论文标题
加速器物理学中的结构保护技术
Structure-preserving techniques in accelerator physics
论文作者
论文摘要
对于非常好的近似值，尤其是对于强子机器，加速器中的充电粒子轨迹服从哈密顿力学。在八个小时或更长时间的日常存储时间中，此类粒子执行了有关机器的$ 10^{8} $转速，$ 10^{10} $涉及设计轨道的振荡，以及$ 10^{13} $ vassages $ 10^{13} $通过各种弯曲和聚焦元素。在构建或修改这样的机器之前，我们试图在如此大量的相互作用上准确确定粒子轨道的长期行为和稳定性。这种苛刻的计算工作并不容易屈服于传统的符号数值集成方法，包括显式吉田型和隐式runge-kutta或高斯方法。作为替代方案，可以计算一个近似的单转图，然后迭代该地图。我们描述了一些基本考虑因素和技术，用于构建高阶和现实磁场模型的此类地图。特别注意保留哈密顿力学的符合性条件特征。
To a very good approximation, particularly for hadron machines, charged-particle trajectories in accelerators obey Hamiltonian mechanics. During routine storage times of eight hours or more, such particles execute some $10^{8}$ revolutions about the machine, $10^{10}$ oscillations about the design orbit, and $10^{13}$ passages through various bending and focusing elements. Prior to building, or modifying, such a machine, we seek to identify accurately the long-term behavior and stability of particle orbits over such large numbers of interactions. This demanding computational effort does not yield easily to traditional methods of symplectic numerical integration, including both explicit Yoshida-type and implicit Runge-Kutta or Gaussian methods. As an alternative, one may compute an approximate one-turn map and then iterate that map. We describe some of the essential considerations and techniques for constructing such maps to high order and for realistic magnetic field models. Particular attention is given to preserving the symplectic condition characteristic of Hamiltonian mechanics.
