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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.
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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

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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