\rm{ergs}}}\right)^{1/3}\left({\frac n{1\,\rm{cm}^{-3}}}\right)^{-1/3}\left(
{\frac{\Gamma_0}{10^2}}\right)^{-2/3}\rm{cm},
\label{rdec}$$

at which deceleration of the wind due to its interaction with an ambient medium becomes important ([@Rees92]), where $n$ is the density of the ambient medium and $Q_{\rm{kin}}$ is the kinetic energy of the outflowing wind, $Q_{\rm{kin}}
\leq Q_{\rm rot}\leq Q^{\rm max}_{\rm rot}$ . Substituting $r_{\rm{dec}}$ for $r$ into equation (\[Bobj\]), we have the following estimate for the magnetic field at the wind front at $r\sim r_{\rm {dec}}$:

$$B_{\rm{dec}}\simeq 2\times 10^4\left(\frac{B_s}{10^{16}\,\rm{G}}\right)\left(
\frac\Omega{10^4\,\rm{s}^{-1}}\right)^2\left(
\frac{Q_{\rm{kin}}}{10^{52}\,\rm{ergs}}\right)^{-1/3}\left(\frac
n{1\,\rm{cm}^{-3}}\right)^{1/3}\left({\frac{\Gamma_0}{10^2}}\right)
^{2/3}\rm{G}\,,
\label{Bdec}$$

For typical parameters of cosmological $\gamma$-ray bursters, $B_{_S}
\simeq 10^{16}$ G, $\Omega\simeq 10^4$ s$^{-1}$, $Q_{\rm{kin}}\simeq
10^{52}-10^{53}$ ergs and $\Gamma_0\simeq 10^2-10^3$, if the ambient medium is an ordinary interstellar gas, $n\sim 1
-10^2$ cm $^{-3}$, from equation (\[Bdec\]) we have $B_{\rm{dec}}\simeq 10^4- 4\times 10^5$ G.

It is suggested by Mészáros and Rees (1992) that in the process of the wind – ambient medium interaction at $r\sim r_{\rm{dec}}$, an essential part of the wind energy may be transferred to high-energy electrons and then to high-frequency (X-ray and $\gamma$-ray) emission. This suggestion is confirmed by our numerical simulations (see [@Smolsky96]; [@Usov98] and below). Hence, in our scenario in a general case, when the rotational axis and the magnetic axis are not aligned $(\vartheta 