A synthesis of the Longo and Eng cathode emission models

An<tex>n</tex>th power generalization of Longo's roll-off curve equation is proposed. A method for finding the exponent<tex>n</tex>from an experimental curve is given. Eng's model corresponds approximately to<tex>n = 5</tex>, Good electron guns have<tex>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>n</tex>is shown to lead to a new formula for the work function.