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

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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.