  Strongly magnetized and fast rotating neutron stars are known to be efficient
particle accelerators within their magnetosphere and wind. They are suspected
to accelerate leptons, protons and maybe ions to extreme relativistic regimes
where the radiation reaction significantly feeds back to their motion. In the
vicinity of neutron stars, magnetic field strengths are close to the critical
value of $B_{\rm c} \sim 4.4\times10^9$T and particle Lorentz factors of the
order $\gamma \sim 10^9$ are expected. In this paper, we investigate the
acceleration and radiation reaction feedback in the pulsar wind zone where a
large amplitude low frequency electromagnetic wave is launched starting from
the light-cylinder. We design a semi-analytical code solving exactly the
particle equation of motion including radiation reaction in the Landau-Lifshits
approximation for a null-like electromagnetic wave of arbitrary strength
parameter and elliptical polarization. Under conventional pulsar conditions,
asymptotic Lorentz factor as high as $10^8-10^9$ are reached at large distances
from the neutron star. However, we demonstrate that in the wind zone, within
the spherical wave approximation, radiation reaction feedback remains
negligible.
