Electron cooling and accumulation of 4$\times$10$^9$ positrons in a system for longterm storage of antihydrogen atoms

For antihydrogen ($\overline{\rm H}$) production, trapping and spectroscopic measurements, large numbers of positrons (e$^+$) and antiprotons are required. These antimatter particles are captured, cooled and manipulated in extremely-high vacuum within our Penning-Ioffe trap system to ensure long lifetimes before annihilation with background gas, as required for precision experiments with antimatter atoms. Our ATRAP collaboration has accumulated up to 4$\times 10^9$ positrons (e$^+$) in our Penning-Ioffe trap apparatus which can be maintained at a temperature of 1.2 K and at a pressure below 6$\times 10^{-17}$ Torr. Realizing this extremely low pressure is particularly challenging given that the Penning-Ioffe trap apparatus is continuously open to the room-temperature e$^+$ accumulator where Ne and N$_2$ gasses are used to slow and capture the e$^+$ that originate from radioactive decay of $^{22}$Na. This low temperature and vacuum pressure should allow for $\overline{\rm H}$ storage times of over 1 year, sufficient time for high-precision tests of antimatter gravity and of CPT invariance.