The electrostatic quadrupole lens mathematical modeling

In this paper a mathematical model of the electrostatic quadrupole lens is presented. The quadrupole lens consist of four equiform electrodes of an infinite length and each of these electrodes is a part of the circular cylinder. The variable separation method is used to solve the boundary-value problem for the Laplace equation in plane polar coordinates. The solution of initial value-boundary problem is reduced to the solution of linear algebraic equations system. The electrostatic potential distribution is calculated for the whole region of the system.