Propriétés des spectromètres électrostatiques à électrodes en spirale logarithmique

Abstract

A study is presented of the properties of the electrostatic deflectors involving electrodes shaped like logarithmic spirals, both from the point of view of energy analysis and electron monochromatization. The optical constants of energy dispersion, angular aberration, and magnification are determined by means of numerical integration of the differential equation describing the electron motion. The maximum luminosity at fixed resolution and normalized dimensions is used as a criterion in order to achieve the definition of optimum conditions (for the beam-entrance parameters) and a figure of merit. Then it is found that the characteristics and the predicted performances do not strongly depend on the degree of curvature of spirals, while the optimum is obtained for the 127.3° cylindrical deflector, a particular case of the spiral deflector. From symmetry considerations, it is shown that for a given curvature the characteristics do not depend on the entrance direction (inward or outward with respect to the spiral center). The space charge limitations for an electron monochromator are discussed too. Then it is suggested that a monochromator involving a strong spiral curvature and outward electron injection could deliver a current of higher intensity than the conventional cylindrical deflector for the same resolution.