Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-26T06:54:34.534Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on the semi-Lagrangian formulation of the Vlasov equation

Published online by Cambridge University Press:  13 March 2009

G. J. Lewak
G. J. Lewak
Affiliation:
Department of Applied Physics and Information Science University of California, San Diego, La Jolla, California, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Extract

In a previous paper [Lewak (1969), see also Pflrsch (1966) for related treatment], it was shown that the Vlasov equation in the Semi-Lagrangian (S.L.) formulation, may be written in a form resembling the fluid equations.

plus Maxwell's equations with the source terms given by

where n is the determinant of the tensor Tij = ∂gi/∂ζj, and N is the constant mean number density of electrons. The averaging notation < > here is defined by

where f(σ) is the electron distribution function to be specified. The equations assume for simplicity a uniform fixed ion background, although this is not a necessary restriction and equations (1) and (2) need only an obvious modification to account for ions. The force fields in (1) are related to the electric field E and magnetic field B in the plasma by .

Type
Research Article
Information
Journal of Plasma Physics , Volume 4 , Issue 1 , February 1970 , pp. 143 - 144
Copyright
Copyright © Cambridge University Press 1970

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

Klimontovich, Yu. L. (1967), Statistical Theory of Non. Equilibrium Process on a Plasma. New York: Pergamon Press Inc.Google Scholar
Lewak, G. J. 1969 J. Plasma Phys. 3, 243.CrossRefGoogle Scholar
Pfirsch, D. 1966 Nuclear Fusion, 6, 301.CrossRefGoogle Scholar