A comparative study of the stigmatic properties of the electrostatic quadrupole triplet and doublet lenses with equal overall geometrical dimensions

The present research provides a comparative study of the performance of the electrostatic quadrupole doublet lens (EQDL) and the electrostatic quadrupole triplet lens (EQTL)with the same overall geometrical dimensions and occupying the same physical volume, in order to provide a greater understanding of how the two lenses operate under the same operation conditions (the initial half-angle (α) and the kinetic energy of the electron beam, and the position of the electron source and the image plane), thus helping designers choose the appropriate type for their system that gives higher performance without any increase in the system dimensions. The performance will be evaluated by calculating the focusing capability and identifying it through studying the beam cross-section in image plane, and the distribution of the kinetic energy at the same plane. To compare the performance of the doublet and triplet lenses, the two types of these lenses were designed with a total length of 260 mm, where this length was divided into three single electrostatic quadrupole lenses (SEQL) with an electrode length of 60 mm for the triplet type and two SEQL with an electrode length of 102.5 mm for the doublet type. The calculations were carried out for different operation conditions; various operation conditions were considered by varying the positions of the source and image plane and the initial half-angle (α) of the electron beam. The electron beam properties after leaving the lens were studied, where both the dimensions of the electron beam and the distribution of the kinetic energy at the image plane were investigated. The EQTL gives the best performance in comparison with the EQDL as shown in the results. According to the results, using the triplet lens enhanced the beam dimensions by 48, 60, and 70% for the y-direction and by 92, 38, and 59% for the z-direction