A novel technique for efficient production of slow positrons is propos
ed. It is based on the trapping of electroproduced relativistic positr
ons in a high field magnetic bottle. By introducing a small drift moti
on the emitted positrons are prevented from re-striking the production
target and they undergo extended radiative cooling. By adding high vo
ltage electrostatic trapping the cooling can proceed down to very smal
l transverse momenta. In the simplest version of the method the wide d
istribution of final longitudinal momenta is conserved until a dedicat
ed extraction procedure converts the trapped positrons into a quasi-co
ntinuous beam of very low energy. What comes out is a slow positron be
am with the same quality as that obtained with the standard moderation
scheme. The conversion efficiency is mound 0.01 e(+)/e(-) and beam in
tensities exceeding 10(11) e(+)/s can be obtained with a moderate lina
c average current.