Relativistic theory of aberrations of electrostatic electron-optical systems

Abstract

Using the central particle method, within the framework of a unified mathematical formalism, the equations of trajectories of charged particles in electrostatic electron mirrors and lenses, including cathode lenses, are obtained, taking into account relativistic effects, with an accuracy of the third order of smallness inclusive. On the basis of the obtained equations, the conditions for the spatial focusing of beams of charged particles in such systems and their coefficients of geometric aberrations of the third order and chromatic aberrations of the second order are determined with full account for relativistic effects. By means of numerical calculations, parameters of the three-electrode electrostatic mirror of rotational symmetry, which provide conditions for simultaneous elimination of spherical and axial chromatic aberrations with allowance for relativistic effects, are determined.