The goal of this article is to present simulations on the extraction from an electron cyclotron resonance ion source (ECRIS). The aim of this work is to find out an extraction system, which allows one to reduce the emittances and to increase the current of the extracted ion beam at the focal point of the analyzing dipole. But first, we should locate the correct software which is able to reproduce the specific physics of an ion beam. To perform the simulations, the following softwares have been tested: SIMION 3D, AXCEL, CPO 3D, and especially, for the magnetic field calculation, MATHEMATICA coupled with the RADIA module. Emittance calculations have been done with two types of ECRIS: one with a hexapole and one without a hexapole, and the dif...