Tune Control in Fixed Field Accelerators

Fixed Field Alternating Gradient Accelerators have been proposed for a wide range of challenges, including rapid acceleration in a muon collider, and large energy acceptance beam transport for medical applications. A disadvantage of these proposals is the highly nonlinear field profile required to keep the tune energy-independent, known as the scaling condition. It has been shown computationally that approximately constant tunes can be achieved with the addition of nonlinear fields which do not follow this scaling law. However the impacts of these nonlinearities are not well understood. We present a new framework for adding nonlinearities to Fixed Field Accelerators, seeking a constant normalised focusing strength over the full energy range, and verify the results by simulation using Zgoubi. As a model use case, we investigate the degree of tune compensation that can be achieved in a Fixed Field Accelerator for ion cancer therapy.