DETERMINATION OF THE MOST FAVORABLE SHAPES FORTHE CYLINDRICAL CONCAVE ELECTROSTATICQUADRUPOLE LENS

Abstract

The optimum design of electrostatic quadrupole lens of cylindrical concave electrodes is computed with the aid of transfer matrices method, where the axial field distribution and the optical properties are determined. The trajectory equation of motion in Cartesian coordinates is solved and the path of charged -particles beam traversing the axial field is determined. Then the beam trajectory along the lens axis is used to calculate the optical properties of the lens.
The optimization calculations are made to find the optimum optical properties and the design of an electrode shape of lens. The calculation procedure include determination both of electrode shape parameter and excitation, then the aberration parameters in both horizontal and vertical planes along the optical axis are computed. Both spherical and chromatic aberration coefficients are reduced via changing the geometrical shapes of electrodes by taking the different gap angles of electrode into account. The results show that the choice of the limited value of the gap angle gives us the optimum optical properties and the best values of the aberration coefficients.