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

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 00, 250, and 500 agree well with laboratory measurements for a 900 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