Resonance crossing and dynamic aperture in nonscaling fixed field alternating gradient accelerators

Abstract

Operation with natural chromaticity in a linear nonscaling fixed field alternating gradient (FFAG) accelerator causes crossing of the low order resonances such as integer and half-integer. Although those resonances are not systematic ones, small errors, such as a typical misalignment of 10 μm rms, significantly increase particle amplitude when the accelerator is operated with a slow acceleration rate. For example, there is practically no dynamic aperture if it takes 1000 turns to finish the whole acceleration cycle. Chromaticity correction with sextupole and octupole reduces the maximum available dynamic aperture in a lattice without errors. On the other hand, the accelerator becomes less sensitive to errors. To use a nonscaling FFAG for applications where, unlike a muon accelerator, the large acceptance is not a high priority demand (such as a proton driver or a particle therapy accelerator), chromaticity correction seems to be an essential ingredient.