具有光耦合的偏振HOM的再循环BBU阈值
Recirculating BBU thresholds for polarized HOMs with optical coupling
摘要：
我们将推导出具有耦合束流光学和偏振高阶偶极模的循环直线加速器中束分裂不稳定性的一般理论。在每个再循环圈期间，聚束不必处于相同的RF相位。这对于描述能量恢复直线加速器（ERLs）是很重要的，其中束流变得非常大，并且耦合光学器件被故意用于增加阈值电流。证明了与跟踪数据的显着一致性。然后分析了几种解析可解的情况下的通用公式，其中显示：（a）为什么不同的高阶模式（HOM）在一个腔可以耦合，不能单独考虑，即使它们的频率被分离的远大于HOM的谐振宽度。对于作为示例的Cornell ERL，应当注意，当腔被设计为具有高于50 MHz的$x$ - $y$ HOM频率分裂时，可以获得耦合光学器件的最佳优点。然后阈值电流远高于该加速器的设计电流。(b)粒子光学中的$x$ - $y$耦合如何决定何时可以单独考虑模式。(c)通过耦合光学和偏振模式获得的阈值电流的增加大致随着HOM的品质因数的平方根而减小。因此，最大的优点是利用没有特别设计成使这些品质因数最小化的腔来实现的，例如通过HOM吸收器。(d)多圈再循环如何干扰用耦合光学器件获得的阈值改进。
英文摘要：
We will derive the general theory of the beam-breakup instability in recirculating linear accelerators with coupled beam optics and with polarized higher order dipole modes. The bunches do not have to be at the same RF phase during each recirculation turn. This is important for the description of energy recovery linacs (ERLs) where beam currents become very large and coupled optics are used on purpose to increase the threshold current. A remarkable agreement with tracking data is demonstrated. The general formulas are then analyzed for several analytically solvable cases, which show: (a) Why different higher order modes (HOM) in one cavity can couple and cannot be considered individually, even when their frequencies are separated by much more than the resonance widths of the HOMs. For the Cornell ERL as an example, it is noted that optimum advantage of coupled optics is taken when the cavities are designed with an $x$-$y$ HOM frequency splitting of above 50MHz. The threshold current is then far above the design current of this accelerator. (b) How the $x$-$y$ coupling in the particle optics determines when modes can be considered separately. (c) That the increase of the threshold current obtainable by coupled optics and polarized modes diminishes roughly with the square root of the HOMs' quality factors. Therefore the largest advantages are achieved with cavities that are not specifically designed to minimize these quality factors, e.g. by means of HOM absorbers. (d) How multiple-turn recirculation interferes with the threshold improvements obtained with a coupled optics.
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