Derivation of Collins' Formulas for Beam-Shape Distortion Due to Sextupoles Using Hamiltonian Method

摘要

The introduction of sextupoles into a storage ring will distort the beam shape in both the horizontal and vertical phase space. The purpose of this note is to rederive the formulas for the lowest-order beam-shape distortion given by Collins using the Hamiltonian approach such as the one used by Ohnuma. Collins' formulas for the second-order tune-shift have been rederived by the Hamiltonian method in a recent note. We go over the Hamiltonian method briefly for two reasons: (1) to make this note more readable; and (2) to conform with the convention of Collins so that a comparison can be made. (ERA citation 10:003124)