Beam Transfer Functions and Nonlinear Dynamics at the IUCF Cooler

与理解相干光不稳定性和冷却器环中的非线性有关的光束动力学问题将被研究。这些研究课题对于提高IUCP冷却环的亮度是不可或缺的，对现代高亮度存储环也是重要的。本研究对加速器物理研究生和本科生的培养也具有重要意义。任务A研究“冷却器的阻抗和不稳定性测量”。感兴趣的主题是在高能(和高亮度)加速器中的相干不稳定性和小发射度束的保存。利用测得的束流传递函数，可以推导出波阻抗。Vlasov方程的模型模拟和分析评估将与实验数据进行比较。这些实验将有助于更好地了解冷却器环的电流限制。为阻尼器系统的设计提供参考。通过这一系列的实验，我们将能够了解相干不稳定性和多维朗道阻尼对相干生长的动力学影响。这些实验对等离子体物理也很重要。任务B学习“参数共振中的相位和幅度调制”。该实验是为了测量射束对射频系统中的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是重要的。利用相位反馈回路，也可以研究高阻尼参数谐振系统。混沌、奇异吸引子和分叉等现象是可以测量的。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.