We examine, theoretically, the feasibility of producing a sample of co
ld (less-than-or-equal-to 4 K), high-denSity (almost-equal-to 10(10)/c
m3) positrons in a Penning trap. We assume Be-9+ ions are first loaded
into the trap and laser-cooled to approximately 10 mK where they form
a uniform density column centered on the trap axis. Positrons from a
moderator are then injected into the trap along the direction of the m
agnetic field through an aperture in one endcap of the trap so that th
ey intersect the Be-9+ column. Positron/Be-9+ Coulomb collisions extra
ct axial energy from the positrons and prevent them from escaping back
out the entrance aperture. Cooling provided by cyclotron radiation an
d sympathetic cooling with the laser-cooled Be-9+ ions causes the posi
trons to eventually coalesce into a cold column along the trap axis. W
e present estimates of the efficiency for capture of the positrons and
estimates of densities and temperatures of the resulting positron col
umn. Positrons trapped in this way may be interesting as a source for
antihydrogen production, as an example of a quantum plasma, and as a p
ossible means to produce a bright beam of positrons by leaking them ou
t along the axis of the trap.