Differential algebraic method for arbitrary-order aberration analysis of electron deflection systems

The differential algebraic method for arbitrary-order aberration analysis of electron deflection system is studied, including principles, expression of deflection fields, classification of coefficients, etc. For magnetic deflection system, a symbolic manipulation program is developed in Mathematics to derive expressions of U and H to arbitrary high order. By this program, the series expressions of magnetic field-strength H for aberration analysis up to 7th order are derived. For the pure deflection system, number of aberration coefficients from the 3rd order to the 7th order is given, and the expressions of the fifth order pure deflection aberrations from the resulting coefficients of differential algebraic method are presented. As an example, aberration up to seventh order for a saddle-coil magnetic deflection system are calculated by using the DA method. The patterns of all the pure deflection aberrations and mixed imaging-deflection aberrations of the 5th order and the 7th order are given.