同步感应加速器耦合的矩阵形式
Matrix formalism of synchrobetatron coupling
摘要：
本文通过对描述直线水平和纵向运动的传递矩阵的研究，给出了一个完整的直线同步辐射加速器耦合形式。利用线性水平-垂直耦合研究中建立的技术[D. Sagan和D. Rubin，Phys. Rev. ST Accel.梁{ \bf 2}，074001（1999）]，我们发现了一个变换块对角化的传输矩阵和解耦的感应加速器运动和同步加速器运动。首先将通常的色散项从水平坐标中分离出来，在合理的近似下，我们能够得到变换的解析表达式。我们还得到了电子感应加速器调谐和Courant-Snyder函数的微扰。利用5 $\times$ 5扩展转移矩阵研究了由于射频腔的有限能量增益和辐射能量损失而引起的闭合轨道变化，其中第五列描述了四维相空间中的反冲。
英文摘要：
In this paper we present a complete linear synchrobetatron coupling formalism by studying the transfer matrix which describes linear horizontal and longitudinal motions. With the technique established in the linear horizontal-vertical coupling study [D. Sagan and D. Rubin, Phys. Rev. ST Accel. Beams {\bf 2}, 074001 (1999)], we found a transformation to block diagonalize the transfer matrix and decouple the betatron motion and the synchrotron motion. By separating the usual dispersion term from the horizontal coordinate first, we were able to obtain analytic expressions of the transformation under reasonable approximations. We also obtained the perturbations to the betatron tune and the Courant-Snyder functions. The closed orbit changes due to finite energy gains at rf cavities and radiation energy losses were also studied by the 5$\times$5 extended transfer matrix with the fifth column describing kicks in the 4-dimension phase space.
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