Automatic differentiation method for aberration analysis of deflection systems of charged particle beam

Based on Automatic Differentiation (AD), a new technique in computer numerical analysis, a new method for aberration analysis of charged particle optical systems was studied. The AD representations for Gaussian properties and third-order geometric aberrations of deflection system are obtained. A package with AD technique inside and including functions for numerical calculation of charged particle optics was developed in Visual C++ language with the advantage of Object Oriented Programming technique. The Gaussian properties and third order aberrations of saddle-coil magnetic deflector were calculated. The results are of extrahigh accuracy while relative errors of the Gaussian properties are on the scale of 10-13 or smaller. It is concluded that AD method is a rather effective tool for the aberration analysis of charged particle optical systems