Modeling and implementation of vertical excursion FFA in the Zgoubi ray-tracing code

Vertical Fixed Field Accelerators (vFFAs) feature complex and highly non-linear magnetic fields, which require simulation codes allowing step-wise particle tracking. Methods to model the 3D magnetic field of scaling vFFAs have been developed in the ray-tracing code Zgoubi. The field modeling and particle tracking methods include the field non-linearities, the fringe fields, and the field superposition of neighboring magnets. The procedure implements the vFFA analytical field expressions, allowing design studies and parameter optimizations using the Zgoubi built-in fit method. The vFFA procedure has been applied to a ten-fold symmetry ring with a triplet focusing structure designed to accelerate protons from 3 MeV to 12 MeV and studied under the ISIS-II proton driver prototype project. Results from particle tracking in externally generated 3D semi-analytical field maps and the developed vFFA analytical model are shown to be in excellent agreement.