The weak equivalence principle, a fundament of Einstein general relativity, states that gravitational mass and inertial mass are equal whatever the body. This equivalence principle has never been directly tested with antimatter. The GBAR experiment intends to test it by measuring the acceleration of ultra cold antihydrogens in free fall. The production of such anti-atoms requires a pulse of about 1e10 positrons in a few tens of nanoseconds. This thesis focuses on the development of a new accumulation technique of positrons in a Penning-Malmberg trap in order to create this pulse. This new method is an improvement of the accumulation technique of Oshima et al.. This technique requires a non-neutral electron plasma to cool down positrons in the trap in order to confine them. A continuous beam delivers positrons and the trapping efficiency is about 0.4%. The new method needs a positron pulsed beam and its efficiency is estimated at 80% . A part of this thesis was performed at RIKEN (Tokyo) on the trap of Oshima et al. to study the behavior of non-neutral plasmas in this type of trap and the first accumulation method. A theoretical model was developed to simulate the positron trapping efficiency. The description and the systematic study of the new accumulation technique with a pulsed positron beam are presented. They includes notably the optimization by simulation of the electromagnetic configuration of the trap and parameters of the used non-neutral plasmas.
