Theory and calculation of electrostatic electron mirrors with allowance for relativistic effects

Trajectory equations of charged particles are derived using the central particle method with an accuracy of up to quantities of the third order of smallness inclusive in an axisymmetric electrostatic mirror with allowance for relativistic effects. Conditions for spatial focusing and coefficients of spatial aberrations are determined in the Gaussian image plane of the mirror with allowance for relativistic effects. Numerical calculations are used to determine conditions for simultaneous elimination of the spherical and axial chromatic aberrations with allowance for relativistic effects in the axisymmetric electrostatic mirror when the object plane of the mirror is matched with the focal plane. It is shown that the Gaussian image plane is displaced and focusing quality is changed when high velocities of particles are taken into account.