Analytical approach to chromatic correction in the final focus system of circular colliders

Abstract

A conventional final focus system in particle accelerators is systematically analyzed. We find simple relations between the parameters of two focus modules in the final telescope. Using the relations, we derive the chromatic Courant-Snyder parameters for the telescope. The parameters are scaled approximately according to (L^{*}/β_{y}^{*})δ, where L^{*} is the distance from the interaction point to the first quadrupole, β_{y}^{*} the vertical beta function at the interaction point, and δ the relative momentum deviation. Most importantly, we show how to compensate its chromaticity order by order in δ by a traditional correction module flanked by an asymmetric pair of harmonic multipoles. The method enables a circular Higgs collider with 2% momentum aperture and illuminates a path forward to 4% in the future.