VARIATIONAL THEORY OF ABERRATIONS IN CATHODE LENSES
阴极透镜象差的变分理论

In this paper, the aberration theory for cathode lenses with combined electrostatic and magnetic focusing is discussed in detail. The more general case, when cathode is situated in both magnetic and transversal electric fields, has also been considered. Based on the variational principle, we have derived the general formulae of aberration coefficients of cathode lenses on any image plane, and transformed them into the linear combination of the well-known aberration coefficients given by Glaser. It follows that the aberrations for both the wide electron beam system (cathode lens) and the narrow electron beam system (conventional electron lens) can be treated by the universal variational theory. Hence the relationship between these two systems is also established.The paraxial electron trajectories of cathode lenses are described in the vector form. The aberrations are expressed in the matrix form, and they are suitable for computer calculation.