Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-09T20:35:04.214Z Has data issue: false hasContentIssue false
  • English
  • Français

Exact damped sinusoidal electric field of nonlinear one-dimensional Vlasov-Maxwell equations

Published online by Cambridge University Press:  13 March 2009

B. Abraham-Shrauner
B. Abraham-Shrauner
Affiliation:
Department of Electrical Engineering, Washington University, St Louis, Missouri 63130
Get access Rights & Permissions [Opens in a new window]

Abstract

An exact solution for a temporally damped sinusoidal electric field which obeys the nonlinear, one-dimensional Vlasov-Maxwell equations is given. The electric field is a generalization of the O'Neil model electric field for Landau damping of plasma oscillations. The electric field is a special case of the form found from the invariance of the one-dimensional Vlasov equation under infinitesimal Lie group transformations. The time dependences of the damping decrement, of the wave-number and of the angular frequency are derived. Use of a time-dependent BGK one-particle distribution function is justified for weak damping where, in general, it is necessary to carry out a numerical calculation of the invariant of which the distribution function is a functional.

Type
Research Article
Information
Journal of Plasma Physics , Volume 32 , Issue 2 , October 1984 , pp. 197 - 205
Copyright
Copyright © Cambridge University Press 1984

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

Abraham-Shrauner, B. 1975 Phys. Fluids, 18, 174.CrossRefGoogle Scholar
Abraham-Shrauner, B. 1984 a Phys. Fluids, 27, 197.CrossRefGoogle Scholar
Abraham-Shrauner, B. 1984 b Workshop on Local and Global Methods of Dynamics. Springer.Google Scholar
Baranov, V. B. 1976 Soviet Phys. Tech. Phys. 21, 724.Google Scholar
Bernstein, I. B., Green, J. M. & Kruskal, M. D. 1957 Phys. Rev. 108, 546.CrossRefGoogle Scholar
Burgan, J. R., Feix, M. R., Fijalkov, E. & Munier, A. 1983 J. Plasma Phys. 29, 139.CrossRefGoogle Scholar
Cohen, A. 1911 An Introduction to the Lie Theory of One-Parameter Groups with Applications to the Solution of Differential Equations. Heath.Google Scholar
Davidson, R. 1972 Methods in Nonlinear Plasma Theory. Academic.Google Scholar
Drummond, W. E. & Pines, D. 1962 Nucl. Fusion Suppl. Part 3, 1049.Google Scholar
Krapshev, V. B. & Ram, A. K. 1980 Phys. Rev. A. 22, 1229.CrossRefGoogle Scholar
Landau, L. 1946 J. Phys. (USSR), 10, 25.Google Scholar
Leach, P. G. L. 1981 J. Math. Phys. 22, 465.CrossRefGoogle Scholar
Leach, P. G. L., Lewis, H. R. & Sarlet, W. 1984 J. Math. Phys. 25, 486.CrossRefGoogle Scholar
Lewis, H. R. 1984 J. Math. Phys. 25, 1139.CrossRefGoogle Scholar
Lewis, H. R. & Leach, P. G. L. 1982 J. Math. Phys. 23, 2371.CrossRefGoogle Scholar
Lewis, H. R. & Leach, P. G. L. 1984 Ann. Phys. (To be published.)Google Scholar
Lewis, H. R. & Symon, K. R. 1984 Phys. Fluids, 27, 192.CrossRefGoogle Scholar
O'Neil, T. 1965 Phys. Fluids, 8, 2255.CrossRefGoogle Scholar
Schwarzmeier, J. L., Lewis, H. R., Abraham-Shrauner, B. & Symon, K. 1979 Phys. Fluids, 22, 1747.CrossRefGoogle Scholar