Electrostatics of Gapped and Finite Surface Electrodes

TL;DR

This paper introduces approximate methods for calculating electric potentials of finite surface electrodes with gaps and substrate effects, demonstrating that these factors minimally impact ion trap frequencies, thus validating common simplifying assumptions.

Contribution

It provides new approximate computational techniques for surface electrode electrostatics, including effects of gaps, thickness, and substrates, with practical validation.

Findings

Gaps and finite electrode size reduce trap frequencies by less than 5%.

Approximate methods effectively model electrostatics of complex electrode geometries.

Neglecting gaps and finite size is justified in realistic scenarios.

Abstract

We present approximate methods for calculating the three-dimensional electric potentials of finite surface electrodes including gaps between electrodes, and estimate the effects of finite electrode thickness and an underlying dielectric substrate. As an example we optimize a radio-frequency surface-electrode ring ion trap, and find that each of these factors reduces the trapping secular frequencies by less than 5% in realistic situations. This small magnitude validates the usual assumption of neglecting the influences of gaps between electrodes and finite electrode extent.