Abstract
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.