Thermionically electron emitting matrix cathodes for magnetohydrodynamic generators: analytical model

Current and voltage drop calculations have been made for matrix cathodes having a number of sharp pins projecting out from its surface in open-cycle magnetohydrodynamic plasmas. It is assumed that from the cathode surface to the cathode sheath edge, the current flows in current tubes formed around the projected pins. The effect of high electric field on the work function of the tip has been taken into account and calculations are made for a variable number of tips and tip area. Work functions of the tip and the slant surface are taken to be different. The current and voltage characteristics have been obtained by solving the current continuity and Poisson’s equations in spherical coordinate geometry. It is observed that the current increases with an increase in the number of pins per unit area and tip area. The theoretical results have been compared with the experimental observations.