Monte Carlo simulations of slow positron production via energetic electron interaction with a solid target have been performed. The aim of the simulations was to determine the expected slow positron beam intensity from a low-energy, high-current electron accelerator. By simulating (a) the fast positron production from a tantalum electron-positron converter and (b) the positron depth deposition profile in a tungsten moderator, the slow positron production probability per incident electron was estimated. Normalizing the calculated result to the measured slow positron yield at the present AIST linear accelerator, the expected slow positron yield as a function of energy was determined. For an electron beam energy of 5 MeV (10 MeV) and current 240 mu A (30 mu A), production of a slow positron beam of intensity 5 x 10(6) s(-1) is predicted. The simulation also calculates the average energy deposited in the converter per electron, allowing an estimate of the beam heating at a given electron energy and current. For low-energy, high-current operation the maximum obtainable positron beam intensity will be limited by this beam heating. (C) 2011 American Institute of Physics. [doi:10.1063/1.3599156]