MODELING OF BARIUM TRANSPORT IN DISPENSER CATHODES

A theoretical modelling of the barium transport in dispenser cathodes has been developed from the general considerations of diffusion as wel l as the fundamental nature of the barium surface migration. Realistic second-order kinetics for the barium desorption has been employed. Th e diffusion of barium from the generating to the emitting sites of the cathode has been considered to be comprised of two independent proces ses, viz., (i) the bulk diffusion to the pore ends on the surface, and (ii) the subsequent surface diffusion/migration. The solution of the first process has been obtained using an approximate analytical method (the integral method), whereas the second process leads to an analyti cal solution. Time-dependent profiles of barium concentration versus d istance from the source (the edge of the pore) were obtained at the ca thode operating temperature (approximately 1300 K) of a type-B cathode . Consequent to the barium evolution on the surface, the increase in t ime-dependent pore depth has been considered in determining the barium surface source location. The variable source strength (content) of th e barium has been incorporated into the problem by means of the bounda ry condition. The results are presented, and a method of estimation of the ideal life of the cathode is presented.