  The limit on the intrinsic brightness temperature, attributed to `Compton
catastrophe', has been established being $10^{12}$~K. Somewhat lower limit of
the order of $10^{11.5}$~K is implied if we assume that the radiating plasma is
in equipartition with the magnetic field --- the idea that explained why the
observed cores of active galactic nuclei sustained the limit lower than the
`Compton catastrophe'. Recent observations with unprecedented high resolution
by the RADIOASTRON revealed systematic exceed in the observed brightness
temperature. We propose means of estimating the degree of non-equipartition
regime in AGN cores. Coupled with the core-shift measurements the method allows
us to estimate independently the magnetic field strength and the particles
number density at the core. We show that the ratio of magnetic energy to
radiating plasma energy is of the order of $10^{-5}$, which means the flow in
the core is dominated by the particle energy. We show that the magnetic field
obtained by the brightness temperature measurements may be underestimated. We
propose for the relativistic jets with small viewing angles the non-uniform MHD
model, and obtain the expression for the magnetic field amplitude about two
orders higher than that for the uniform model. These magnetic field amplitudes
are consistent with the limiting magnetic field suggested by the `magnetically
arrested disk' model.
