Model calculations of the electron-optical properties of compact Faraday cups

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Abstract
Calculations are made of compact model Faraday cups comprising an earthed outer box with a small aperture surrounding an inner box, coated internally with graphite, which may be positively biased. The trajectories of incident electrons of positive ions are calculated for a range of energy-to-bias ratios to define the change in effective cup aperture as a function of the bias or energy value. The effect of the bias is then calculated to determine the number of generated secondary electrons that may escape from the cup. These calculations define the cup efficiency for four types of measurement: electron beam currents; electron beam current densities; positive ion beam currents; and positive ion beam current densities. Traditional criteria, developed for measuring electron beam currents, are shown not to be valid for the other three categories. General design rules are evaluated separately for all four types of measurement in compact Faraday cups.