ABSTRACT
Special characteristics of particle loss at a betatron sum resonance is discussed. Particle motion at the nonlinear resonance region are decomposed into a Courant-Snyder invariant circle and a resonance curve. Intersection points in the phase space of these two curves correspond to unstable fixed points. These unstable fixed points form an unstable fixed curve, which is the resonance curve. Particles are found to stream out of the invariant surface through the nonlinear resonance line, which is the passage to unbounded motion at a sum resonance. Careful studies of the pathway may lead to understanding of the Diffusion process as well as the fast beam loss observed in particle tracking calculations.
