Hostname: page-component-848d4c4894-4hhp2 Total loading time: 0 Render date: 2024-05-01T13:28:38.343Z Has data issue: false hasContentIssue false
  • English
  • Français

Large-amplitude electron plasma oscillations

Published online by Cambridge University Press:  01 August 2008

BARBARA ABRAHAM-SHRAUNER
BARBARA ABRAHAM-SHRAUNER*
Affiliation:
Department of Electrical and Systems Engineering, Washington University, St. Louis, MO 63130, USA (bas@wustl.edu)
Get access Rights & Permissions [Opens in a new window]

Abstract

Large-amplitude electron plasma oscillations in a one-dimensional, cold electron plasma are investigated for a spatially varying, immobile ion density. The Eulerian variables are transformed to Lagrangian variables. The problem is then treated as an effective one-dimensional particle in a potential. Two examples of spatially varying ion densities that lead to analytic functions for the electron position, velocity and electric field are found by Gauss' law to have zero electron density, an unphysical result. A generic solution that includes the two examples is shown to have a spatially homogeneous ion density. A nonlinear ordinary differential equation is the condition for the appropriate form of the electron density and is solved by Lie group symmetries. A more general form of a solution is presented that possesses a spatially varying ion density, but when the necessary conditions are specified it has either zero electron density or secular terms in the electron density.

Type
Papers
Information
Journal of Plasma Physics , Volume 74 , Issue 4 , August 2008 , pp. 437 - 444
Copyright
Copyright © Cambridge University Press 2007

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

[1]Dawson, J. M. 1959 Phys. Rev. 113, 383.CrossRefGoogle Scholar
[2]Kalman, G. 1960 Ann. Phys. 10, 1, 29.CrossRefGoogle Scholar
[3]Davidson, R. C. and Schram, P. P. 1968 Nucl. Fusion 8, 183.CrossRefGoogle Scholar
[4]Davidson, R. C. 1972 Methods in Nonlinear Plasma Theory. New York: Academic Press.Google Scholar
[5]Infeld, E. and Rowlands, G. 1987 Phys. Rev. Lett. 58, 2063.CrossRefGoogle Scholar
[6]Schamel, H., Yu, M. Y. and Shukla, P. K. 1977 Phys. Fluids 20, 1286.CrossRefGoogle Scholar
[7]Amiranashvili, Sh., Yu, M. Y., Stenflo, L., Brodin, G. and Servin, M. 2002 Phys. Rev. E 66, 046403.Google Scholar
[8]Aliev, Y. M. and Stenflo, L. 1994 Phys. Scripta 50, 701.CrossRefGoogle Scholar
[9]Stenflo, L. 1996 Phys. Scripta. T 63, 59.CrossRefGoogle Scholar
[10]Stenflo, L. and Gradov, O. M. 1998 Phys. Rev. E 58, 8044.Google Scholar
[11]Stenflo, L, Marklund, M., Brodin, G. and Shukla, P. K. 2006 J. Plasma Phys. 72, 429.CrossRefGoogle Scholar
[12]Infeld, E., Rowlands, G. and Torven, S. 1989 Phys. Rev. Lett. 62, 2269.CrossRefGoogle Scholar
[13]Karimov, A. R. 2002 Phys. Scripta 65, 356.CrossRefGoogle Scholar
[14]Koch, P. and Albritton, J. 1974 Phys. Rev. Lett. 32, 1420.CrossRefGoogle Scholar
[15]Nappi, C., Forlani, A. and Fedele, R. 1991 Phys. Scripta 43, 301.CrossRefGoogle Scholar
[16]Kovalenko, A. V. and Kovalenko, V. P. 1997 Phys. Plasmas 4, 3200.CrossRefGoogle Scholar
[17]Byrd, P. F. and Friedman, M. D. 1971 Handbook of Elliptic Integrals for Engineers and Scientists. New York: Springer.CrossRefGoogle Scholar
[18]Abraham-Shrauner, B., Govinder, K. L. and Arrigo, D. 2006 J. Phys. A: Math. Gen. 39, 5739.CrossRefGoogle Scholar