Improved 3-D boundary charge method for high-accuracy electric field calculation

In this paper we propose an improved 3-D Boundary Charge Method for high accuracy calculation of the electric field distribution, where differentiation of the coefficient matrix element (= the potential coefficient) with respect to each coordinate component is needed. The differentiated potential coefficient, which is called the field coefficient, is expressed as a double integral. We have found that the first integral of the field coefficient can be done analytically in much the same ways as that of the potential coefficient, thereby greatly improving the computation time of the electric field distribution without any loss of accuracy. As a practical application of the method to field analysis, we have treated the misaligned diode system of a field emission gun.