A synthesis of the Longo and Eng cathode emission models

Abstract

An <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> th power generalization of Longo's roll-off curve equation is proposed. A method for finding the exponent <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> from an experimental curve is given. Eng's model corresponds approximately to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n = 5</tex> , Good electron guns have <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> values in the 6 to 10 range. The use of n as a figure of merit for quality control is discussed. The construction for finding <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> is shown to lead to a new formula for the work function.