Particle flight times through electrostatic and magnetic sector fields and quadrupoles to second order

Abstract

The difference between the flight times of a reference particle — moving along the optic axis of some electric or magnetic optical element — and some particle moving along an arbitrary trajectory is calculated. Taken into account are all terms of first and second order in the small quantities χ, α, γ, δ, γ and β. The results are presented in the form of transfer matrices including mass and energy dispersion so as to match magnetic and electrostatic fields.