Theory of coherent transition radiation generated at a plasma-vacuum interface

Transition radiation generated by an electron beam, produced by a laser wakefield accelerator operating in the self-modulated regime, crossing the plasma-vacuum boundary is considered. The angular distributions and spectra are calculated for both the incoherent and the coherent radiation. The effects of the longitudinal and transverse momentum distributions on the differential energy spectra are examined. Diffraction radiation from the finite transverse extent of the plasma is considered and shown to strongly modify the spectra and energy radiated for long-wavelength radiation. This method of transition radiation generation has the capability of producing high peak power terahertz radiation, of order $100\mu \mathrm{J}/\mathrm{p}\mathrm{u}\mathrm{l}\mathrm{s}\mathrm{e}$ at the plasma-vacuum interface, which is several orders of magnitude beyond current state-of-the-art terahertz sources.