论文标题
在有被动谐波腔的存在下，任意束火车的平衡：通过耦合的ha \“ Issinski方程的解决方案
Equilibrium of an Arbitrary Bunch Train in Presence of a Passive Harmonic Cavity: Solution through Coupled Ha\" issinski Equations
论文作者
论文摘要
我们研究一个被动谐波腔的效果，引入了电子存储环中引起束延长的效果。我们从高$ q $的腔体中得出了诱导电压的公式，并由一系列束序列激发，从而使序列和任意电流中的任意间隙允许。除了可以迭代确定的次要术语外，要以束形式的傅立叶变换的单个模式给出电压，即在腔的谐振频率下的模式。假设唯一的唤醒场来自谐波腔，我们得出了一个耦合的HaïsSinski方程系统，该系统确定了平衡状态下的束位置和轮廓。系统中未知数的数量仅是束数量的两倍，并且可以通过牛顿迭代迅速解决，首先是通过从弱电流下从解决方案中遵循途径来确定的猜测。我们探讨了填充模式对束延长的影响，以及对腔的分流阻抗和使腔的依赖性远离主要加速腔的第三个谐波。我们考虑了减少差距效应的两项措施：1）在允许的最大程度上分布环上的间隙，以及2）“后卫束”，较高的电荷与间隙相邻，以补偿间隙中缺少的电荷。提出了即将面临的ALS-U光源参数的结果。
We study the effect of a passive harmonic cavity, introduced to cause bunch lengthening, in an electron storage ring. We derive a formula for the induced voltage from such a cavity with high $Q$, excited by a a sequence of bunches, allowing for arbitrary gaps in the sequence and arbitrary currents. Except for a minor term that can be determined iteratively, the voltage is given in terms of a single mode of the Fourier transforms of the bunch forms, namely the mode at the resonant frequency of the cavity. Supposing that the only wake field is from the harmonic cavity, we derive a system of coupled Haïssinski equations which determine the bunch positions and profiles in the equilibrium state. The number of unknowns in the system is only twice the number of bunches, and it can be solved quickly by a Newton iteration, starting with a guess determined by path-following from a solution at weak current. We explore the effect of the fill pattern on the bunch lengthening, and also the dependence on the shunt impedance and detuning of the cavity away from the third harmonic of the main accelerating cavity. We consider two measures to reduce the effects of gaps: 1) distribution of the gaps around the ring to the greatest extent allowed, and 2) "guard bunches" with higher charges adjacent to the gaps, compensating for the charge missing in gaps. Results for parameters of the forthcoming ALS-U light source are presented.
