Non-Contact Friction for Ion-Surface Interactions

TL;DR

This paper investigates non-contact friction forces in ion-surface interactions, proposing an experimental setup to measure energy loss due to these forces, mediated by virtual quanta and influenced by dielectric properties.

Contribution

It introduces a novel experimental design to isolate non-contact friction effects in ion-surface interactions and provides theoretical calculations for energy loss in various materials.

Findings

Energy loss due to non-contact friction is quantified for helium ions.

The proposed setup minimizes image charge interaction effects.

Theoretical models involve advanced mathematical functions like Gamma and Hurwitz zeta.

Abstract

Non-contact friction forces are exerted on physical systems through dissipative processes, when the two systems are not in physical contact with each other, or, in quantum mechanical terms, when the overlap of their wave functions is negligible. Non-contact friction is mediated by the exchange of virtual quanta, with the additional requirement that the scattering process needs to have an inelastic component. For finite-temperature ion-surface interactions, the friction is essentially caused by Ohmic resistance due to the motion of the image charge moving in a dielectric material. A conceivable experiment is difficult because the friction force needs to be isolated from the interaction with the image charge, which significantly distorts the ion's flight path. We propose an experimental setup which is designed to minimize the influence of the image charge interaction though a compensation mechanism, and evaluate the energy loss due to non-contact friction for helium ions (He+) interacting with gold, vanadium, titanium and graphite surfaces. Interactions with the infinite series of mirror charges in the plates are summed in terms of the logarithmic derivatives of the Gamma function, and of the Hurwitz zeta function.