Abstract
The development of methods for calculating the physical and instrument characteristics of mass spectrometers based on correct physical and mathematical theories that allow us to design and calculate devices with improved analytical capabilities is an urgent task of corpuscular optics and scientific instrumentation. Currently, quadrupole electrostatic systems are widely used. These are primarily quadrupole lenses, quadrupole aberration correctors, quadrupole traps and quadrupole mass spectrometers. The quadrupole mass analyzer refers to the so-called antiresonance mass spectrometers, in which a part of the ions, when a beam of ions moves through an electric field having both a constant and a time-varying component, passes a field with a limited amplitude of vibrations, while the amplitude of vibrations of the other part of the ions increases indefinitely with time, and drop out of the bundle. Since the nature of the motion of charged particles depends on the mass-to-charge ratio, such an electric field can work as a mass filter, that is, pass through itself only ions having a certain value of the mass-to-charge ratio. Quadrupole systems with complex electrode geometries are usually used to create quadrupole fields, which makes their practical implementation difficult. Therefore, the development and research of quadrupole systems with a fairly simple geometry of electrodes, the fields of which can be described analytically, is quite relevant. Using a simple analytical formula for the potential and its derivatives, which accurately describes the electrostatic potential of a quadrupole field, it is possible to accurately calculate the stability regions of quadrupole ion traps when additional radio frequency fields are applied.