Frequency map analysis of a three-dimensional particle in the core model of a high intensity linac

We consider the dynamical properties of a particle-core model for a uniformly filled triaxial ellipsoid in a periodic lattice of a high intensity linac. The mismatched oscillation modes are analytically computed in the smooth approximation and are compared with the numerical results of a tracking program. The study of the phase space in the mismatched case is performed by the frequency map analysis. In particular, we can analyze the effect of the nonlinear resonances between the envelope modes and the single particle sincrobetatron frequencies. A chaoticity criterion based on the frequency map analysis allows one to compute the stability region around the beam core. An estimate of the transport and its enhancement due to mismatch is provided by tracking orbits at the border of the stability region.