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Note on the existence of stationary shockwaves in collisionless plasmas

Published online by Cambridge University Press:  13 March 2009

D. Pfirsch  and
K. Schindler
D. Pfirsch
Affiliation:
Institut für Plasma-physik, Garching bei München, Germany
K. Schindler
Affiliation:
European Space Research Institute, †Frascati (Roma), Italy
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Abstract

We first discuss wave propagation perpendicular to a magnetic field. Variables depend on x only. The medium is collision-free, described by the Vlasov theory. We can prove that there exist two, and only two, unique constants of the motion, that are independent of y, z and t, and that at least one of them depends on x. Thus a necessary condition for the existence of stationary shocks is fulfilled. Examples show that the existence proof also suggests a practical tool for solving problems. The oblique case which is also briefly discussed turns out to be qualitatively different in that, owing to the presence of reflected particles, a uniform upstream state cannot be prescribed a priori.

Type
Articles
Information
Journal of Plasma Physics , Volume 5 , Issue 1 , January 1971 , pp. 123 - 130
Copyright
Copyright © Cambridge University Press 1971

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References

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