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Bright gamma-rays from betatron resonance acceleration in near critical density plasma

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.