A model for the simulation of ion beam extraction from an electron cyclotron resonance ion source is proposed. It is based on the simple fact that charged particles follow magnetic field lines. Therefore magnetic field lines are used to generate initial conditions for ray-tracing. This model reproduces in simulation experimentally obtained results. The importance of correlations in phase-space caused by the magnetic field is shown in simulation. This model also describes the physics of space-charge and its compensation in the extracted (fast) ion beam by low energy electrons. Simulation provides the possibility to test theoretical assumptions, as well as to optimize technical designs.