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

Area of Science:

• Plasma Physics
• Computational Electromagnetics
• Nonlinear Dynamics

Background:

• The Euler-Poisson system describes charged particle dynamics.
• Klystron amplifiers are essential for high-power microwave generation.
• Multivalued solutions arise from wave breaking in electron beams.

Purpose of the Study:

• To develop and validate Eulerian methods for computing multivalued solutions to the Euler-Poisson system.
• To analyze electron beam behavior in klystron amplifiers.
• To compare Eulerian results with kinetic and Lagrangian methods.

Main Methods:

• Derivation of an Eulerian formulation from a kinetic description and moment closure.
• Computation of Eulerian moment equations for a velocity-modulated electron beam.
• Comparison with direct kinetic equation computations and a novel Lagrangian method.

Main Results:

• The Eulerian formulation successfully computes multivalued solutions.
• The methods accurately model electron beam wave breaking.
• Wave breaking time and location were explicitly computed using the Lagrangian formulation.

Conclusions:

• The developed Eulerian methods provide a robust way to compute multivalued solutions for the Euler-Poisson system.
• These methods are applicable to klystron amplifier simulations.
• The study validates computational approaches for nonlinear plasma phenomena.