Beam Transfer Functions and Nonlinear Dynamics at the IUCF Cooler

与理解相干光束不稳定性和冷却环中的非线性有关的光束动力学问题将被研究。这些研究课题对提高IUCP冷环亮度的工作是必不可少的，对现代高亮度存储环也具有重要意义。本研究对培养加速器物理专业的研究生和本科生具有重要意义。任务A研究“冷却器的阻抗和不稳定性测量”。感兴趣的主题是相干不稳定性和高能量（和高亮度）加速器中的小发射率光束的保存。利用测得的波束传递函数，可以推导出阻抗。将Vlasov方程的模型仿真和分析评价与实验数据进行比较。这些实验将有助于更好地了解冷却环的电流限制。为阻尼系统的设计提供参考。通过这一系列的实验，我们将能够理解相干不稳定性和多维朗道阻尼对相干生长的动力学作用。这些实验对等离子体物理学也很重要。任务B研究“参数共振中的相位和振幅调制”。该实验是测量射频系统中波束对相位或幅度调制的响应。这些响应函数是参数共振方程的解。这些实验对于理解纵向相空间中的扩散过程具有重要意义。利用相位反馈回路，也可以研究高阻尼的参数谐振系统。诸如混沌、奇异吸引子和分岔等现象都是可以测量的。有了这些实验工具，我们可以建立一个很好的非线性动力学实验室。

Beam dynamics problems relevant to the understanding of the coherent beam instabilities and the nonlinearity in the Cooler Ring will be investigated. These research topics are indispensable to the effort of increasing luminosity at the IUCP Cooler Ring and are also important to modern high brightness storage rings. The proposed research is also important in training the accelerator physics graduate and undergraduate students. The task A studies "Impedances and Instabilities measurement of the Cooler". Topics of interest are coherent instabilities and preservation of small emittance beam in high energy (and high brightness) accelerators. Using the measured beam transfer function, the impedance can be deduced. Model simulation and analytic evaluation of the Vlasov equation will be compared with experimental data. These experiments will help to understand better the current limitation of the Cooler Ring. It will also provide information for the design of damper system. Through this series of experiments, we will be able to understand the dynamics of coherent instability and multidimensional Landau damping on the coherent growth. These experiment can also be important to Plasma physics. The task B studies "Phase and Amplitude Modulations in Parametric Resonances". The experiment is to measure beam responses to the phase or amplitude modulations in the rf system. These response functions are solutions of parametric resonant equations. These experiments are important to understand the diffusion process in the longitudinal phase space. Using the phase feedback loop, highly damped parametric resonant system can be studied as well. Phenomena such as chaos, strange attractors, and bifurcations can be measured. With these experimental tools, we can set up an excellent laboratory for nonlinear dynamics.