We have simulated the trapping and cooling of moderated positrons in a Penning trap in which the positrons lose energy through collisions with a simultaneously stored laser-cooled ${}^9{\mathrm{Be}}^{+}$ plasma. Once the positrons are trapped, they cool through sympathetic cooling with the ${}^9{\mathrm{Be}}^{+}$ plasma. After the positrons cool, their motion parallel to the magnetic field reaches a state of thermal equilibrium with the ${}^9{\mathrm{Be}}^{+}$ ions and they rotate about the trap axis at the same frequency as the ${}^9{\mathrm{Be}}^{+}$ 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 techniques, indicates a capture efficiency of as high as $0.3\%$ for 300 K moderated positrons passing through a ${}^9{\mathrm{Be}}^{+}$ plasma with a density of ${10}^{10}$ atoms ${\mathrm{cm}}^{-3}$ and a column length of 1 cm. This capture efficiency leads to the positron capture rate of $\sim 1000$ positrons per second, assuming a 100 mCi positron source and ${10}^{-3}$ for the efficiency for moderating positrons from the source. The resulting dense reservoirs of cold positrons may be useful for antihydrogen production and for reaching a plasma state in which the mode dynamics must be treated quantum mechanically.

• Received 13 January 2000

DOI:https://doi.org/10.1103/PhysRevA.62.023405