Abstract. Significant experimental and theoretical progress has been made in the U.S heavy-ion fusion program on the transport of space-charge-dominated intense heavy-ion and electron beams, particularly in measurements and modeling of current density non-uniformities and halo formations due to mismatches in transport over a few to 10 focusing lattice periods. An experiment shows control of high beam current with an aperture, and reduced beam emittance near theoretical limits while avoiding secondary electrons. A new high-brightness Argon plasma source for HIF experiments will be described. New theory and simulations of neutralization of intense beam space charge with plasma in various focusing chamber configurations indicate that near-emittance-limited beam focal spot sizes can be obtained even with beam perveance (ratio of beam space potential to ion energy) >10 x higher than in earlier HIF focusing experiments. Progress in a new focusing experiment with plasma neutralization up to 10- 3 perveance, and designs for a next-step experiment to study beam brightness evolution from source to target will be described.