Construction of an electron-optical scheme for electrostatic quasi-spherical deflector-type energy analyzer

This study investigates electrostatic spherical deflector-type energy analyzers designed to analyze energy of charged particle beams. The research aims to eliminate quadratic angular aberrations characteristic of classical spherical deflector-type energy analyzers, which limit the quality of angular focusing and the energy resolution of the instruments. An electron-optical scheme of an electrostatic quasi-spherical deflector-type energy analyzer has been proposed, whose field is synthesized using a multipole approach. The electrostatic field of the energy analyzer is a superposition of an axisymmetric hexapole and a spherical field. Analytical calculations have shown that by choosing the coefficient that determines the weighting contribution of the axisymmetric hexapole, it is possible to completely compensate for second-order angular aberrations and significantly improve the focusing properties of the quasi-spherical energy analyzer. The profile of the deflecting electrodes of the energy analyzer has been determined, providing the necessary spatial distribution of the deflecting field potential to achieve the specified electron-optical parameters. Numerical simulation of the electron-optical scheme of the quasi-spherical energy analyzer and calculation of the trajectories of charged particles were carried out using the "Focus" numerical program. The electron-optical scheme of the energy analyzer implements a second-order angular focusing mode of the "axis-ring" type. The instrumental function of the scheme has been constructed. The relative energy resolution and luminosity of the energy analyzer were estimated. The numerical results show that the relative energy resolution of the energy analyzer is 1.6% at a luminosity of 17.5% of 2π, which confirms effectiveness of the proposed scheme. The proposed electron-optical scheme could be used to design real structures of new high-resolution spectrometers intended for the analysis of charged particle beams.