A theoretical investigation is carried out by using an analytical expression for paraxial trajectory of an electron in a magnetic lens to estimate the optimum properties of the magnetic lens.The aberration coefficients of the magnetic lens are studied, such as the spherical, chromatic, radial distortion and spiral distortion aberration coefficients. The Glaser's bell-shaped model is adopted to represent the axial field distribution of magnetic lens. The initial momentum of the electrons is taken into account, where the calculations are made for two cases: when the electrons have zero and non-zero initial momentum values . The optimization role is achieved by changes some of the effective parameters at the range of the half-width at half maximum (a = 2.01, 2.02, 2.03 and 2.04 mm), the maximum magnetic flux density (Bm = 0.001, 0.002, 0.003 and 0.004 Tesla) and the electron emission angle (θ = 0.2, 0.4, 0.5 and 0.6 rad). In the present results the optimum values for both cases of the initial momentum is found at the half-width at half maximum equal to 2.04 mm, and the values of the spherical, chromatic and spiral distortion aberration coefficients decreased as the half-width at half maximum (a) increased, while the minimum values of the spherical and radial distortion aberration coefficients are found at Bm = 0.004 Tesla in the first case.However the best angle is found at θ = 0.2 rad which is directly proportional which chromatic and spiral distortion aberration coefficients.On the other hand the calculations appeared that the negative values for both spherical and radial distortion aberration coefficients are estimated and these coefficients can be used as corrector in the optical systems.
