Blade-like field cathode with a dielectric coating mathematical modeling

In this paper the results of a two-dimensional diode emission system based on a blade-like field cathode in a polar coordinate system modeling is presented. The top of the emitter is a circle with a dielectric coating. The anode is a circle coaxial to the top of the emitter. The boundary condition of the first kind is set on the cathode, and the first and second kind on the anode. The problem of calculating the electrostatic potential distribution is reduced to solving a system of linear algebraic equations with constant coefficients. All the geometric dimensions of the system and the values of the potentials on the electrodes are the parameters of the problem.