  Particles moving in current sheets under extreme conditions, such as those in
the vicinity of pulsars or those predicted on upcoming multipetawatt laser
facilities, may be subject to significant radiation losses. We present an
analysis of particle motion in fields of a relativistic neutral
electron-positron current sheet in the case when radiative effects must be
accounted for. In the Landau-Lifshitz radiation reaction force model, when
quantum effects are negligible, an analytical solution for particle
trajectories is derived. Based on this solution, for the case when quantum
effects are significant an averaged quantum solution in the semiclassical
approach is obtained. The applicability region of the solutions is determined
and analytical trajectories are found to be in good agreement with those of
numerical simulations with account for radiative effects. Based on these
results we gain new insights into current sheet phenomena expected on upcoming
laser facilities.
