Analysis and computation of Gauss trajectory and aberration in the electrostatic-magnetic complex system

In this paper, the complex system-electrostatic lens of two equal radial cylinders superimposed with the deflection field-has been introduced. Using the principle of minimal action, the functional minimum and Euler equation have been solved. The results show properties of the Gauss trajectory and third order aberration. Aberrations include three parts, and can be expressed in matrix form. The electrons can go back to the Z axis. The aberrations can cancel out each other, and better spot performance can be obtained. When an electrostatic lens is placed near a screen, large aberrations will be produced