The trapping of neutrals from a fast atom beam impinging on an electron-cyclotron-plasma target is studied. The electron-cyclotron plasma is assumed to be fed by an influx of molecular hydrogen. Radial attenuation of the feed gas and the H0 formed by its dissociation is considered in detail. Both the addition of neutrals and depletion of the target by charge exchange with the beam are also taken into account, as is reflux from nearby walls. Given a sufficiently high target density (≥ 1013 protons/cm3), a sufficiently low background density, and a 0.01-1.0 A neutral beam, it is calculated that 1011-1013 protons/cm3 can be accumulated with a trapping efficiency of several per cent.