the BATSE range. Before considering high-frequency radiation from the region ahead of the wind front, we discuss briefly some general properties of radiation of high-energy electrons in the fields of electromagnetic waves.

LAEMWs and synchro-Compton radiation of electrons
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The motion of electrons and their radiation in the fields of electromagnetic waves is characterized by the following dimensionless Lorentz-invariant parameter (e.g., [@BT74]):

$$\eta ={e B_w\over m_ec\omega}\,,
\label{eta}$$

where $ B_w$ is the amplitude of the waves and $\omega$ is their frequency. At $\eta \ll 1$, electrons radiate via Compton scattering. In this case, the typical energy of photons $\langle{\varepsilon}_c\rangle$ after scattering depends on the wave frequency, $\langle{\varepsilon}_c\rangle\propto \omega \Gamma_e^2$, and does not depend on the wave amplitude (e.g., [@BT74]).

Electromagnetic waves with $\eta \gg 1$ are called large-amplitude electromagnetic waves (LAEMWs). Radiation of electrons in the fields of LAEMWs is called synchro–Compton radiation. In the most simple case which is interesting for us (see below) when the bulk of radiating electrons has such a high velocity $v_\perp=c\sin \psi$ transverse to the wave vector that

$$(v_\perp /c)\Gamma_e = \Gamma_e\sin\psi \gtrsim \eta\,,
\label{psi}$$

synchro–Compton radiation of these electrons closely resembles synchrotron radiation ([@BT74]), where $\psi$ is the angle between the electron velocity 