Study of Insertion Device's Influence on Nonlinear Beam Dynamics in Electron Storage Ring Using Lie Algebra

Abstract：

In designing the 3rd generation synchrotron radiation light source, many long, and dispersion free straight sections are left for installing undulators to produce coherent radiation. For the damping ring used as pre-injector of next generation linear collider, many wigglers are used to increase radiation damping rate. So it is important to understand those Insertion devices'(ID) influence on beam dynamics in design and optimization stage. This paper introduces the study of insertion device's influence on beam dynamics in electron storage ring using the symplectic Lie mapping. Firstly the Hamiltonian of charged particle's motion along ID axis is given, then two methods are adopted to analyse ID's influence on beam dynamics. One method is expanding Hamiltonian to 4th order Taylor series, then all kinds of multipole components (till to octupole) can be obtained; another is constructing a second order symmetrical, symplectic integrator using Lie map product by similar transformation directly. The simulation results show those two methods are consistent. The primary results of influence on beam dynamics of UD-1, a new undulator which will be installed in Hefei Light Source storage ring soon, are also given. The tune-shift and decrease of dynamic aperture caused by UD-1 can be found in simulation results.