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Suppression of runaway of electrons in a Lorentz plasma.: I. Harmonically time varying electric field

Published online by Cambridge University Press:  13 March 2009

Barbara Abraham-Shrauner
Affiliation:
Department of Electrical Engineering, Washington University, St Louis, Missouri 63130

Abstract

The suppression of runaway electrons in a Lorentz plasma is demonstrated for a two-component, fully ionized plasma in the presence of a high frequency, weak, uniform electric field. The time for runaway to occur for electric field frequencies high compared to the collision frequency is longer than the runaway time for low electric field frequencies or zero frequency, by the ratio of the frequency of the electric field to the collision frequency squared. Both the resolvant method developed by Prigogine and co-workers and the double perturbation scheme of the Poincaré—Lighthill method are employed to derive the diffusion equation for the modified one-particle distribution function in the collision-dominated region of velocity space.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1970

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References

REFERENCES

Bakshi, P. & Gross, E. 1969 Sixth International Symposium on Rarified Gas Dynamics, 2. New York: Academic Press.Google Scholar
Balescu, R. 1963 Statistical Mechanics of Charged Particles, New York: Interscience Pubs.Google Scholar
Bernstein, W., Chen, F. F., Heald, M. A. & Kranz, A. F. 1958 Phys. Fluids 1, 430.CrossRefGoogle Scholar
Bogoliubov, N. & Krylov, N. 1947 Introduction to Nonlinear Mechanics. Princeton: New Jersey: Princeton University Press.Google Scholar
Coor, T., Cunningham, S. P., Ellis, R. A., Heald, M. A. & Kranz, A. F. 1958 Phys. Fluids 1, 411.CrossRefGoogle Scholar
Delcroix, J. L. 1960 Introduction to the Theory of Ionized Gases, Ch. 7. New York: Interscience Pubs.Google Scholar
Dreicer, H. 1957 Proc. of the Second United Nations International Conference on the Peaceful Uses of Atomic Energy, Geneva, 1958, vol. 31, 57.Google Scholar
Dreicer, H. 1959 Phys. Rev. 115, 238.CrossRefGoogle Scholar
Dreicer, H. 1960 Phys. Rev. 117, 329.CrossRefGoogle Scholar
Field, B. C. & Fried, B. D. 1964 Phys. Fluids 7, 1937.CrossRefGoogle Scholar
Frieman, E. A. 1963 J. Math. Phys. 4, 410.CrossRefGoogle Scholar
Gurevich, A. V. 1961 Soviet Phys. JETP 12, 904.Google Scholar
Holstein, T. 1946 Phys. Rev. 70, 367.CrossRefGoogle Scholar
Kruskal, M. & Bernstein, I. B. 1964 Phys. Fluids 7, 407.CrossRefGoogle Scholar
Kruskal, M. & Bernstein, I. B. 1965 Princeton Plasma Physics Annual Report, Princeton, New Jersey. Princeton University Press.Google Scholar
Lighthill, M. J. 1949 Phil. Mag. 40, 1179.CrossRefGoogle Scholar
Poincaré, H. 1892 Les Methods Nouvelles de la Mechanique Celeste, vol. 1. Paris: Dover Press.Google Scholar
Prigogine, I. 1962 Non-equilibrium Statistical Mechanics. New York: Interscience Pubs.Google Scholar
Sandri, G. 1965 Nuovo Cimento X, 67.Google Scholar