A different algebraic method for the fifth-order combined geometric–chromatic aberrations of practical magnetic electron lenses

In this paper, differential algebraic (DA) method is applied to fifth-order combined geometric–chromatic aberrations of practical magnetic electron lenses. The magnetic fields of magnetic electron lenses, which are computed by FEM or FDM method, are in the form of discrete arrays. Thus the developed new DA method is applicable to engineering design and programs were written for computing the fifth-order combined geometric–chromatic aberrations of practical magnetic electron lenses. An example is given. The combined geometric–chromatic aberrations up to fifth order are calculated. It is proved that the numerical results for the magnetic fields in the form of discrete arrays have good accuracy compared with the results computed by using the magnetic fields expressed in analytical form. The accuracy is limited only by the accuracy of the numerical computation of the fields and the arithmetic errors. Finally, a practical magnetic electron lens is analyzed and discussed as an example.