A Radio Frequency Quadrupole Cooler (RFQC) prototype was adapted for insertion into a high uniformity magnetic field, with Bz up to 0.2 T, to improve radial confinement. While the RFQC purpose is to reduce (by gas collisions) the energy spread and emittance of a beam of radioactive nuclei, to finely select ion mass in nuclear physics, the prototype is tested in a setup including a stable ion source, a pepper pot emittance meter, and two Faraday cups; this makes a precise characterization of the RFQC feasible. The ion extraction was studied in detail by simulations, both to match it to the emittance meter granularity and to verify the effect of the typical nonuniformity of the longitudinal electric field Ez inside the RFQC; an average motion description (including friction force from gas collisions) was used, introducing the ballistic and diffusive regimes. With a preliminary optimization of the electrode shape, buffer gas pressure pg, and radio frequency voltage, the ion beam can be extracted with a significant cooling margin.