Modeling of tip evolution of point cathode for numerical calculation of electric field in electron gun

The numerical modeling of the tip evolution of the point cathode has been studied to obtain a more realistic shape of the cathode and to improve the numerical calculation of the electric field in the electron gun. The modeling method is based on the numerical integration of the differential equation describing the matter transport phenomena caused by surface diffusion of atoms. The tip evolution is examined for different initial shapes and for different heating conditions, considering the influence of thermal evaporation. The method provides the characteristic profile of the cathode tip. The tip radius varies depending on the heating temperature and time. The field calculation of the Schottky emission gun shows that the modeled cathode shape gives a continuous field distribution in a wide area of the tip surface. The field distribution is compared to that on the interpolated cathode shape.