Modeling the extended Schottky cathode by a boundary element method

A boundary element method has been used to analyze electron emission from an extended Schottky cathode, consisting of an infinitely long array of parallel heated wires. Space charge was ignored. It was found that the current density may be expressed by a Richardson-Duschman equation in which the argument of the exponential term is corrected by an additive factor, Q, which is a function of temperature, wire radius, wire separation, and voltage. Over the range of temperatures, wire radii, and voltages examined, Q is a nearly linear function of the square root of the applied voltage. Tentative agreement with experiment was found