近日，瑞士欧洲核子研究中心的F. Schmidt&H. Bartosik及其研究团队与德国法兰克福歌德大学的G. Franchetti合作并取得一项新进展。经过不懈努力，他们对欧洲核子研究中心(CERN)超级质子同步加速器非线性共振诱导的固定线进行观测。相关研究成果已于2024年3月20日在国际知名学术期刊《自然—物理学》上发表。

该研究团队通过观察所谓的固定线，证实了单个二维耦合共振动力学的理论预测。具体而言，研究人员使用欧洲核子研究中心的超级质子同步加速器来测量粒子束在加速器周围离散定位的位置。这些测量数据让研究人员成功构建出剖面的庞加莱曲面，该曲面精准地捕捉了周期系统动力学的核心特征。在这一设置中，任何通过庞加莱剖面表面的共振粒子都会沿着一条曲线运动，这条曲线嵌入在四维相空间中，被称之为固定线。

这些发现对于解决光束退化问题至关重要，对于实现当前和未来加速器项目所需的高强度、高亮度光束具有深远的意义。

据悉，具有线性回复力和周期性非线性扰动的系统的运动在物理学中是非常重要的。当系统的固有振动频率与非线性回复力的频率满足一定的代数关系时，系统的动力学就会发生共振。在加速器物理学中，对共振和非线性动力学的理解对于避免束流粒子的损失至关重要。

附：英文原文

Title: Observation of fixed lines induced by a nonlinear resonance in the CERN Super Proton Synchrotron

Author: Bartosik, H., Franchetti, G., Schmidt, F.

Issue&Volume: 2024-03-20

Abstract: The motion of systems with linear restoring forces and recurring nonlinear perturbations is of central importance in physics. When a system’s natural oscillation frequencies and the frequency of the nonlinear restoring forces satisfy certain algebraic relations, the dynamics become resonant. In accelerator physics, an understanding of resonances and nonlinear dynamics is crucial for avoiding the loss of beam particles. Here we confirm the theoretical prediction of the dynamics for a single two-dimensional coupled resonance by observing so-called fixed lines. Specifically, we use the CERN Super Proton Synchrotron to measure the position of a particle beam at discrete locations around the accelerator. These measurements allow us to construct the Poincaré surface of section, which captures the main features of the dynamics in a periodic system. In our setting, any resonant particle passing through the Poincaré surface of section lies on a curve embedded in a four-dimensional phase space, the fixed line. These findings are relevant for mitigating beam degradation and thus for achieving high-intensity and high-brightness beams, as required for both current and future accelerator projects.

DOI: 10.1038/s41567-023-02338-3

Source: https://www.nature.com/articles/s41567-023-02338-3