Tutorial and comprehensive computational study of acceptance and transmission of sinusoidal and digital ion guides

A quadrupoles acceptance is a measure of its ability to catch ions with certain trajectories. One way to calculate acceptance is the method of ellipses. The method arose partly from a simplification that trajectories could be calculated for an electrode axis independently of others. It has been used to calculate the acceptance and transmission of sine-driven quadrupole mass filters for over 50 years. Although the method is straightforward, it is generally described with little detail or presented as a confusing string of equations. As such, it may not be decipherable by all practitioners. For this reason, the first half of this paper presents a practical explanation of the method of ellipses and the concepts that make it work. Only equations necessary to describe the method are introduced. The tutorial also prepares the reader for the second half, which presents an alternative approach for calculating acceptance based on an array of initial trajectories. The alternative approach is used to compare the acceptance of simplified sinusoidal and digital ion guides. The method of ellipses was applied to validate results of the new approach for calculation of acceptance.