The space-charge compensated state of drifting dc beams ofHe+ions of 10 keV ion energy and 0.14 and 1.5 mA current was determined with an electron beam probe, a rf resonance probe, the analysis of residual gas ion energies, and emittance measurement. The results are compatible with a basic model describing a two-dimensional multiplicity of possible self-consistent radial density distributions of beam ions, residual gas ions, and compensating electrons. The effects of electron drainage and beam current oscillations on space-charge compensation are pointed out. ©1998 American Institute of Physics.