The Vaccaro stability diagram of scaling FFAs

Fixed Field Accelerators (FFAs) are a promising candidate for future high intensity machines such as ISIS-II. It follows that the largely unexplored topic of coherent transverse beam instabilities in these machines is of increasing importance. Transverse instabilities, such as head-tail, can be mitigated in synchrotrons by adjusting the chromaticity appropriately. However, in scaling FFAs, the chromaticity is fixed at zero by design. On the other hand, the relatively strong tune shift with amplitude caused by the nonlinear field of FFA magnets provides a source of Landau damping. Here we evaluate the resulting stability region in the complex tune shift plane comparing an analytical prediction based on the extracted detuning with amplitude with the results from numerical tracking simulations. Hence, the impedance threshold of FFAs can be established.