and the wave vector of LAEMWs. Indeed, it is well known that electromagnetic radiation of relativistic electrons is concentrated in the direction of the particle’s velocity within a narrow cone of angle $\Delta \varphi\simeq 1/\Gamma_e \ll 1$ (e.g., [@Rybicki79]). For nearly transverse motion of electrons in a magnetic field $B$, the formation length of radiation is about $\Delta l \simeq 2 R_{Be}\Delta \varphi\simeq 
2m_ec^2/eB$, where $R_{Be}=m_ec^2\Gamma_e/eB$ is the electron gyroradius. For synchro–Compton radiation, $\eta\gg 1$, the formation length is much smaller than the wavelength, $\lambda =2\pi c/\omega$, of LAEMWs :

$$\Delta l\simeq \left({m_ec \omega \over \pi eB}\right)\lambda 
\simeq {\lambda \over \pi\eta} \ll \lambda\,,
\label{Deltal}$$

and the electromagnetic fields of LAEMWs may be considered as homogeneous and static. Therefore, synchro–Compton radiation is similar to synchrotron radiation in a magnetic field which is equal to the local field of LAEMWs. \[For details on synchro–Compton radiation see ([@GO71]; [@BT74]).\]

The mean frequency of synchro-Compton radiation of high-energy electrons with the Lorentz factor $\Gamma_e$ is (e.g., [@BT74])

$$\nu_{sc}\simeq {e\langle B_w\rangle \Gamma^2_e
\over 2\pi mc}\simeq 3\times 10^6\langle B_w\rangle
\Gamma_e^2\,\,\,\,{\rm Hz}\,,
\label{nu}$$

where $\langle B_w\rangle$ is the mean field of LAEMWs.

LAEMWs generated at the wind front
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At $\alpha\sim 1$, low-frequency electromagnetic waves are generated 