Calculating a multipole cylindrical electrostatic system

The results of simulations of a multipole electron-optical system has been considered. The electrodes of the system consist of an even number of identical parts of one circular cylinder that is cut parallel to the generatrix with infinite length. To determine the potential distribution, the Laplace equation has been solved by the method of variable separation in the polar coordinates. All of the geometrical dimensions of the system and the number of electrodes are parameters of the problem.