  We show that electron betatron resonance acceleration by an ultra-intense
ultra-short laser pulse in a near critical density plasma works as a
high-brightness gamma-ray source. Compared with laser plasma X-ray sources in
under-dense plasma, near critical density plasma provides three benefits for
electron radiation: more radiation electrons, larger transverse amplitude, and
higher betatron oscillation frequency. Three-dimensional particle-in-cell
simulations show that, by using a 7.4J laser pulse, 8.3mJ radiation with
critical photon energy 1MeV is emitted. The critical photon energy $E_c$
increases with the incident laser energy %faster than a linear relation. $W_I$
as $E_c \propto W_I^{1.5}$, and the corresponding photon number is proportional
to $W_I$. A simple analytical synchrotron-like radiation model is built, which
can explain the simulation results.
