Study on differential algebraic aberration method for electrostatic electron lenses

Differential algebraic method is a powerful technique in computer numerical analysis. It presents a straightforward method for computing arbitrary ord er derivatives of functions with extreme high accuracy limited only by the machine error. When applied to nonlinear dynamics systems, the arbitrary hi gh order transfer properties of the system can be derived directly. In this paper, the principle of differential algebraic method is applied to calcul ate high order aberrations, of electrostatic electron lenses. Gaussian prop erties and third order geometric aberration coefficients of an electrostati c lens with analytical expressions have been calculated. Relative errors of the Gaussian properties and spherical aberration coefficient of the lens c ompared with the analytic solutions are of the order 10(-11) or smaller. It is proved that differential algebraic aberration method is very helpful fo r high order aberration analysis and computation of electrostatic electron lenses.