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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.

A vacuum autoresonance accelerator scheme for electrons, which employs terahertz radiation and currently available magnetic fields, is suggested. Based on numerical simulations, parameter values, which could make the scheme experimentally feasible, are identified and discussed.

Theoretical investigations are presented, and their results are discussed, of the laser acceleration of a single electron by a chirped pulse. Fields of the pulse are modeled by simple plane-wave oscillations and a $\cos^2$ envelope. The dynamics emerge from analytic and numerical solutions to the relativistic Lorentz-Newton equations of motion of the electron in the fields of the pulse. All simulations have been carried out by independent Mathematica and Python codes, with identical results. Configurations of acceleration from a position of rest as well as from injection, axially and sideways, at initial relativistic speeds are studied., Comment: 10 pages, 15 figures