  The recently developed manufacturing technologies use high pressure and
various doping additions to prepare bulk MgB2-based materials with a high
critical current density measured by the magnetization methods. We use a
contactless transformer method, which is based on studying the superconductor
response to an induced transport current, to measure AC losses in bulk MgB2
rings synthesized under high pressure. The obtained dependence of the losses on
the primary current (applied magnetic field) is fitted by the power law with
the exponent ~2.1 instead of the cubic dependence predicted by Bean's model and
power-law electric field-current density (E-J) characteristics with a large
exponent. The unusually strong dependence of AC losses on the frequency was
also observed. It was shown that the E-J characteristic of bulk MgB2 is well
fitted by the dependence used in the extended critical state model based on
account of the viscous vortex motion in the flux flow regime. Numerical
simulation using this E-J characteristic gives the current and frequency AC
loss dependencies which well agree with the experimental results.
