The project to measure the gravitational acceleration of antihydrogen atoms requires the production of a dense target of positronium atoms, the e+e- bound state with a lifetime in the triplet state of 142 ns. A large amount of "slow" positrons (energy range from eV to a few keV) is necessary. Radioactive sources based on 22Na are not intense enough. Moreover, the efficiency of the moderation process, which allows to slow down the positrons, must be taken into account .