High Dispersive Electrostatic Mirrors of Rotational Symmetry with the Third Order Time-of-Flight Focusing by Energy

Abstract

Expressions describing the time of flight of charged particles taking into account time-of-flight chromatic aberrations in electrostatic mirrors with rotational symmetry are presented. By numerical calculations, the conditions of time-of-flight focusing of particles by energy up to the third order inclusively in the three-electrode mirrors, the electrodes of which are coaxial cylinders of equal diameter, are determined. Various operating modes of such mirrors are considered: (1) spatial time-of-flight focusing in the Gaussian plane of the mirror; (2) spatial time-of-flight focusing in the focal plane of the mirror; (3) time-of-flight focusing in the telescopic mode; (4) time-of-flight focusing in the collimator mode. The results of calculations are presented as a function of two fundamental solutions to the equation of paraxial trajectories. One of these solutions describes trajectories whose direct and reverse branches coincide, and the second solution describes trajectories whose direct and reverse branches are symmetric with respect to the axis of symmetry of the field. It is shown that for all modes of operation the time-of-flight dispersion of the mirror by mass, determined on the basis of the second solution, is several times higher than that obtained on the basis of the first solution.