Parametrizations of coupled betatron motion for strongly coupled lattices

Abstract

The coupling of transverse motion is a natural occurrence in particle accelerators, either in the form of a residual coupling arising from imperfections or originating by design from strong systematic coupling fields. While the first can be treated perturbatively, the latter requires a robust approach adapted to strongly coupled optics, and a parametrization of the linear optics must be performed to explore beam dynamics in such peculiar lattices. This work highlights the key physical interpretations of the main parametrization formalisms to describe linear coupled optics, along with explicit links and comparisons of these parametrizations. Concepts rarely illustrated in other works, such as forced mode flips and local coupling, are explored in detail, clarifying some anomalies that can arise in lattice functions. The analytical methods have been implemented in a reference Python package and connected with ray-tracing and integration codes to explore examples of strongly coupled lattices, which are discussed in detail to highlight the key physical interpretations of the parametrizations and characteristics of the lattices.

Dynamic aperture studies for vertical fixed field accelerators

“…Their magnetic field satisfies the scaling condition B = B 0 exp[k(z − z 0 )], where k = (1/B)(∂B/∂z) is the normalized field gradient, z 0 is a vertical reference position and B 0 is the bending field at that reference position. vFFA magnetic fields exhibit longitudinal and skew quadrupolar components, inducing strongly coupled linear optics that requires adequate coupling parametrization [3] for studying their linear beam dynamics [4]. In addition, the exponential form produces a highly nonlinear field, resulting in nonlinear coupling between the linearly decoupled planes.…”