Nonlinear optimization of the modern synchrotron radiation storage ring based on frequency map analysis

In this paper, we present a rule to improve the nonlinear solution with frequency map analysis （FMA）, and without frequently revisiting the optimization algorithm. Two aspects of FMA are emphasized. The first one is the tune shift with amplitude, which can be used to improve the solution of harmonic sextupoles, and thus obtain a large dynamic aperture. The second one is the tune diffusion rate, which can be used to select a quiet tune. Application of these ideas is carried out in the storage ring of the Shanghai Synchrotron Radiation Facility （SSRF）, and the detailed processes, as well as better solutions, are presented in this paper. Discussions about the nonlinear behaviors of off-momentum particles are also presented.     

简单体系温度涨落的发散问题

平衡体系热力学推导涨落的前提是涨落必须很小，如果得到一个发散的结果说明这一涨落是不可靠的.对一些体系温度涨落的热力学结果，在温度趋于绝对零度时是发散的，这时必须用统计物理来处理.对这些体系进行统计物理处理的结果表明，涨落在温度趋于绝对零度时是趋于零的. 关键词： 热力学与统计物理 涨落