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A 2004MeV proton storage ring has been constructed at Fermilab for studying techniques for increasing the phase-space density of the protons by using electron cooling or stochastic cooling. The experiments performed on these complementary types of cooling systems over the past year have reinforced the design of an antiproton collection system using both methods of cooling. Antiprotons from a target bombarded by 80-GeV protons are collected in a storage ring at 4.5 GeV and stochastically cooled in a stepwise deceleration scheme to achieve a momentum-spread reduction of a factor of about 250 in about 9 seconds. The antiprotons are then transferred to a lower-energy electron cooling ring for further cooling and accumulation. This system, using the virtues of both stochastic and electron cooling, will allow the accumulation of enough antiprotons in a few hours to give luminosities of 1030 cm-2 sec-l for collisions between protons and antiprotons at about 2-TeV center-of-mass energy in the Fermilab Tevatron.