Analysis of cathode-spot behavior in high-pressure discharge lamps.

Abstract

The operation of hot cathodes in high pressure discharge lamps has been investigated in a manner similar to that described by Ecker5). The formalism of Dyke and Dolan8) has been used to calculated emission of electrons from the cathode as a function of temperature and electric field. The electric field at the cathode surface is calculated from ion current and cathode fall, the largest contribution to that field being developed in the free-fall sheath less than one mean free path in thickness at the cathode surface. Two solutions to the coupled system of equations are found: a low-field, diffuse-mode solution in which electron emission is by the Shottky-amplified thermionic process, cathode fall increases with increasing current density, and the cathode spot tends to expand to fill the entire extent of the cathode tip; and a high field, hot-spot mode in which electrons are emitted as a result of the temperature-field mechanism. The lowest cathode fall in the latter mode occurs when the potential drop across the free fall sheath equals the cathode fall required by the cathode energy balance. The operating mode of the discharge in a given lamp depends on which of the two modes has the lowest cathode fall. Examples of each occur in various lamps and can be accounted for with reasonable values of material constants. It is shown that the hot-spot mode is favored over the diffuse mode by high pressures and low cathode work function. The latter surprising result is accounted for by the fact that field emission, varying as exp (-φ3/2), is even more favored by low work function than thermionic emission.