We have started an experimental and theoretical program to better understand the extraction and transport of intense multiply charged ion beams from an electron cyclotron resonance ion source (ECRIS). In this paper we present the first results of this program concerning a simple, monocomponent He(+) beam extracted from an ECRIS. We have calculated the ion trajectories starting from the ECRIS plasma electrode up to the image plane of the analyzing magnet taking into account space-charge effects and fringe fields. The initial phase-space distribution of the He(+) beam at the extraction aperture has been calculated with a particle-in-cell code. To check the simulations we have measured beam profiles with a viewing screen both before and after the analyzing magnet. In addition also measurements with a pepperpot emittance meter located behind the analyzing magnet have been performed. We find good agreement between these measurements and simulations showing that (i) there is a significant compensation of the space charge and that (ii) our analyzing magnet causes a severe increase in effective beam emittance.