We have adapted the ZEUS code to model magnetic interactions in partially ionized gas. When two regions of opposite polarity come into contact with each other, ions drifting in response to the Lorentz force fall into the minimum of the magnetic field, and then the drifting ions force the neutrals to take part in the flow. Because of the finite time required for ion-atom collisions to occur, the gas which emerges from the interaction site has an ion/atom ratio which may be altered relative to that in the ambient medium. In order to model this effect, we adapt the Zeus code to a two-step iterative process involving a cycle between the hydrodynamic (HD) and the magnetohydrodynamic (MHD) versions of the code. The ion and atom fluids are coupled by collisions. Our simulations show that in chromospheric conditions, outflowing gas exhibits enhancements in ion/atom ratios which may be as large as a factor of 10 or more. The magnitude of the enhancements is determined by two key ratios which enter into the problem: the degree of ionization (ni/na), and the plasma β parameter. We show that, in the context of the mechanism we propose here, the amplitude of the ion/atom enhancements in the solar chromosphere is subject to a remarkable self-regulation because the ion density ni is almost invariant over the height range of interest to us. Our results are relevant in the context of the Sun, where the coronal abundances of elements with low first ionization potential (FIP) are systematically enhanced in certain magnetic structures. Although data for stars other than the Sun are sparse, we point out that our results are also useful for interpreting the available stellar data.