  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.
