We present a numerical technique for self-consistently calculating plasma equilibria with prescribed sources and sinks on the boundaries, i.e. a scattering system. The method is applied to the earth’s magnetotail. The method follows individual particles through a prescribed magnetic field, while calculating the density, current and pressure that the particle contributes on a uniformly spaced grid. The individual particles are weighted to model a given source distribution and the total equilibrium properties, including the r esulting magnetic field, are evaluated. The calculated and prescribed magnetic fields are then compared. If the fields differ significantly, the two fields are mixed and the p rocess repeated. Convergence to the self-consistent field typically takes between 100 and 150 iterations.