Doppler effects due to thermal macromotion of ions in an rf quadrupole trap

The second-order Doppler shift is an important source of systematic error in rf quadrupole trapped ion frequency standards. This shift can be reduced by cooling the secular motion of the ion cloud with a light background gas at low pressure. Using a thermalized ion cloud model, it is possible to relate the Doppler shift to the temperature of the ion cloud. It is shown that, in practice, the measured frequency of the first-order Doppler sidebands can be used to determine the ion cloud temperature.