Mathematical simulation of a 2D diode system with a blade-shaped field emitter

The electrostatic potential distribution in a 2D diode system with a blade-shaped field emitter on a flat substrate has been calculated. The anode of the system represents a plane that is parallel to the substrate. In calculating the potential distribution, the influence of the emitter is replaced by the influence of a charged filament, so that the emitting surface serves as a zero equipotential. The boundary-value problem has been solved by the method of separation of variables in Cartesian coordinates. All geometrical dimensions are the parameters of the problem.