  Current sheets in the vicinity of pulsars or those predicted on upcoming
multipetawatt laser facilities can feature extremely high electromagnetic
fields. As a result, charged particles in such sheets may experience
significant radiation losses. We present an analysis of particle motion in
model fields of a relativistic neutral current sheet with two magnetic field
components in the case when radiative effects must be accounted for. In the
Landau-Lifshitz radiation reaction model the method of slowly changing
parameters is used to quantify the influence of radiative effects. A
quasiadiabatic invariant of dissipative motion is found. It is shown how the
presented method can be used in a wider range of problems.
