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ONERA plasma tank JONAS is populated with drifting Ar+ argon ions representative of a low Earth orbit environment, produced by a Kaufman source, and slow ions created by charge exchange with the background pressure of argon. When testing a mock-up or space equipment in this tank, it is often important to determine the drifting and slow ion densities in various locations. The orbital and radial motion models are compared to experimental current-voltage measurements and to numerical results. In the range of parameters used in this paper, the radial motion model is more adapted than the orbital-motion-limited model to determine slow ion density. Nevertheless, the number of measurements is necessarily limited and discriminating between fast and slow ions is not easy. A complementary approach consists in performing a numerical simulation of the plasma dynamics in the tank. Provided the modeled physics is validated, and the modeling is calibrated through measurements, this approach supplies fast and slow ion densities everywhere with an acceptable factor of uncertainty. This approach has been followed by characterizing in detail a given plasma configuration in JONAS and modeling it with Spacecraft Plasma Interaction Software open source code. The mock-up was a simple plate. We measured the plasma characteristics through numerous current-voltage sweeps and current space profiles at given probe potential. The modeling was based on fast ion beam measurements close to the source and the residual pressure.