arXivDaily arXiv每日学术速递 周一至周五更新
arXiv physics/0311058physics.acc-phmath.DS
收藏

映射的一阶平均原理及其在粒子加速器束流动力学中的应用

First-Order Averaging Principles for Maps with Applications to Beam Dynamics in Particle Accelerators

Scott Dumas, James A. Ellison, Mathias Vogt

摘要:

对于缓慢演化的离散时间相关差分方程组(迭代映射),我们认为证明一阶平均方法有效性的最简单方法是通过我们称为Besjes不等式的引理。在本文中,我们建立了具有扰动的恒等映射的Besjes不等式,这些扰动是(i)在低阶共振(具有短周期的周期性)和(ii)在离散时间内远离低阶共振。我们使用这些不等式证明相应的一阶平均原则,连同延长时间尺度上的绝热不变性的原则,我们推广和应用这些数学结果模型问题的加速器束动力学,和Henon映射。

英文摘要:

For slowly evolving, discrete-time-dependent systems of difference equations (iterated maps), we believe the simplest means of demonstrating the validity of the averaging method at first order is by way of a lemma that we call Besjes' inequality. In this paper, we develop the Besjes inequality for identity maps with perturbations that are (i) at low-order resonance (periodic with short period) and (ii) far from low-order resonance in the discrete time. We use these inequalities to prove corresponding first-order averaging principles, together with a principle of adiabatic invariance on extended timescales; and we generalize and apply these mathematical results to model problems in accelerator beam dynamics, and to the Henon map.

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。

↑