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Eulerian method for computing multivalued solutions of the Euler-Poisson equations and applications to wave breaking in klystrons.

Abstract

We provide methods of computing multivalued solutions to the Euler-Poisson system and test them in the context of a klystron amplifier. An Eulerian formulation capable of computing multivalued solutions is derived from a kinetic description of the Euler-Poisson system and a moment closure. The system of the moment equations may be closed due to the special structure of the solution in phase space. The Eulerian moment equations are computed for a velocity modulated electron beam, which has been shown by prior Lagrangian theories to break in a finite time and form multivalued solutions. The results of the Eulerian moment equations are compared to direct computation of the kinetic equations and a Lagrangian method also developed in the paper. We use the Lagrangian formulation for the explicit computation of wave breaking time and location for typical velocity modulation boundary conditions.

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BibTeXRIS

Xiantao Li, John G Wöhlbier, Shi Jin, John H Booske. 2004-07-07. Eulerian method for computing multivalued solutions of the Euler-Poisson equations and applications to wave breaking in klystrons.. https://doi.org/10.1103/physreve.70.016502

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