Electron cooling of positrons is the essential peculiarity of the method of
antihydrogen and positronium fluxes generation, which is based on low-ener
gy positron storage ring. The design of the positron ring equipped with an
electron cooling system is discussed. The positron beam circulates in a lon
gitudinal (quasitoroidal) magnetic field. Electron drift inside special "se
ptum" coils and toroidal sections is used for superposition and separation
of the cooling electron beam and the circulating positron one. The working
cycle of the ring is described. Peculiarities of the electron cooling of ma
gnetised positrons are discussed. The general parameters of the Low-Energy
Positron Toroidal Accumulator (LEPTA), which is under construction in the J
INR, are presented. (C) 2000 Elsevier Science B.V. All rights reserved.