求解Vlasov-Poisson方程的Hamilton形式及其在周期聚焦系统和相干光束相互作用中的应用
Hamiltonian Formalism for Solving the Vlasov-Poisson Equations and Its Applications to Periodic Focusing Systems and the Coherent Beam-Beam Interaction
摘要：
本文发展了一种求解Vlasov-Poisson方程的Hamilton方法。基于非线性正则变换，原哈密顿量中的快速振荡项被变换掉，产生一个新的哈密顿量，它只包含慢变项。该方法已被应用于强流光束通过周期性聚焦晶格的动力学过程，以及相干光束-光束相互作用。得到了变换后的Vlasov方程的稳态解。
英文摘要：
A Hamiltonian approach to the solution of the Vlasov-Poisson equations has been developed. Based on a nonlinear canonical transformation, the rapidly oscillating terms in the original Hamiltonian are transformed away, yielding a new Hamiltonian that contains slowly varying terms only. The formalism has been applied to the dynamics of an intense beam propagating through a periodic focusing lattice, and to the coherent beam-beam interaction. A stationary solution to the transformed Vlasov equation has been obtained.
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