High intensity beams may suffer from serious beam quality degradation if the focusing scheme allows for occurrence of resonances or instabilities. For transverse focusing a commonly accepted and respected lattice design rule is to choose the phase advance per structure period below the 90° resonant stop band, which was implicitly applied to the longitudinal phase advance the same way. A recent study pointed out that for lattice structures with more than one rf gap per period the 90° restriction needs not to be applied the same way to the longitudinal focusing as to the transverse one [I. Hofmann and Oliver Boine-Frankenheim, Phys. Rev. Lett. 118, 114803 (2017)], thus offering more design flexibility. The present paper is motivated by an interest to accelerate intense proton beams above longitudinal 90° in the new poststripper drift tube linac of the GSI universal linear accelerator by using the rf power supplies optimized for the much stiffer heavy ions. We confirm that a strictly periodic prolongation of the first cavity could allow acceleration above longitudinal 90° with only minor beam quality degradation. However, the combination of a high longitudinal phase advance with intercavity sections breaking the periodicity shows that matching challenges—rather than resonances—determine emittance growth. In the present case it is found tolerable for up to three such sections. This confirms the validity of the principle and at the same time its limits under practical conditions.

中文翻译：

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纵向阶段运行的高强度线性加速器的仿真研究超过90°

如果聚焦方案允许发生共振或不稳定性，则高强度光束可能遭受严重的光束质量下降。对于横向聚焦，一个公认的且受人尊敬的晶格设计规则是在每个结构周期内选择低于90°共振阻带的相位超前，该隐式以相同的方式隐式应用于纵向相位超前。最近的一项研究指出，对于每周期具有一个以上rf间隙的晶格结构，不需要对纵向聚焦和横向聚焦采用相同的方式施加90°限制。霍夫曼和奥利弗Boine-Frankenheim，物理学。牧师 118，114803（2017）]，从而提供更多的设计灵活性。本文的兴趣是通过使用针对更硬得多的重离子进行了优化的射频电源，在GSI通用线性加速器的新型后剥离器漂移管直线加速器中将强质子束加速到纵向90°以上。我们确认，严格限制第一腔的周期性延长，可以使纵向90°以上的加速度加速，而光束质量只有很小的下降。但是，高纵向相位超前与腔间断面的结合打破了周期性，这表明匹配的挑战而非共振决定了发射率的增长。在当前情况下，发现最多可容纳三个这样的部分。这证实了该原理的有效性，同时也证实了其在实际条件下的局限性。