Compact laser-driven electron acceleration, bunch compression and coherent nonlinear Thomson scattering

Coherent hard x-rays have many medical, commercial and academic research applications. To facilitate the design of a table-top coherent hard x-ray source, this thesis studies the linear acceleration of electrons by optical lasers in unbounded vacuum, the linear acceleration and compression of electron bunches by coherent terahertz pulses in cylindrical waveguides, and the generation of coherent hard x-ray radiation by nonlinear Thomson scattering of compressed electron bunches. The Lawson-Woodward theorem describes conditions prohibiting net electron acceleration in laser-electron interactions. We point out how the Lawson-Woodward theorem permits net linear acceleration of a relativistic electron in unbounded vacuum and verify this with electrodynamic simulations. By hypothesizing that substantial net linear acceleration is contingent on the field's ability to bring the particle to a relativistic energy in its initial rest frame, we derive a general formula for the acceleration threshold, which is useful as a practical guide to the laser intensities that linear vacuum acceleration requires. We characterize the scaling laws of linear acceleration by a pulsed radially-polarized beam in infinite vacuum, showing that greater energy gain is achievable with tighter focusing and the use of pre-accelerated electrons. We propose a two-color linear acceleration scheme that exploits changes in the interference pattern caused by the Gouy phase shift to achieve over 90% the one-color theoretical gain limit, more than twice the 40% achievable with a one-color paraxial beam. Interested in capitalizing on the larger wavelengths of coherent terahertz radiation to accelerate larger electron bunches, we study electron acceleration and bunch compression in a cylindrical metal-coated dielectric waveguide. We numerically predict an achievable acceleration gradient of about 450 MeV/m using a 20 mJ terahertz pulse, and separately achieve a 50 times compression to a few-femtosecond duration of a 1.6 pC relativistic electron bunch. Finally, we numerically study the production of coherent hard x-rays via nonlinear Thomson scattering for different degrees of laser focusing. We derive an approximate analytical formula for the optimal incident field intensity that maximizes the radiation intensity spectral peak for a given output and input frequency