arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2007.14613physics.acc-ph
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电子储存环中自旋动力学的布洛赫方程:计算和理论方面

The Bloch equation for spin dynamics in electron storage rings: computational and theoretical aspects

Klaus Heinemann, Daniel Appelö, Desmond P. Barber, Oleksii Beznosov, James A. Ellison

摘要:

在本文中,我们描述了我们的工作在高能电子存储环的自旋极化,我们的基础上的极化密度的布洛赫方程,并针对未来的圆形对撞机(FCC-ee)和拟议的圆形电子正电子对撞机(CEPC)的e-/e+选项。Bloch方程考虑了由同步辐射引起的非自旋翻转和自旋翻转效应,包括自旋扩散效应和Sokolov-Ternov效应及其Baier-Katkov推广,以及动力学偏振效应。该数学模型是基于Derbenev-Kondratenko公式的标准数学模型的替代方案。对于我们的数值和分析研究的布洛赫方程,我们开发了一个近似后者,以获得一个有效的布洛赫方程。这是通过找到第三个数学模型的基础上的随机微分方程系统的布洛赫方程,并通过近似该系统的平均方法从微扰常微分方程理论。我们也给出了我们的算法的概述数值积分的有效布洛赫方程。该方法利用谱方法对相空间进行离散,并利用高阶半隐式的Runge-Kutta方法对时间进行离散。我们还讨论了第三个数学模型的相关性自旋跟踪。

英文摘要:

In this paper we describe our work on spin polarization in high-energy electron storage rings which we base on the Bloch equation for the polarization density and which aims towards the e-/e+ option of the proposed Future Circular Collider (FCC-ee) and the proposed Circular Electron Positron Collider (CEPC). The Bloch equation takes into account non spin-flip and spin-flip effects due to synchrotron radiation including the spin-diffusion effects and the Sokolov-Ternov effect with its Baier-Katkov generalization as well as the kinetic-polarization effect. This mathematical model is an alternative to the standard mathematical model based on the Derbenev-Kondratenko formulas. For our numerical and analytical studies of the Bloch equation we develop an approximation to the latter to obtain an effective Bloch equation. This is accomplished by finding a third mathematical model based on a system of stochastic differential equations underlying the Bloch equation and by approximating that system via the method of averaging from perturbative ODE theory. We also give an overview of our algorithm for numerically integrating the effective Bloch equation. This discretizes the phase space using spectral methods and discretizes time via the additive Runge-Kutta method which is a high-order semi-implicit method. We also discuss the relevance of the third mathematical model for spin tracking.

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