The feasibility of generation of bright ultrashort gamma-ray pulses is demonstrated in the interaction of a relativistic electron bunch with a counterpropagating tightly-focused superstrong laser beam in the radiation dominated regime. The Compton scattering spectra of gamma-radiation are investigated using a semiclassical description for the electron dynamics in the laser field and a quantum electrodynamical description for the photon emission. We demonstrate the feasibility of ultrashort gamma-ray bursts of hundreds of attoseconds and of dozens of megaelectronvolt photon energies in the near-backwards direction of the initial electron motion. The tightly focused laser field structure and radiation reaction are shown to be responsible for such short gamma-ray bursts which are independent of the durations of the electron bunch and of the laser pulse. The results are measurable with the laser technology available in a near-future.
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