Quasi-linear diffusion (QLD), driven by the cyclotron instability, is proposed as a mechanism for the possible generation of synchrotron emission in the nearby zone of SgrA$^*$. For physically reasonable parameters, the QLD, by causing non-zero pitch angle scattering lets electrons with the relativistic factors of the order of $10^8$ emit synchrotron radiation in the hard $X$-ray spectral band $sim120$ keV.
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