Theory of dipolar dc excitation and dc tomography in the rf quadrupole ion trap

Abstract

A theory of dipolar dc excitation and dc tomography in the rf quadrupole ion trap is presented. The equation of motion for ions subject to a dipolar dc field is written in the form of a Mathieu equation with time independent inhomogeneity and solved analytically. Three cases are considered explicitly: application of continuous dipolar dc fields, application of dipolar pulses for translational excitation of ion motion, and application of dipolar pulses for selective ejection of ions. The effect of monopolar pulses and nonlinear fields is investigated by simulations of ion motion. It is shown that translational excitation of ions by dipolar dc pulses has a near linear response of oscillation amplitude to the voltage of the dipolar dc pulse and is nearly mass independent for a large mass range, provided the pulse width is chosen appropriately. Formulae are given for optimum choice of pulse voltage and width. Dc tomography, a technique which probes ion motion by selective ejection of ions due to the application of short dipolar dc pulses, is shown to be a feasible method for monitoring the secular oscillation of a coherent group of ions, sensitive to even small changes in ion position.