Mathematical Sciences: Improved Long-Time Estimates for the Stability of Motion in Hamiltonian Models of Accelerator Dynamics

数学科学：加速器动力学哈密顿模型中运动稳定性的长期估计的改进

• 批准号: 9106812
• 金额: $ 3.67万
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-06-01 至 1994-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9106812&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Improved; Long; Time

The investigator will develop realistic stability estimates "of Nekhoroshev type" for nearly integrable Hamiltonian models of physical systems, beginning with models for the motion of charged particles in accelerator storage rings. He uses results from averaging theory for ordinary differential equations and from a theory for the motion of energetic charged particles based on Nekhoroshev-type estimates. By combining recent progress in long-time estimates with quasiconvex unperturbed part (due to Lochak and Poeschel), and in averaging theory for ordinary differential equations (Ellison, Saenz, and Dumas), he expects to develop improved estimates for specific model systems. This expectation is based on the way averaging methods are embedded in Lochak's new approach: his methods reduce the problem --- in what is probably an optimal way --- to a high-order, single-phase, periodic averaging problem of the type for which improved estimates were recently developed. The proposed estimates could prove to be valuable tools in the development and design of increasingly complex particle accelerators. Such estimates might augment or even partly supplant some of the costly experimental methods now used to design and test accelerator lattices (the collections of multipole magnetic elements used to stabilize particle beams orbiting in accelerator storage rings). In view of the enormous development costs of the next generation of accelerators (such as the Superconducting Super-Collider, now in the initial phases of construction in Waxahachie, Texas, even as its development continues), even a small contribution to the design theory could result in a sizable savings of time and money. Moreover, estimates of the same type might be useful in much the same way in the design and development of "toroidal confinement fusion machines" (hot fusion reactors).

研究者将制定切合实际的稳定性估计值 “Nekhoroshev型”的近可积哈密顿模型， 物理系统，从带电粒子的运动模型开始， 加速器储存环中的粒子 他使用的结果来自 平均理论的常微分方程和从一个 高能带电粒子运动的理论， Nekhoroshev型估计。 通过结合最近的进展， 具有拟凸未扰动部分的长时间估计（由于 Lochak和Poeschel），并在平均理论为普通 微分方程（埃里森，萨恩斯，和大仲马），他希望 为具体的模型系统制定更好的估计数。 这 期望是基于平均方法嵌入的方式， Lochak的新方法：他的方法减少了问题-在什么方面 可能是一种最佳的方式-高阶，单相， 改进的周期平均问题 估计数是最近制定的。 拟议的估计数可证明是宝贵的工具， 越来越复杂的粒子的开发和设计 加速器。 这种估计可能会增加，甚至部分增加 取代了一些昂贵的实验方法， 设计和测试加速器晶格（ 用于稳定粒子束的多极磁性元件 在加速器储存环中运行）。 鉴于 下一代加速器的开发成本（例如 超导超级对撞机，现在处于初始阶段， 德克萨斯州瓦沙哈基的建筑，即使它的发展 即使是对设计理论的一个小小的贡献， 节省了大量的时间和金钱。 此外，委员会认为， 同一类型的估计可能以大致相同的方式有用 在“环形约束聚变”的设计和发展中， 热聚变反应堆（Hot Fusion Reactors）