Quasi-linear diffusion driving the synchrotron emission in active
  galactic nuclei
  We study the role of the quasi-linear diffusion (QLD) in producing X-ray
emission by means of ultra-relativistic electrons in AGN magnetospheric flows.
We examined two regions: (a) an area close to the black hole and (b) the outer
magnetosphere. The synchrotron emission has been studied for ultra-relativistic
electrons and was shown that the QLD generates the soft and hard X-rays, close
to the black hole and on the light cylinder scales respectively. By considering
the cyclotron instability, we show that despite the short synchrotron cooling
timescales, the cyclotron modes excite transverse and longitudinal-transversal
waves. On the other hand, it is demonstrated that the synchrotron reaction
force and a force responsible for the conservation of the adiabatic invariant
tend to decrease the pitch angles, whereas the diffusion, that pushes back on
electrons by means of the aforementioned waves, tends to increase the pitch
angles. By examining the quasi-stationary state, we investigate a regime in
which these two processes are balanced and a non-vanishing value of pitch
angles is created.
