Thermalization of199Hg ion macromotion by a light background gas in an RF quadrupole trap

The largest systematic uncertainty in the performance of atomic frequency standards using a cloud of ions stored in an rf quadrupole trap is the second-order Doppler shift which depends on ion temperature and trapping parameters. This paper presents evidence that cooling the ions by collisions with atoms of a background gas light compared to the ions results in the condensation of the ions into a cloud of almost uniform density determined by space charge versus potential well forces. In this condition the second-order Doppler shift is simple to calculate and is found to depend only on readily measured characteristics of the ion cloud. This along with already observed good signal-to-noise ratio shows that the frequency standard we have constructed using the hyperfine splitting of singly ionized¹⁹⁹Hg, with helium cooling can have an order of magnitude better performance in accuracy, stability, and reproducibility than presently available commercial cesium beam standards.