Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-26T00:30:44.524Z Has data issue: false hasContentIssue false

Stability of Vlasov equilibria. Part 3. Models

Published online by Cambridge University Press:  13 March 2009

Charles E. Seyler
Affiliation:
Los Alamos National Laboratory, University of California, Los Alamos, New Mexico 87545
H. Ralph Lewis
Affiliation:
Los Alamos National Laboratory, University of California, Los Alamos, New Mexico 87545

Extract

In this third of a series of papers on the stability of Vlasov equilibria, the dispersion functional technique developed in part 1 is applied to the multi-species Vlasov plasma and to the Vlasov-fluid model. An alternative form of the dispersion functional is derived for the Vlasov-fluid model in which magnetohydrodynamic and kinetic aspects of the problem are separated explicitly. A necessary and sufficient condition is derived for stability with the Vlasov-fluid model. Stability of the multi-species Vlasov plasma is discussed and a necessary and sufficient condition for stability near a marginal point is derived. Explicit formulae for quantities occurring in the dispersion functional are given in cylindrical co-ordinates for the Vlasov-fluid model when there is one nonignorable co-ordinate in the equilibrium. The dispersion functional for a multi-species Vlasov plasma is shown to be related to the ponderomotive Hamiltonian.

Type
Articles
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

Berk, H. L. & Dominguez, R. R. 1977 Plasma Phys. 18, 31.CrossRefGoogle Scholar
Cary, J. R. & Kaufman, A. N. 1977 Phys. Rev. Lett. 39, 402.CrossRefGoogle Scholar
Cary, J. R. & Kaufman, A. N. 1981 Phys. Fluids, 24, 1238.CrossRefGoogle Scholar
Freidberg, J. P. 1972 Phys. Fluids, 15, 1102.CrossRefGoogle Scholar
Kruskal, M. D. & Oberman, C. R. 1958 Phys. Fluids, 1, 275.CrossRefGoogle Scholar
Lewis, H. R. 1982 (in preparation).Google Scholar
Lewis, H. R. & Seyler, C. E. 1982 J. Plasma Phys. 27, 25.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
Newcomb, W. A. 1958 see Appendix of Bernstein, I. B. 1958 Phys. Rev. 109, 10.Google Scholar
Schindler, K., Pfirsch, D. & Wobig, H. 1973 Plasma Phys. 15, 1165.CrossRefGoogle Scholar
Seyler, C. E. & Barnes, D. C. 1981 Phys. Fluids. (in press).Google Scholar
Seyler, C. E. & Freidberg, J. P. 1980 Phys. Fluids, 23, 331.CrossRefGoogle Scholar
Sudan, R. N. & Rosenbluth, M. N. 1979 Phys. Fluids, 22, 282.CrossRefGoogle Scholar
Symon, K. R., Seyler, C. E. & Lewis, H. R. 1982 J. Plasma Phys. 27, 13.CrossRefGoogle Scholar