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The coupling of transverse motion is a natural occurrence in particleaccelerators, either in the form of a residual coupling arising fromimperfections or originating by design from strong systematic coupling fields.While the first can be treated perturbatively, the latter requires a robustapproach adapted to strongly coupled optics and a parametrization of the linearoptics must be performed to explore beam dynamics in such peculiar lattices.This paper reviews the main concepts commonly put forth to describe coupledoptics and clarifies the proposed parametrization formalisms. The links betweenthe generalized Twiss parameters used by the different approaches are formallyproven, and their physical interpretations are highlighted. The analyticalmethods have been implemented in a reference Python package and connected witha ray-tracing code to explore strongly coupled lattices featuring complex 3Dfields. Multiple examples are discussed in detail to highlight the key physicalinterpretations of the parametrizations and characteristics of the lattices.

Review of coupled betatron motion parametrizations and applications to strongly coupled lattices