should be helical (e.g., [@Coroniti90]). This is because the magnetic flux originates in a single polar cap. Near the rotational equator, the toroidal magnetic field of the wind should be striped and alternates in polarity on a scalelength of $\pi (c/\Omega )\sim 10^7$ cm. These magnetic stripes are separated by thin current sheets $(J_\theta)$. Off the equator, the magnetic flux in the toward and away stripes is unequal if $\vartheta\neq  \pi/ 2$. In other words, in the striped region, the wind field is a superposition of a pure helical field and a pure striped field with nearly equal magnetic fluxes in adjacent stripes.

Since the luminosity of a $\gamma$-ray burster in a relativistic magnetized wind drops in time, $L_{_P} 
\propto t^{-\beta}$, the wind structure at the moment $t\gg\tau_{_\Omega}$ is similar to a shell with the radius $r\simeq ct$, where $\beta$ is a numerical index, $1\leq \beta\leq 2$, and $\tau_{_\Omega}\sim 10^{-2}-10^2$ s is the characteristic time of deceleration of the compact object rotation due to the action of the electromagnetic torque and the torque related to generation of gravitational radiation ([@Usov92]; [@Yi98]). The thickness of the shell is $\sim c\tau_{_\Omega}$.

The strength of the magnetic field at the front of the 