We have simulated the trapping and cooling of moderated positrons in a Penn
ing trap in which the positrons lose energy through collisions with a simul
taneously stored laser-cooled Be-9(+) plasma. Once the positrons are trappe
d, they cool through sympathetic cooling with the Be-9(+) plasma After the
positrons cool, their motion parallel to the magnetic field reaches a state
of thermal equilibrium with the Be-9(+) ions and they rotate about the tra
p axis at the same frequency as the Be-9(+) ions. Therefore, a centrifugal
separation will occur, forcing the positrons to coalesce into a cold column
along the trap axis. A simulation which, in part, utilizes Monte Carlo tec
hniques, indicates a capture efficiency of as high as 0.3% for 300 K modera
ted positrons passing through a Be-9(+) plasma with a density of 10(10) ato
ms cm(-3) and a column length of 1 cm. This capture efficiency leads to the
positron capture rate of similar to 1000 positrons per second, assuming a
100 mCi positron source and 10(-3) for the efficiency far moderating positr
ons from the source. The resulting dense reservoirs of cold positrons may b
e useful for antihydrogen production and for reaching a plasma state in whi
ch the mode dynamics must be treated quantum mechanically.