Computation of Ion Trajectories in the Monopole Mass Spectrometer by Numerical Integration of Mathieu's Equation

A high speed digital computer used with an off-line curve plotter enabled ion trajectories to be readily obtained in terms of the initial conditions and the parameters appearing in the differential equation of motion (Mathieu's equation). A study of these trajectories has led to the conclusion that ions should not be injected parallel to the axis of the instrument, as is done at present, but through the axis and at an angle to it. A simple empirical expression enables the variation of position of ion focus with mass and operating parameters to be predicted.