Electrostatic patch effects in Casimir force experiments performed in the sphere-plane geometry

TL;DR

This paper derives exact analytical formulas for electrostatic patch effects in sphere-plane Casimir experiments, improving accuracy over previous approximations and enabling precise quantification of patch forces.

Contribution

It provides the first exact solution for patch interaction energy and force in sphere-plane geometry, surpassing the proximity force approximation.

Findings

Derived exact formulas for patch interaction energy and force

Analyzed distance dependence of minimizing potential

Quantified patch force for specific patch layouts

Abstract

Patch potentials arising from the polycrystalline structure of material samples may contribute significantly to measured signals in Casimir force experiments. Most of these experiments are performed in the sphere-plane geometry, yet, up to now all analysis of patch effects has been taken into account using the proximity force approximation which, in essence, treats the sphere as a plane. In this paper we present the exact solution for the electrostatic patch interaction energy in the sphere- plane geometry, and derive exact analytical formulas for the electrostatic patch force and minimizing potential. We perform numerical simulations to analyze the distance dependence of the minimizing potential as a function of patch size, and quantify the sphere-plane patch force for a particular patch layout. Once the patch potentials on both surfaces are measured by dedicated experiments our formulas can be used to exactly quantify the sphere-plane patch force in the particular experimental situation.