Transfer matrices of ideal spherical condenser sectors for the Keplerian charged particle paths

The transfer matrix elements of the ideal electric field sectors created between spherical electrodes were derived for the charged particles following the Keplerian orbits. Based on the Keplerian orbit description as function of the particle energy and momentum, accounting for the initial conditions, the transfer matrix elements were determined for the particle position, angle and energy in a second order approximation. The resulted transfer matrices allow the calculation of the focusing properties of spherical electrostatic sectors operating with the Keplerian orbits intentionally or due to tuning errors.