Perturbation analysis of the octupole-induced resonances in a storage ring

This note is a continuation from LS-126, in which the authors derived a formula for the lowest-order amplitude-dependent tune shift for octupole-induced resonances. Here, the authors apply the canonical perturbation theory to the octupolar Hamiltonian and attempt to extend the analysis further in order to obtain much clearer insight on the octupole-induced resonances. The authors derive the distortion functions, which measure the distortions of the particle oscillation phase and amplitude in phase space. Based upon these distortion functions, they derive the higher-order amplitude-dependent tune shifts for octupoles