The Gravitational Behaviour of Antimatter at Rest experiment (GBAR) is designed to perform a direct measurement of the weak equivalence principle on antimatter by measuring the acceleration of anti-hydrogen atoms in the gravitational field of the Earth. The experimental scheme requires a high density positronium (Ps) cloud as a target for antiprotons, provided by the Antiproton Decelerator (AD) - Extra Low Energy Antiproton Ring (ELENA) facility at CERN. The Ps target will be produced by a pulse of few 10(10) positrons injected onto a positron-positronium converter. For this purpose, a slow positron source using an electron Linac has been constructed at Saclay. The present flux is comparable with that of Na-22-based sources using solid neon moderator. A new positron accumulation scheme with a Penning-Malmberg trap has been proposed taking advantage of the pulsed time structure of the beam. In the trap, the positrons are cooled by interaction with a dense electron plasma. The overall trapping efficiency has been estimated to be similar to 70% by numerical simulations.