Paraxial imaging electron optics and its spatial-temporal aberrations for a bi-electrode concentric spherical system with electrostatic focusing

As is known, the paraxial solutions play an important role in studying electron optical imaging system and its aberrations, but the investigation of a bi-electrode concentric spherical system with electrostatic focusing directly from paraxial electron ray equation and paraxial electron motion equation has not been done before. In this paper, we shall use the paraxial equations to study the spatial-temporal trajectories and their aberrations for a bi-electrode concentric spherical system with electrostatic focusing. In the present paper, start from the paraxial electron ray equation and paraxial electron motion equation, the paraxial spatial-temporal trajectory of moving electron emitted from the cathode has been solved for a bi-electrode concentric spherical system with electrostatic focusing. The paraxial static and dynamic imaging electron optics, as well as the paraxial spatial-temporal aberrations in this system are then discussed, the regularity of paraxial imaging optical properties has been given. The paraxial spatial aberrations, as well as the paraxial temporal aberrations with different orders, have been defined and deduced, that are classified by the order of (εz/Φac)1/2 and (εr/Φac)1/2. The same conclusions about paraxial spatial and temporal aberrations as we have done before will be given.