Computer simulation studies of the stability and transport properties of trapped non-neutral plasmas require the numerical realization of a three-dimensional plasma distribution. This paper presents a new numerical method for obtaining, without an explicit model for physical collisions in the code, a low noise three-dimensional computational equilibrium distribution. This requires both the loading of particles into an idealized distribution and the relaxation from that distribution toward an approximate numerical equilibrium. The equilibrium can then be modified through a slow change of system parameters, to generate other equilibria. In the present, work we apply this method to a UC Berkeley experiment on electron confinement in magnetic geometries appropriate for the ALPHA anti-hydrogen experiment, using the three-dimensional particle-in-cell code WARP. WARP’s guiding center mover and its option to switch between different solvers during a simulation are highly valuable because they speed up the simulations; they enable the practical use of the new technique for generating numerical equilibrium states of trapped non-neutral plasmas.