Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-29T13:34:39.036Z Has data issue: false hasContentIssue false
  • English
  • Français

Interaction of a relativistic electron beam with an inhomogeneous plasma*

Published online by Cambridge University Press:  13 March 2009

G. Dorman
G. Dorman
Affiliation:
Department of Physics, Polytechnic Institute of Brooklyn, Brooklyn, New York
Get access Rights & Permissions [Opens in a new window]

Abstract

The investigation of the high-frequency interaction of a relativistic electron beam and a plasma is extended to include arbitrary variation of the plasma density. Analysing the coupled linearized Vlasov—Maxwell equations by means of a low-temperature expansion of the orbit integrals, a general equation for the electric field accurate to first order in the plasma temperature, beam temperature, and betatron frequency is obtained. This equation is applied to the investigations of transverse and longitudinal modes. A new transverse mode with |ω − kV0| ∼ ωβ is found to be collisionally unstable. The electrostatic instability is found to be slowed down by both low plasma temperature and low beam temperature, but the betatron oscillations increase the growth rate. A new longitidinal mode with |ω − kV0| ∼ ωβ, is found to be unstable for nonzero beam temperatures. The lowest order correction to the electrostatic growth rate due to a small plasma nonuniformity is obtained. The sign of this correction is found to depend critically on the shape of the inhomogeneity.

Type
Research Article
Information
Journal of Plasma Physics , Volume 2 , Issue 4 , December 1968 , pp. 557 - 580
Copyright
Copyright © Cambridge University Press 1968

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

RFERENCES

Barston, E. M. (unpublished).Google Scholar
Bludman, S. A., Watson, K. M. & Rosenbluth, M. N. 1960 Phys. Fluids 3, 747.CrossRefGoogle Scholar
Briggs, R. J. & Rather, J. D. 1967 Bull. Am. Phys. Soc. 12, 818.Google Scholar
Christofilos, N. C., Hester, R. E., Spoerlein, R. L. & Weiss, P. B. 1967 Bull. Am. Phys. Soc. 12, 818.Google Scholar
Dorman, G. 1966 J. Appl. Phys. 37, 2321.Google Scholar
Frieman, E. A., Goldberger, M. L., Watson, K. M., Weinberg, S. & Rosenbluth, M. N. 1962 Phys. Fluids 5, 196.Google Scholar
Mjolsness, R. C. 1963 Phys. Fluids 6, 1729.Google Scholar
Mjolsness, R. C., Enoch, J. & Longmire, C. L. 1963 Phys. Fluids 6, 1741.Google Scholar
Parker, J. V. 1963 Phys. Fluids 6, 1657Google Scholar
Parker, J. V., Nickel, J. C. & Gould, R. W. 1964 Phys. Fluids 7, 1489.CrossRefGoogle Scholar
Rosenbluth, M. N. 1960 Phys. Fluids 3, 932.Google Scholar
Self, S. A. 1963 Phys. Fluids 6, 1762.Google Scholar
Singhaus, H. 1964 Phys. Fluids 7, 1534.Google Scholar
Weinberg, S. 1964 J. Math. Phys. 5, 1371.Google Scholar
Weinberg, S. 1967 J. Math. Phys. 8, 614.Google Scholar