AbstractWe present results of experiments on space-charge waves and longitudinal instabilities in space-charge-dominated beams, which are important to the design and development of induction accelerators as heavy-ion fusion drivers. By employing localized space-charge waves, the geometry factor-an important beam parameter for heavy-ion fusion accelerator design-has been measured and its correct formula has been verified. Space-charge waves have been found to reflect back on the shoulder of an eroded rectangular beam bunch. This phenomenon has significant implications for the understanding and analysis of longitudinal instabilities. A resistive-wall instability experiment has clearly shown the growth of slow waves and the decay of fast waves. For localized perturbations, the amplitude change that results from the instability is smaller than expected.