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Self-similar solutions for Vlasov and water-bag models

Published online by Cambridge University Press:  13 March 2009

J. R. Burgan ,
J. Gutierrez ,
E. Fijalkow ,
M. Navet  and
M. R. Feix
J. R. Burgan
Affiliation:
C. R. P. E./C. N. R. S., Université d'Orléans
J. Gutierrez
Affiliation:
C. R. P. E./C. N. R. S., Université d'Orléans
E. Fijalkow
Affiliation:
C. R. P. E./C. N. R. S., Université d'Orléans
M. Navet
Affiliation:
C. R. P. E./C. N. R. S., Université d'Orléans
M. R. Feix
Affiliation:
C. R. P. E./C. N. R. S., Université d'Orléans
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Abstract

Using finite group theory, self-similar solutions for the one-dimensional Vlasov– Poisson system are considered, both for electron plasmas, with a fixed ion background, and for a single species beam. Difficulties arising from the Poisson equation are pointed out and handled by using an exponential group of transformations. Introducing, for the beam, a water-bag model, we find that the boundary condition problem, imposed by self-similarity, can be solved through the introduction of a ‘virtual particle’ concept. In order to test the analytical solution obtained, we perform a numerical simulation using a particle code. Complete agreement is found.

Type
Research Article
Information
Journal of Plasma Physics , Volume 19 , Issue 1 , February 1978 , pp. 135 - 146
Copyright
Copyright © Cambridge University Press 1978

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References

REFERENCES

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