Frequency map analysis of nonlinear dynamics in the NLC main damping rings

To avoid radiation damage, the acceptance of linear collider damping rings must be large enough that injection efficiency close to 100 percent can be achieved. Survival plots based on tracking particles in the NLC Main Damping Ring lattice suggest a dynamic aperture with some margin over the specified injected beam size and energy spread. Here, we apply Frequency Map Analysis to give a more detailed picture of the dynamical stability of particle trajectories in the presence of lattice nonlinearities arising from the sextupoles and the damping wiggler. The techniques that we use are of general applicability to nonlinear elements in beamlines, and in particular will be used for analysis of wiggler effects in future damping ring designs.