Emittance growth mechanisms for space-charge dominated beams in fixed field alternating gradient and proton driver rings

Systematic space-charge resonances are found to cause substantial emittance growth in proton driver rings and non-scaling fixed field alternating gradient (FFAG) accelerators. To avoid systematic nonlinear resonances, the phase advance of each cell must avoid π/2 and π/3. This limits the betatron tune range and the momentum acceptance for non-scaling FFAG accelerators. The emittance growth factor (EGF), defined as the ratio of final emittance to the initial emittance, is found to obey scaling properties in the linear space-charge tune shift parameter, the tune ramping rate, and stop-band widths of random quadrupole and skew-quadrupole errors.