Calculations of time-of-flight aberrations in practical electrostatic electron lenses using the differential algebraic method

The high order time-of-flight (TOF) aberrations in a practical electrostatic electron lens are calculated using the differential algebraic (DA) method. The electrostatic fields of the electrostatic lens, which are calculated by the FEM methods, are in the form of discrete arrays. Thus, the proposed DA method is applicable for engineering designs, and programs are written to compute up to fifth order TOF aberrations of practical electrostatic electron lenses. An example is given, and TOF aberrations up to the fifth order are calculated. It is proven that the numerical results for the electrostatic fields in the form of discrete arrays have a good accuracy compared with the theoretical solutions. The accuracy is limited only by the accuracy of the numerical computation of the fields and the numerical computation algorithms for interpolation and integration. Finally, a practical electrostatic electron lens is analysed and discussed as an example.