Eur. Phys. J. D (2015) 69: 119
https://doi.org/10.1140/epjd/e2015-50811-7

Regular Article

Non-contact friction for ion-surface interactions

¹ Department of Physics, Missouri University of Science and Technology, Rolla, Missouri 65409, USA
² International Institute of Molecular and Cell Biology, Ksiȩcia Trojdena 4, 02-109 Warsaw, Poland
³ Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland

^a e-mail: ulj@mst.edu

Received: 11 November 2014
Received in final form: 26 January 2015
Published online: 28 April 2015

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.