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arXiv 2307.01286physics.acc-ph
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由Haissinski方程推导的理论及其在电子储存环中的应用

Theories derived from Haissinski equation and their applications to electron storage rings

Demin Zhou, Takuya Ishibashi, Gaku Mitsuka, Makoto Tobiyama, Karl Bane, Linhao Zhang

AI总结:

本研究从Haissinski方程自洽推导出束团质心偏移、束长、阻抗提取等相关方程,拓展得到适用于任意阻抗的势阱束团伸长广义二次方程,经电子储存环阻抗模型验证,可有效衔接阻抗计算与束流测量。

摘要:

作为Vlasov-Fokker-Planck方程的稳态解,Haissinski方程可预测给定尾场函数下,在储存环中循环的束团的平衡线密度。本文表明,若干关于束团质心偏移、束团分布峰值位置、束团长度以及从束团分布提取阻抗的方程,可通过Haissinski方程自洽推导得出。特别地,本文得到了适用于任意绝对阻抗模型的势阱束团伸长广义二次方程,对主要适用于感性阻抗的Zotter三次方程进行了拓展。本文利用部分电子储存环的计算阻抗模型对推导得到的方程进行了验证,展现出阻抗效应的机器依赖特性。我们得出结论,这些方程可应用于电子储存环,有效填补阻抗计算与基于束流的测量之间的空白。

英文摘要:

As a stationary solution of the Vlasov-Fokker-Planck equation, the Haissinski equation predicts the equilibrium line density of a bunch that circulates in a storage ring for a given wake function. This paper shows that some equations regarding the centroid shift of the bunch, the peak position of the bunch profile, bunch length, and extraction of impedance from the bunch profile can be derived from the Haissinski equation in a self-consistent manner. In particular, a generalized quadratic equation for potential-well bunch lengthening is obtained to accommodate any absolute impedance model, expanding upon Zotter's cubic equation, which is primarily applicable to inductive impedance. The equations derived in this paper are tested using computed impedance models for some electron storage rings, showing machine-dependent properties of impedance effects. We conclude that these equations can be employed in electron storage rings to effectively bridge the gap between impedance computations and beam-based measurements.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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