Investigation of the accuracy of ion optics simulations using Kepler orbits in a spherical capacitor

Benchmark evaluations of the accuracy of Simion 3D, a finite difference ion optics package, are presented for electron motion in a spherical capacitor (SC) or ideal hemispherical deflector analyzer (HDA). The fractional errors (FE) [FE≡(simulation-exact)/exactFE≡(simulation-exact)/exact] for potential, electric field, trajectory radius and time-of-flight (TOF) are characterized in detail over a wide range of systems and include comparisons of Monte Carlo generated line shapes at the first-order focusing plane. Simple theoretical models based on a first-order perturbation treatment are provided to explain, predict, and even correct the trajectory radius and TOF errors over the central region of any HDA. Our results are summarized in tables, scaling formulas, and practical guidelines.