A physical parametrization of coupled transverse dynamics based on generalized Courant-Snyder theory and its applications

A physical parametrization of coupled transverse dynamics is developed by generalizing the Courant-Snyder (CS) theory for one degree of freedom to the case of coupled transverse dynamics with two degrees of freedom. The four basic components of the original CS theory, i.e., the envelope equation, phase advance, transfer matrix, and CS invariant, all have their counterparts with remarkably similar expressions in the generalized theory. Applications of the new theory are given. It is discovered that the stability of coupled dynamics is completely determined by the generalized phase advance.