thickness of the ring. There are two widely different time scales (short or STS of the order of a bounce time in the ring, and long or LTS) that characterize the system. The Vlasov equations for a system which is stationary on the STS can be solved in the ion-pickup region by an approximation in which each species of particle essentially sees only a potential well formed by the other species. This gives a generalization of the classical Bernstein–Greene–Kruskal (BGK) problem, in which both species move in the same potential. The conditions under which this generalized BGK problem is well defined are given, and broad classes of quasi-equilibria (i.e. equilibria on the STS) are obtained. The time dependence on the LTS of some of these quasi-equilibria is then obtained by invoking charge conservation, momentum conservation and the adtained invariance of longitudinal action integrals. The stability of these quasi-equilibria (i.e. their behaviour under time-dependent perturbations on the STS) is deferred to a subsequent paper.

Type
Research Article
Information
Journal of Plasma Physics , Volume 12 , Issue 2 , October 1974 , pp. 233 - 269
Copyright
Copyright © Cambridge University Press 1974

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References

REFERENCES

Berg, R. E., Kim, H., Reiser, M. P. & Zorn, G. T. 1969 Phys. Rev. Letters, 22, 419.CrossRefGoogle Scholar
Bernstein, I. B., Greene, J. M. & Kruskal, M. D. 1957 Phys. Rev. 108, 546.CrossRefGoogle Scholar
Boris, J. P. 1970 Proc. 4th Conf on Numerical Simulation of Plasmas, p. 3. Washington, D.C.: N.R.L.Google Scholar
DePackh, D. 1962 J. Electronics and Control, 13, 417.CrossRefGoogle Scholar
DePackh, D. 1969 Proposal for Electron Ring Accelerator Studies. Washington, D.C.: N.R.L.Google Scholar
DePackh, D. 1970a First-Order Analysis of the Transmission of a Single Electron Through a Cusped Magnetic Field. Washington, D.C.: N.R.L.Google Scholar
DePackh, D. 1970b Drag Forces on a Moving Charge Ring. Washington, D.C.: N.R.L.Google Scholar
Ehrman, J. B. 1960 Phys. of Fluids 3, 121.CrossRefGoogle Scholar
Ehrman, J. B. 1966 Plasma Phys. 8, 377.Google Scholar
Keefe, D. 1970 Particle Accelerators, 1, 1.Google Scholar
Kegel, W. H. 1970 Plasma Phys. 12, 105.CrossRefGoogle Scholar
Lee-Whiting, G. E. 1970 Planar formation of an electron ring in a static magnetic field. Chalk River, Ont., AECL-3779.Google Scholar
Lewis, W. B. 1968a Symp. on Electron Ring Accelerators, Berkeley, Calif., UCRL-18103, p. 6.Google Scholar
Lewis, W. B. 1968b Electron ring accierator: 1650B injector. Chalk River, Ont., AECL Rep. DM-99.Google Scholar
McMillan, E. M. 1968 Symp. on Electron Ring Accelerators, Berkeley, Calif., UCRL-18103.Google Scholar
Reiser, M. 1972 On the equilibrium orbit and linear oscillations of charged particles in axisymmetric E x B fields and application to the electron ring accelerator. M.P.I. für Plasmaphysik, Garching bei München, IPP 0/14.Google Scholar
Veksler, V. I. 1956 Symp. on High Energy Accelerators and Pion Phys. CERN.Google Scholar