Analytical calculation of the space charge potential and the temperature of stored ions in an rf quadrupole trap

摘要: The use of a stored ion cloud in an rf quadrupole trap has shown its possibilities as high-performance frequency standard. most important source systematic error such standard is the second-order Doppler shift, effect special relativity, which produces relative shift approximated by ratio mean kinetic energy to rest mass ion. Assuming that can be characterized temperatureT, determination ofT paramount importance evaluating shift. In this paper, analytical expression ion-cloud temperature established taking space-charge effects into account and involving only physical parameters easily measured. validity approximate discussed it compared numerically results published elsewhere.