The electrostatic potential distribution of crossed-field systems

The research and simulation of crossed-field systems of both classical and inverted construction require together the solution of motion equation, equation of excitation and Poisson´s equation. In many problems of vacuum electronics it is necessary to define the distribution of electrostatic potential between electrodes. On the first stage of theoretical research of physical processes we must define the initial and boundary conditions which have an influence on device operation. One of such conditions is the distribution of electrostatic potential in interaction space. Using the Laplace equation solution, and defining unknown coefficients by Fourier methods, it is possible to find electrostatic potential distribution in systems with complex electrode configurations. The offered method may be used to define initial conditions before the simulation such important systems as crossed-field systems.