Design of the Most Favorable Shapes for the Spherical Electrostatic Quadrupole Lens

Using transfer matrices method, a computation has been carried out on the axial field distribution and the optical properties of the spherical electrostatic quadrupole lens. The path of charged- particles beam traversing the field model has been determined by solving the tTaj ectory equation of motion in Cartesian coordin tes. The optical properties of the lens have . been computed with the aid ofthe beam trajectory along the lens axis. Optimization calculations have been conducted to determine the most favorable optical properties and the design specifications of an electrode shape of lens. The computations have been mainly concentrated on determining the electrode shape parameter, excitation, magnification and aberration parameters in both horizontal and vertical planes of the trajectory along the optical ax is. The optimization calculations are made to find the optimum values of spherical and chromatic aberration coefficients by changing the geometrical shape of electrodes via taking the different gap angles of electrode into account. Results show that the choice of the selected range of geometrical dimensions such as the range of gap angle or electrode radius to aperture radius ratio give us the optimum optical properties and the best values of aberration coefficients .