Relativistic magnetic lensing of electron beams using superconducting spheres

In this paper, the theoretical design of magnetic electron lens made of macroscopic superconducting spheres in rotation is proposed. The relativistic quantum behavior of an electron in the magnetic field induced by rotating bulk superconductors is described based on the Dirac equation, and electron beam transport is manifested in specific cases. Based on this approach, the focal length of magnetic electron lens made of macroscopic superconductors is theoretically calculated. Subsequently, the characterization of relativistic electron beam manipulating capability of newly designed magnetic electron lens is carried out by variation of the system parameters. Owing to the ability to focus the relativistic electron beam in versatile and precise manner, this approach offers a new way to study a macroscopic system of superconductors based on special relativity, and it sets a milestone in the construction of a new generation of magnetic electron lenses with superconducting spheres. The model is inherited and developed based on previous calculations of the field induced by spherical and cylindrical superconductors (L.B. Holdeman, NASA TR R-443 (1975); R.G. Rystephanick, Can. J. Phys. 51 (1973) 789?794) and the quantum theory of electron propagation through an electron lens (R. Jagannathan, Phys. Rev. A 42 (1990) 6674).