Eulerian method for computing multivalued solutions of the Euler-Poisson equations and applications to wave breaking in klystrons.
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.
The Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA.
Xiantao
X
Li
John G
JG
Wöhlbier
Shi
S
Jin
John H
JH
Booske