强流光束通过光滑聚焦场中的孤波
Solitary Waves in an Intense Beam Propagating Through a Smooth Focusing Field
摘要：
从描述自洽非线性光束动力学和集体过程的Vlasov-麦克斯韦方程组出发，研究了强流片状光束通过周期聚焦场的演化.在文献[1]中曾指出，对于相空间密度均匀的光束，Vlasov-麦克斯韦方程组可以精确地用具有三重绝热压力定律的宏观温流体-麦克斯韦方程组代替。本文证明了从宏观流体-麦克斯韦方程组出发，可以导出一个缓变波振幅的非线性薛定谔方程（或在多波相互作用的情况下，导出一组耦合的非线性薛定谔方程）。本文讨论了非线性薛定谔方程的性质以及强流粒子束中孤子的形成。
英文摘要：
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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