Modification of the method of the perturbation theory in application to the theory of tolerances for ion linear accelerators

A method for calculation of tolerances for linear ion accelerators by means of an original modification of perturbation theory is suggested. The equation of motion is converted so that the regular motion is separated from perturbated trajectory without the change of perturbation function. Errors of the channel are simulated in the form of thin lenses. Regular solution is determined in approximation of smooth envelopes. Simple recurrent ratio for mean square radius of the beam is obtained. The method can be useful for strong-focusing linear accelerators of any type