Three-dimensional trap with excitation of ion oscillations at the stability boundary of the Mathieu diagram

Vibrations of charged particles in compositions of three-dimensional high-frequency quadrupole and static homogeneous electric fields in the stable region and in the vicinity of the stability boundary of the Mathieu diagram are investigated. Using a pseudopotential model of a rapidly oscillating field, it is shown that the motion of charged particles during linear scanning of a secular frequency is described by the Airy differential equation. Based on the properties of solutions of the Airy equation, a method of ion mass separation with resonant excitation of oscillations at the stability boundary of the Mathieu diagram has been developed. To implement the method, the ion-optical system of the three-dimensional trap is supplemented with corrective electrodes. Computer modeling has determined the optimal potentials of the correcting electrodes, at which the errors of the distributions of quadrupole and homogeneous fields do not exceed 10$^{-4}$ and 2$\cdot$10$^{-3}$.