哈密顿形式下的粒子运动
Particle Motion in Hamiltonian Formalism
AI总结：
本文介绍哈密顿形式在粒子加速器等线性与非线性动力系统中的应用，从拉格朗日量出发推导加速器环哈密顿量，并将束流动力学概念推广到作用-角变量与辛映射，为非线性运动研究奠定基础。
摘要：
本文旨在介绍理论力学中的哈密顿形式，用于分析包括粒子加速器在内的一般线性与非线性动力系统中的运动。该框架能够推导并积分运动方程，以描述粒子轨迹随时间的演化。首先，回顾通过求解微分方程描述粒子传播的基本概念，并将其应用于线性与非线性运动。这些运动方程可由系统的拉格朗日量得到，这是通向哈密顿形式及其性质的自然步骤。从粒子在电磁场影响下的相对论哈密顿量出发，经过一系列正则（或辛）变换与近似，推导出加速器环的哈密顿量。由此，诸如不变量和传输矩阵等束流动力学的入门概念被重新审视，并扩展到作用-角变量和辛映射等一般概念。为此，本文为研究粒子加速器中非线性运动的高级方法和工具奠定了基础。
英文摘要：
The goal of this contribution is to introduce the Hamiltonian formalism of theoretical mechanics for analysing motion in generic linear and non-linear dynamical systems, including particle accelerators. This framework allows the derivation and integration of equations of motion, in order to describe the particle trajectory evolution with respect to time. First, basic concepts are re-visited for describing particle propagation through the resolution of differential equations, applied to linear and non-linear motion. These equations of motion can be obtained by the Lagrangian of the system, which is the natural step leading to Hamiltonian Formalism and its properties. The accelerator ring Hamiltonian is derived, starting with the relativistic Hamiltonian of particles in the influence of E/M fields and a series of canonical (or symplectic) transformations and approximations. Thereby, introductory concepts of beam dynamics such as invariants and transport matrices are revisited and extended towards generic concepts such as action-angle variables and symplectic maps. To this end, the ground is prepared for the advanced methods and tools used for studying non-linear motion in particle accelerators.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
