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Solitary Waves in an Intense Beam Propagating Through a Smooth Focusing Field

Stephan I. Tzenov·Ronald C. Davidson
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Abstract

Based on the Vlasov-Maxwell equations describing the self-consistent nonlinear beam dynamics and collective processes, the evolution of an intense sheet beam propagating through a periodic focusing field has been studied. In an earlier paper [1] it has been shown that in the case of a beam with uniform phase space density the Vlasov-Maxwell equations can be replaced exactly by the macroscopic warm fluid-Maxwell equations with a triple adiabatic pressure law. In this paper we demonstrate that starting from the macroscopic fluid-Maxwell equations a nonlinear Schroedinger equation for the slowly varying wave amplitude (or a set of coupled nonlinear Schroedinger equations for the wave amplitudes in the case of multi-wave interactions) can be derived. Properties of the nonlinear Schroedinger equation are discussed, together with soliton formation in intense particle beams.

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Stephan I. Tzenov, Ronald C. Davidson. 2002-05-23. Solitary Waves in an Intense Beam Propagating Through a Smooth Focusing Field. https://arxiv.org/abs/physics/0205064

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