  A scenario for the enhanced laser-driven ion acceleration from a thin solid
target at high laser intensity is considered, where the target is enclosed in a
reflecting cavity. The laser pulse reflected from the target is redirected
towards the target by reflection at the inner cavity wall. This scenario is
discussed in the context of sub-wavelength foil acceleration in the radiation
pressure regime, when plasma dynamics is known to be reasonably well described
by the light-sail model. A semi-analytic formula is presented that describes
the effect of cavity reflections in one-dimensional geometry. The effect of
cavity reflections on sub-wavelength foil acceleration is then evaluated for
two concrete examples of ultra-intense laser pulses of picosecond and
femtosecond duration.
