Application of a modified perturbation theoretic method to the theory of tolerances in linear ion accelerators

A method is proposed for calculating tolerances in linear ion accelerators using a novel perturbation theoretic method. The equation of motion is transformed in such a way that the regular motion is found from the perturbed trajectory without changing the perturbation function. The faults in the channel are treated by modeling them as thin lenses. A regular solution is found in the smooth-envelope approximation, and a simple recurrence equation is derived for the mean-square beam radius.