Empirical condition of betatron resonances with space charge
Empirical condition of betatron resonances with space charge
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空间电荷电子感应加速器共振的经验条件
DOI：
10.1103/physrevaccelbeams.22.074201
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
and Y. Tokashiki
中科院分区：
文献类型：
--
作者：
K. Kojima;H. Okamoto;and Y. Tokashiki
本文讨论了半个多世纪前由Courant和Snyder导出的单粒子电子共振条件的推广。最近，从Sacherer、Okamoto和Yokoya [K.]的一维Vlasov预测中，推测出了包含空间-电荷相互作用影响的二维共振条件。我等，物理学家。启Accel。[6].梁与梁，2016,064201 (2017):PRABCJ2469-988810.1103/PhysRevAccelBeams.20.064201。该条件非常简单，仅包含几个可测量的量，并表明在高光束密度下可能存在两倍于传统非相干图像所期望的共振阻带。系统地进行了自洽多粒子模拟，以定位调图中的低阶阻带。提出的共振公式解释了数值观测的基本特征，表明在与外部线性聚焦势匹配的密束相空间核内没有激活严重的非相干共振。在典型的高强度存储环中，任何集体模态的相干频移因子都小于1，实际上被认为是整个音调空间的常数。讨论了在相干图像的基础上寻找环的最佳工作点的过程，而不是依靠非相干音波传播概念的常用图像。尽管许多研究人员进行了多年的理论努力，但相干共振概念仍然没有被用于构建稳定调谐图。我们在这里提供一个简单的处方来快速绘制图表。本研究还表明，通过选择适当的发射率比，可以完全抑制特定差共振上的发射率交换。
This paper addresses the generalization of the single-particle betatron resonance condition derived by Courant and Snyder more than a half century ago. A two-dimensional resonance condition including the effect of space-charge interaction was recently conjectured from one-dimensional Vlasov predictions made by Sacherer, Okamoto, and Yokoya [K. Itoet al., Phys. Rev. Accel. Beams 20, 064201 (2017)PRABCJ2469-988810.1103/PhysRevAccelBeams.20.064201]. The condition is remarkably simple which only contains a few measurable quantities and indicates the possibility that twice as many resonance stop bands as expected from the conventional incoherent picture may exist at high beam density. Self-consistent multiparticle simulations are performed systematically to locate low-order stop bands in the tune diagram. The proposed betatron resonance formula is shown to explain the basic feature of numerical observations, which suggests that no serious incoherent resonance is activated inside the phase-space core of a dense beam matched to the external linear focusing potential. It is confirmed that the coherent tune-shift factor of any collective mode is less than unity and practically considered as a constant over the whole tune space in a typical high-intensity storage ring. The procedure for finding the optimum operating point of the ring is discussed on the basis of the coherent picture instead of the commonly used picture relying on the concept of incoherent tune spread. Despite years of theoretical efforts by many researchers, the coherent resonance concept is still not being employed for the construction of a stability tune diagram. We here provide a simple prescription to draw the diagram quickly. The present study also indicates the possibility of complete suppression of emittance exchange on particular difference resonances by choosing a proper emittance ratio.