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Stability of Vlasov equilibria. Part 2. One non-ignorable co-ordinate

Published online by Cambridge University Press:  13 March 2009

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

The solution of the linearized Vlasov equation is given for an arbitrary equilibrium Hamiltonian in which there is only one non-ignorable co-ordinate. The solution written in terms of integrals with respect to time which only extend over the bounce period of an equilibrium orbit in its equivalent one-dimensional potential. A closed-form solution and a solution based on a Fourier expansion are given. Explicit formulae are presented for Cartesian and cylindrical co-ordinates.

Type
Articles
Information
Journal of Plasma Physics , Volume 27 , Issue 1 , February 1982 , pp. 25 - 35
Copyright
Copyright © Cambridge University Press 1982

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References

REFERENCES

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