Spherical sector electrostatic analyzers for measurements of energy and angular distributions

Abstract

A method is presented for three-dimensional trajectory calculations of charged particles in a spherical sector electrostatic analyzer. The particle motion in the entrance and exit fringe fields for particular geometries is included. With the initial conditions as input (the analyzer voltages and the particle position and velocity as it enters the analyzer field), the trajectory calculation provides the following information: (1) the position of the particle as it exits the analyzer; (2) the velocity direction of the particle as it exits the analyzer; and (3) the radial extrema of the particle trajectory within the analyzer sectors. Functions (3) determine whether the particle strikes the analyzer electrodes, while functions (1) and (2) can by used for predicting the particle’s position at any point after exiting the analyzer. Functions (2), here given for the first time, are especially useful for quantifying the response of the analyzer for position-sensitive detection of narrow angular distributions. These functions can be expressed as a Taylor series expansion in five variables which are simply related to the initial conditions. The expansion coefficients are given for a commercially available electron analyzer (Comstock Inc., 129 Valley Ct., Oak Ridge, TN 39812). The utility of the approach is demonstrated for determining its focusing properties, energy response, and energy-angle response.