Prediction of Collective Characteristics for Ion Ensembles in Quadrupole Ion Traps Without Trajectory Simulations

Abstract

Fundamental aspects are presented of a two-temperature moment theory for quadrupole ion traps developed via transformation of the Boltzmann equation. Because the Boltzmann equation reflects changes to an ion distribution as a whole, the resulting general moment equation describes changes in the ensemble average for any function of ion velocity. Thus, the system of differential equations, formed from the general moment equation, can be solved directly (normally, by numerical methods) for average values of the velocity and of the effective temperature (or equivalently, center-of-mass energy), each as a function of time and position. The equations contain parameterized variables ! � a and ! � q , which are similar to those commonly used in ion trap studies, and ! � b and ! � d , which are parameterized forms of the voltages applied to the endcaps, to account for both ideal and commonly used ion trap configurations. Examples illustrate some of the capabilities of moment theory for predicting the time- and position-dependent characteristics of ion ensembles during various processes in ion traps of selected configurations.