We propose a novel scheme for the calculation of bunch profiles and synchronous phase shifts for arbitrary fill patterns in electron storage rings considering both the effects of the passive harmonic cavity and the short range wakefield. This scheme treats the bunch as a charge distribution rather than a point charge with a bunch form factor, and divides the voltage induced in the cavity into two groups: that induced by the previous passages and that by the present passage, where the latter is integrated with the short range wakefield from all the other vacuum components. An iteration loop for computing the bunch profiles, including a subloop using Newton iteration for calculating the synchronous phase deviations, is built and implemented into a matlab-based code. Using this code, we study the bunch lengthening and centroid transient effects for several possible fill patterns in the Hefei Advanced Light Facility storage ring under design. We find the method is very efficient, and the CPU time for the whole calculation on a regular personal computer is less than 30 seconds for each case even with more than 700 bunches. Using the case of a long gap fill as a benchmark example, both the results given by our code and the multiparticle tracking simulation with elegant are in very good agreement.

中文翻译：

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有无源谐振腔和短程尾波场时任意填充束的纵向平衡密度分布

考虑到无源谐波腔和短程尾波场的影响，我们提出了一种新颖的方案，用于计算电子存储环中任意填充图案的束轮廓和同步相移。该方案将束视为电荷分布，而不是具有束形状因数的点电荷，并将空腔中感应的电压分为两组：由先前通道感应的电压和由当前通道感应的电压，将当前通道积分具有来自所有其他真空组件的短程尾流场。建立了一个用于计算束轮廓的迭代循环，其中包括一个使用牛顿迭代计算同步相位偏差的子循环，并将其实现到Matlab中基于代码。使用此代码，我们研究了设计中的合肥高级轻型设施储能环中几种可能的填充模式的束延长和质心瞬态效应。我们发现该方法非常有效，并且即使有700多个束，在每种情况下，普通个人计算机上整个计算的CPU时间也少于30秒。以长间隙填充的情况为基准示例，我们的代码给出的结果与优雅的多粒子跟踪模拟都非常吻合。