In the present study, an aberration theory for both wide and narrow electron beams in a combined electromagnetic focusing spherical cathode lens system is discussed. The general formulae of aberration coefficients for first and third order transversal geometrical and chromatic aberrations on any ideal image plane have been derived under following conditions, i.e., when the objective and image fields have finite curvatures and when the cathode is immersed in magnetic and transversal electric fields. Based on the variational analysis method and the trajectory calculation method, the relationship between the wide electron beam slstem and the narrow electron beam system has been considered in detail. It has been shown that these two different electron beam systems can be treated equally and their aberration equations and coefficients can be expressed in a universal form, if one considers the definite energy and angular initial distributions and utilizes the first order linear trajectory equation. In the present paper, electron frajectories are described in the vector form. The aberrations are expressed in the matrix form and are thus appropariate for computer calculations.
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