The electrostatic quadrupole lens mathematical modeling

The mathematical model of the quadrupole lens is presented. The quadrupole lens is composed of four uniform electrodes. The electrode is the part of the circular cylinder. The potentials of the electrodes are the same modulus and opposite sign for neighboring electrodes. The boundary-value problem's solution of Laplace equation for the electrostatic potential distribution is presented. The variable separation method to find the unknown coefficients for the potential distribution is used. So the initial value-boundary problem is reduced to the system of the linear algebraic equations. The potential distribution is calculated for the whole region of the system. Refs 9. Figs 3.