Abstract
High frequency High Order Modes can significantly affect the coupled-bunch stability in a circular accelerator. With a large enough shunt impedance they may drive a coupled-bunch transverse instability. We have developed an analytical model and implemented it in the NHT Vlasov solver. The results show that the instability is characterized by the excitation of many azimuthal intra-bunch modes, which have similar growth rates, that make the traditional remedies such as a flat resistive feedback and chromaticity inefficient in suppressing it. For the High Luminosity Large Hadron Collider this could result in a significant increase of the stabilizing Landau octupole current, up to $\sim 100$ A ($\sim 20\%$ of the maximum available current). In order to limit the increase below 10 A ($\sim 2\%$), the transverse shunt impedance has to be kept below 1 M$\Omega$/m.
Highlights
Crab cavities are a key technology in many future colliders
In order to assess the impact of crab cavities on the transverse stability in High Luminosity (HL)-Large Hardon Collider (LHC) we have extended the nested airbag approach of Ref. [11] to describe fast oscillating coupled-bunch wakes of the crab cavity higher order modes (HOMs) and implemented it in the nested head-tail Vlasov solver code
The analysis shows that a single HOM from one HL-LHC crab cavity may require a significant amount of octupole current to be Landau damped even in the absence of other sources of impedance
Summary
Crab cavities are a key technology in many future colliders They allow increasing the luminosity at a given beam crossing angle by rotating the bunches in the plane of collision and restoring an effective head-on collision at the interaction point [1,2,3]. The nested head-tail (NHT) Vlasov solver [11] offers an efficient way to treat the multi-bunch problem, but the coupled-bunch approximation it has employed so far cannot be applied to the high frequency HOMs. We have extended the NHT code to include an exact solution of the coupled-bunch problem and used it to study the effect of crab cavity HOMs on the. It is worth mentioning that already this simple and apparently not realistic approximation already incorporates all the physics of the problem and is a powerful tool for qualitative estimates
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