The presence of the insertion devices (IDs) in a storage ring impacts the electron beam properties in different ways. Passing the electrons through the ID changes the betatron tunes, betatron amplitude function, and equilibrium parameters like emittance and energy spreads. The expression of equilibrium parameters in terms of radiation integrals is a common method for computing the effect of IDs on beam parameters. The effect of coupling is not included in the radiation integral method, so it is expected that in the case of using elliptically polarized undulators or modeling the real lattice with errors, this method could not express the beam parameters precisely. On the other hand, the equilibrium distribution of the electron beam and its related parameters could be determined directly by the envelope method. The envelope formalism is the most accurate method to compute the beam properties. In this study, we investigated the effect of IDs and lattice errors on beam parameters with both radiation integral and envelope methods. The results show that the envelope method could project the effect of magnetic imperfection and induced coupling from IDs on beam parameters.

存储环中插入装置 (ID) 的存在以不同方式影响电子束特性。使电子通过 ID 会改变电子感应器的调谐、电子感应器振幅函数和平衡参数，如发射率和能量传播。用辐射积分表示平衡参数是计算 ID 对光束参数影响的常用方法。辐射积分法不考虑耦合效应，因此预计在使用椭圆偏振波荡器或模拟有误差的真实晶格的情​​况下，该方法无法准确表达光束参数。另一方面，电子束的平衡分布及其相关参数可以通过包络法直接确定。包络形式是计算光束特性的最准确方法。在这项研究中，我们使用辐射积分和包络方法研究了 ID 和晶格误差对光束参数的影响。结果表明，包络法可以预测磁缺陷和 ID 的感应耦合对光束参数的影响。