Differential algebraic theory and calculation for arbitrary high order aberrations of a bipotential electrostatic lens

摘要

Differential algebraic method is a powerful technique in computer numerical analysis based on nonstandard analysis and formal series theory. It can compute arbitrary high order derivatives with excellent accuracy. When applied to nonlinear dynamics systems, the arbitrary high order transfer properties of the system can be derived directly. In this article, the principle of differential algebraic method is applied to calculate high order aberrations of a bipotential electrostatic electron lens. All the third order geometric aberration coefficients of the bipotential electrostatic lens have been calculated. The patterns of the third order aberrations and the fifth order aberrations are also given, and some types of the fifth order aberrations are observed.