Space charge tune shifts, fast resonance traversals, and current limits are important design issues for low energy, high power circular accelerators. Areas of interest are accumulator rings and fast cycling synchrotrons, and typical applications are for pulsed spallation neutron sources, heavy ion fusion storage ring drivers, and booster injectors for high energy proton and ion facilities. Aspects of the three topics are discussed in the paper. ©1996 American Institute of Physics.