We present a theory that can compute the transverse coupled-bunch instability growth rates at any chromaticity and for any longitudinal potential provided only that the long-range wakefield varies slowly over the bunch. The theory is expressed in terms of the usual coupled-bunch eigenvalues at zero chromaticity, and when the longitudinal motion is simple harmonic our solution only requires numerical root-finding that is easy to implement and fast to solve; the more general case requires some additional calculations, but is still relatively fast. The theory predicts that the coupled-bunch growth rates can be significantly reduced when the chromatic betatron tune spread is larger than the coupled-bunch growth rate at zero chromaticity. Our theoretical results are compared favorably with tracking simulations for the long-range resistive wall instability, and we also indicate how damping and diffusion from sychrotron emission can further reduce or even stabilize the dynamics.

中文翻译：

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色度和同步辐射对存储环耦合束横向动力学的稳定作用

我们提出了一种理论，该理论可以计算在任何色度和任何纵向电势下的横向耦合束不稳定性增长率，前提是远程束流场在束中缓慢变化。该理论用零色度下通常的耦合束本征值表示，当纵向运动为简谐时，我们的解决方案仅需要易于实现且易于求解的数值根查找。更一般的情况需要进行一些额外的计算，但仍然相对较快。该理论预测，当彩色倍速子调谐传播大于零色度下的耦合束增长速率时，可以大大降低耦合束增长速率。