medium was studied numerically ([@Smolsky96]; [@Usov98]), and it was shown that electrons of the ambient medium which are reflected from the wind front are accelerated up to the mean energy of reflected protons. In this paper we study both the spectrum of electrons accelerated at the wind front and their non-thermal radiation.

A plausible model of cosmological GRBs is discussed in § 2. The main results of our numerical simulations of the interaction between a relativistic strongly magnetized wind and an ambient medium are presented in § 3. The spectrum of electrons which are accelerated at the wind front and their non-thermal radiation are considered in § 4. Finally, our main conclusions are summarized and discussed in § 5.

Relativistic strongly magnetized winds from cosmological $\gamma$-ray bursters and their non-thermal radiation: a plausible scenario {#model}
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The energy output of cosmological $\gamma$-ray bursters in $\gamma$-rays typically is $10^{51}-10^{53}$ ergs ([@Wickramasinghe93]; [@Tamblyn93]; [@Lipunov95] ) and may be as high as $3\times 10^{53}$ ergs ([@Kulkarni98]) or even more ([@Kulkarni99]). These estimates assume isotropic emission of GRBs. Such a high energetics of cosmological $\gamma$-ray bursters and a short time scale of $\gamma$-ray flux variability call for very compact objects as sources of GRBs 