Parametrizations of coupled betatron motion for strongly coupled lattices

The coupling of transverse motion is a natural occurrence inparticle accelerators, either in the form of a residual couplingarising from imperfections or originating by design from strongsystematic coupling fields. While the first can be treatedperturbatively, the latter requires a robust approach adapted tostrongly coupled optics, and a parametrization of the linear opticsmust be performed to explore beam dynamics in such peculiarlattices. This work highlights the key physical interpretations ofthe main parametrization formalisms to describe linear coupledoptics, along with explicit links and comparisons of theseparametrizations. Concepts rarely illustrated in other works, suchas forced mode flips and local coupling, are explored in detail,clarifying some anomalies that can arise in lattice functions. Theanalytical methods have been implemented in a reference Pythonpackage and connected with ray-tracing and integration codes toexplore examples of strongly coupled lattices, which are discussedin detail to highlight the key physical interpretations of theparametrizations and characteristics of the lattices.