Hostname: page-component-76fb5796d-zzh7m Total loading time: 0 Render date: 2024-04-28T09:51:06.542Z Has data issue: false hasContentIssue false
  • English
  • Français

Stability of Vlasov equilibria. Part 1. General theory

Published online by Cambridge University Press:  13 March 2009

K. R. Symon ,
C. E. Seyler  and
H. R. Lewis
K. R. Symon
Affiliation:
University of Wisconsin, Department of Physics, Madison, Wisconsin 53706
C. E. Seyler
Affiliation:
Los Alamos National Laboratory, University of California, Los Alamos, New Mexico 87545
H. R. Lewis
Affiliation:
Los Alamos National Laboratory, University of California, Los Alamos, New Mexico 87545
Get access Rights & Permissions [Opens in a new window]

Extract

We present a general formulation for treating the linear stability of inhomogeneous plasmas for which at least one species is described by the Vlasov equation. Use of Poisson bracket notation and expansion of the perturbation distribution function in terms of eigenfunctions of the unperturbed Liouville operator leads to a concise representation of the stability problem in terms of a symmetric dispersion functional. A dispersion matrix is derived which characterizes the solutions of the linearized initial-value problem. The dispersion matrix is then expressed in terms of a dynamic spectral matrix which characterizes the properties of the unperturbed orbits, in so far as they are relevant to the linear stability of the system.

Type
Articles
Information
Journal of Plasma Physics , Volume 27 , Issue 1 , February 1982 , pp. 13 - 24
Copyright
Copyright © Cambridge University Press 1982

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

Finn, J. M. & Sudan, R. N. 1978 Phys. Rev. Lett. 41, 695.CrossRefGoogle Scholar
Lewis, H. R. & Symon, K. R. 1979 J. Math. Phys. 20, 413;CrossRefGoogle Scholar
also Erratum 1979 J. Math. Phys. 20, 2372.CrossRefGoogle Scholar
Lewis, H. R. & Turner, L. 1976 Nucl. Fusion, 16, 993.CrossRefGoogle Scholar
Schwarzmeier, J. L., Lewis, H. R., Abraham-Shrauner, B. & Symon, K. R. 1979 Phys. Fluids, 22, 1747.CrossRefGoogle Scholar
Schwarzmeier, J. L. & Symon, K. R. 1979 J. Math. Phys. 20, 979.CrossRefGoogle Scholar
Schindler, K., Pfirsch, D. & Wobig, H. 1973 Plasma Phys. 15, 1165.CrossRefGoogle Scholar
Seyler, C. E. 1979 Phys. Fluids, 22, 2324.CrossRefGoogle Scholar
Seyler, C. E. & Freidberg, J. P. 1980 Phys. Fluids, 23, 331.CrossRefGoogle Scholar