Electron Cyclotron Resonance Ion Sources (ECRIS) are capable of delivering high currents of Highly Charged Ions (HCIs) to heavy ion accelerators (e.g.: to the future FRIB). The use of a sextupole magnet for confinement of the plasma inside the source imposes a unique triangular structure on the beam. This, together with the multitude of ion species that are extracted at the same time and the high axial magnetic field at the plasma aperture, resulting from additional confining solenoids, make the simulation and design of ECRIS extraction systems particularly challenging. The first objective of this thesis was to refine and test a semi-empirical simulation model of the formation and extraction of HCIs from ECR ion sources as well as their transport through the subsequent Low Energy Beam Transport (LEBT) system. To this end, a set of utility functions was written to simplify performing the simulations. In the LEBT system, another interesting, yet so far unanswered, question arises: The influence of space-charge effects on the beam and the level of space-charge compensation in the ECRIS beam line.This interesting topic quickly became the second main objective of the thesis. A Retarding Field Analyzer (RFA) was built and systematic measurements of the neutralization level in ECRIS LEBT systems were done for the first time as part of this thesis (this intensity and pressure regime was previously not well explored).The measured neutralization levels for typical ECRIS beams were found to be between 0% and 50% and agreed reasonably well with a simple formula developed by Gabovich et al. for highly neutralized proton and H- beams after it was re-derived and extended in this thesis for low neutralization and multiple species. Preliminary tests of the refined and integrated simulation model for the ECR ion sources VENUS and SuSI and their respective low energy beam transport systems include comparisons of measured beam currents, cross sections and emittances with the simulation results. These tests suggest that the model is suited for the simulation of ion beam extraction and transport for medium to high charge states of medium to heavy ions, but not for the lowest charge states and lightest ions (He1+, protons).Finally, as an example application of the developed software, a variable-energy (300 kV - 3 MV) electrostatic accelerator was simulated and redesigned for the DIANA project, a new proposed underground laboratory for nuclear astrophysics.
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