Study on axially symmetric aperture lenses with extension of an inhomogeneous electric field

We analyzed a compact lens by using a modified analytical theory and three-dimensional particle-in-cell simulations. In a compact lens, in which the thin lens and paraxial trajectory approximations are not acceptable, an inhomogeneous electric field can be extended to the entire region of the object and the image spaces. Computer simulations of the current density and the electron beam temperature, quantities which cannot be estimated by the analytical theory, show that an aperture lens utilizing the extended inhomogeneous electric field can possibly be used to provide a vacuum microelectronic device with a high-current-density focused electron beam of several hundred amperes per square centimeter.