Nonlinear dependence of synchrotron radiation on beam parameters

Synchrotron radiation has been traditionally treated as an effect which only depends on the linear beam dynamics. Electrons in advanced accelerators and storage rings, however, can lose several percent of their energy in one turn, especially when the ring incorporates synchrotron radiation sources or free electron lasers. In these machines nonlinear effects can become important, not only because of the high variation of the particle´s energy around the ring, but also because of the necessity to have very good beam quality in wigglers, undulators, and free electron lasers. Since these instruments can have helical structure, a general reference frame with torsion is used and the Lorenz-Dirac radiation reaction of the charged particle is taken into account. We will utilize the differential algebra technique to compute nonlinear transfer maps of general optical elements. Applications include radiation damping in multipoles, its effect on closed orbit distortion in a storage ring, and nonlinear tune shifts due to various radiating devices. The software provided will also be useful in simulating Siberian snakes