Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-03T00:00:24.195Z Has data issue: false hasContentIssue false
  • English
  • Français

Electrostatic oscillations in cold inhomogeneous plasma Part 2. Integral equation approach

Published online by Cambridge University Press:  13 March 2009

Z. Sedláček
Z. Sedláček
Affiliation:
Institute of Plasma Physics, Czechoslovak Academy of Sciences, Prague
Get access Rights & Permissions [Opens in a new window]

Extract

Small amplitude electrostatic oscillations in a cold plasma with continuously varying density have been investigated. The problem is the same as that treated by Barston (1964), and in part 1 of this paper, but, instead of starting from a differential equation, we base our treatment on an integro-differential equation for the transverse component of the electric field. This equation is very similar to the Vlasov equation, and we show this to be the cause of the striking similarities between the two theories pointed out in part 1. The normal-mode analysis utilizes the similarity of the integral equation for the eigenfunctions to the equation of anisotropic neutron transport. The continuum eigenfunctions are found in the form of a generalized van Kampen eigenmode, and their calculation is reduced to solving a non-singular integral equation. Equivalence of the eigenfimctions found in this way and of those found by solving the equivalent differential equation is proved, and the question of orthogonality and normalization is discussed.

Type
Articles
Information
Journal of Plasma Physics , Volume 6 , Issue 1 , August 1971 , pp. 187 - 199
Copyright
Copyright © Cambridge University Press 1971

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

Barston, E. M. 1964 Ann. Phys. (N.Y.) 29, 282.CrossRefGoogle Scholar
Case, K. M. 1959 Ann. Phys. (N.Y.) 7, 349.CrossRefGoogle Scholar
Friedmann, B. 1956 Principles and Techniques of Applied Mathematics. Wiley.Google Scholar
Kampen, N. G.Van, 1955 Physica 21, 949.CrossRefGoogle Scholar
Sattinger, D. H. 1966 a J. Math. Phys. 45, 188.Google Scholar
Sattinger, D. H. 1966 b J. Math. Anal. Appl. 15, 497.CrossRefGoogle Scholar
Sedláček, Z. 1968 Czech. J. Phys. B 18, 618.CrossRefGoogle Scholar
Sedlá, Z. 1971 J. Plasma Physis, 5, 239.Google Scholar