高阶自旋轨道共振的强度
Strength of Higher-Order Spin-Orbit Resonances
摘要：
当极化粒子在同步加速器中加速时，自旋进动可以由粒子穿过的电磁场的傅立叶分量周期性地驱动。当自旋进动频率接近轨道频率的线性组合时，这导致共振扰动。当这样的共振条件交叉时，可以发生部分去极化或自旋翻转。在共振交叉之后存留的极化的量是共振强度和交叉速度的函数。这个函数通常被称为Froissart-Stora公式。它对于预测同步加速器加速周期后的偏振量或计算保持所需偏振量所需的加速周期速度非常有用。然而，共振强度一般只能计算一阶共振和同步加速器边带。当西伯利亚蛇将自旋调谐调整为1/2时，正如高能加速器所要求的那样，一阶共振不会出现，高阶共振成为主导。本文介绍了高阶自旋轨道共振的强度，并给出了一种计算高阶自旋轨道共振强度的有效方法，几个跟踪例子表明，计算出的共振强度确实可以用在Froissart-Stora公式中。HERA-p用于这些例子，这表明我们的结果与现有的加速器非常相关。
英文摘要：
When polarized particles are accelerated in a synchrotron, the spin precession can be periodically driven by Fourier components of the electromagnetic fields through which the particles travel. This leads to resonant perturbations when the spin-precession frequency is close to a linear combination of the orbital frequencies. When such resonance conditions are crossed, partial depolarization or spin flip can occur. The amount of polarization that survives after resonance crossing is a function of the resonance strength and the crossing speed. This function is commonly called the Froissart-Stora formula. It is very useful for predicting the amount of polarization after an acceleration cycle of a synchrotron or for computing the required speed of the acceleration cycle to maintain a required amount of polarization. However, the resonance strength could in general only be computed for first-order resonances and for synchrotron sidebands. When Siberian Snakes adjust the spin tune to be 1/2, as is required for high energy accelerators, first-order resonances do not appear and higher-order resonances become dominant. Here we will introduce the strength of a higher-order spin-orbit resonance, and also present an efficient method of computing it. Several tracking examples will show that the so computed resonance strength can indeed be used in the Froissart-Stora formula. HERA-p is used for these examples which demonstrate that our results are very relevant for existing accelerators.
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