Effects of a long entrance aperture upon the azimuthal response of spherical section electrostatic analyzers

Abstract

The transmission characteristics of spherical section electrostatic analyzers with long entrance apertures have been studied. The presence of a long entrance aperture appreciably broadens the normally narrow azimuthal response of such analyzers at large incident polar angles. A technique for calculating the transmission at any polar angle is presented. Calculated azimuthal response curves at polar angles of 0 degrees , 25 degrees , and 50 degrees agree well with laboratory measurements for a 90 degrees section analyzer. In the limit of zero polar angle, our calculations reveal that a previously derived and widely used analytical expression for the integrated energy-angle response underestimates that response by 12%-25% depending upon the analyzer bending angle. An analytical expression that better approximates the true response is presented.