This work studies the production and measurement of longitudinally coherent, ultrashort pulses of light from a self-amplified spontaneous emission free-electron laser (SASE FEL) by using an energy-chirped electron beam in conjunction with a tapered undulator. This scheme effectively preserves the FEL gain only where an appropriate undulator taper compensates for the detuning experienced by an amplifying radiation spike as it slips forward in the electron beam rest frame. The simultaneous time and frequency-domain measurement of ultrashort pulses of light generated in this manner were made with an advanced transient-grating frequency-resolved optical gating (TG FROG) diagnostic, which has the potential to push ultrashort light pulse measurement at FEL facilities to shorter wavelength regimes.

The theoretical framework presented in this dissertation has two components. The FEL theory presented here includes an analysis of the coupled wave and Vlasov equations, which are linearized in the one-dimensional case, and are solved in the frequency domain by the Laplace transform technique. The exponential gain regime for SASE FEL light is explored in detail to clearly identify concepts that are relevant to the energy-chirp and undulator tapering experiment. Some of these concepts are illustrated with fully three-dimensional, time-dependent numerical particle simulations using the FEL code GENESIS for the supportive case of ultrashort, low-charge electron beams. In addition, nonlinear optics, the foundation upon which all FROG diagnostics are built, is briefly explored using two complementary perspectives as they apply to the TG FROG geometry.

The experimental section describes in detail the first direct time-domain measurements of a single coherent radiation spike from a SASE FEL amplifier employing the energy-chirped electron beam and tapered undulator technique at the SPARC FEL test facility in Frascati, Italy. Electron beams were accelerated and compressed using the velocity bunching technique, which leaves a residual

energy-chirp in the longitudinal phase space. The energy-chirp was compensated by appropriately tapering individual undulator sections. This process was optimized at a resonant wavelength of λ = 530 nm. The ultrashort light pulses that were generated had a temporal full-width at half-maximum of 98 fs and a time-bandwidth product of TBP ∼ 1.2, indicating that the Fourier limit was nearly achieved. This experiment provides further insight into methods that can be used to shape the SASE FEL longitudinal profile and enhance coherence properties. In addition, the measurements were taken with an advanced, and relatively simple, TG FROG diagnostic that can potentially be used to measure ultrashort UV pulses at FEL facilities.