  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.
