MeV (Usov 1994a,b; Blackman et al. 1996; [@Blackman98]). A long high-energy tail of the $\gamma$-ray spectrum may exist up to $\sim 10^4$ MeV. This is consistent with the observed spectra of GRBs ([@Band93]; [@Schaefer94]; [@FM95]).

The radiative damping length for LAEMWs generated at $r\sim r_f$ is a few orders of magnitude less than $r_f$ ([@Usov94a]). Therefore, at $r\gg r_f$ LAEMWs decay almost completely, and their energy is transferred to high-energy electrons and then to X-ray and $\gamma$-ray photons. It is worth noting that when the magnetic axis is perpendicular to the rotational axis, $\vartheta = \pi /2$, the electromagnetic field of the Poynting flux–dominated wind is purely striped just as vacuum magnetic dipole waves ([@Michel71]). In this case, almost all energy of the wind is radiated in X-rays and $\gamma$-rays at $r\sim r_f$ ([@Usov94a]; [@Blackman96]; [@Blackman98]), and the total energy output in hard photons per a GRB may be as high as $Q^{\rm max}_{\rm rot}
\simeq$ a few $\times 10^{53}$ ergs.

At $r\gg r_f$ and $\vartheta \neq \pi /2$, the magnetic field is helical everywhere in the outflowing wind (see Fig. 1). Such a relativistic strongly magnetized wind expands more or less freely up to the distance

$$r_{\rm{dec}}\simeq 5\times 10^{16}\left({\frac{Q_{\rm{kin}}}{10^{52}\,
