Beam dynamics studies of four-gap low-beta superconducting resonators

The four-gap superconducting resonators which have been developed at Argonne for use in the low-beta positive ion-injector for ATLAS have potential applications for ions with velocities less than 0.007c and q/m less than 0.1. It was previously observed that at low velocities these structures can be focussing in both longitudinal and transverse phase spaces due to an inherent alternating-phase-focussing property. Studies are underway to determine the optimum combination of multi-gap structures and solenoids at low velocity and low q/m. We present the results of acceptance studies for the first three resonators at the front of the positive-ion injector linac, with and without the focussing solenoids. These studies include the effects of higher-order distortions in longitudinal and transverse phase spaces since minimising each aberrations is very important for most nuclear physics applications of such accelerators