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This thesis presents results from two strands of work towards realizing a free-electron laser (FEL) driven by electron bunches generated by a laser-wakefield accelerator (LWFA). The first strand focuses on selecting operating parameters for such a light source, on the basis of currently achievable bunch parameters as well as near-term projections. The viability of LWFA-driven incoherent undulator sources producing nanojoule-level pulses of femtosecond duration at wavelengths of 5 nm and 0.5 nm is demonstrated. A study on the prospective operation of an FEL at 32 nm is carried out, on the basis of scaling laws and full 3-D time-dependent simulations. A working point is selected, based on realistic bunch parameters. At that working point saturation is expected to occur within a length of 1.6 m with peak power at the 0.1 GW-level. This level, as well as the stability of the amplification process, can be improved significantly by seeding the FEL with an external radiation source. In the context of FEL seeding, we study the ability of conventional simulation codes to correctly handle seeds from high-harmonic generation (HHG) sources, which have a broad bandwidth and temporal structure on the attosecond scale. Namely, they violate the slowly-varying envelope approximation (SVEA) that underpins the governing equations in conventional codes. For this purpose we develop a 1-D simulation code that works outside the SVEA. We carry out a set of benchmarks that lead us to conclude that conventional codes are adequately capable of simulating seeding with broadband radiation, which is in line with an analytical treatment of the interaction. The second strand of work is experimental, and focuses on on the use of coherent transition radiation (CTR) as an electron bunch diagnostic. The thesis presents results from two experimental campaigns at the MPI für Quantenoptik in Garching, Germany. We present the first set of single-shot measurements of CTR over a continuous wavelength range from 420 nm to 7 μm. Data over such a broad spectral range allows for the first reconstruction of the longitudinal profiles of electron bunches from a laser-wakefield accelerator, indicating full-width at half-maximum bunch lengths around 1.4 μm (4.7 fs), corresponding to peak currents of several kiloampères. The bunch profiles are reconstructed through the application of phase reconstruction algorithms that were initially developed for studying x-ray diffraction data, and are adapted here for the first time to the analysis of CTR data. The measurements allow for an analysis of acceleration dynamics, and suggest that upon depletion of the driving laser the accelerated bunch can itself drive a wake in which electrons are injected. High levels of coherence at optical wavelengths indicate the presence of an interaction between the bunch and the driving laser pulse.

Investigations of soft matter using ultrashort high intensity pulses have been made possible through the advent of X-ray free-electrons lasers. The last decade has seen the development of a new type of protein crystallography where femtosecond dynamics can be studied, and single particle imaging with atomic resolution is on the horizon. The pulses are so intense that any sample quickly turns into a plasma. This thesis studies the ultrafast transition from soft matter to warm dense matter, and the implications for structural determination of proteins.                    We use non-thermal plasma simulations to predict ultrafast structural and electron dynamics. Changes in atomic form factors due to the electronic state, and displacement as a function of temperature, are used to predict Bragg signal intensity in protein nanocrystals. The damage processes started by the pulse will gate the diffracted signal within the pulse duration, suggesting that long pulses are useful to study protein structure. This illustrates diffraction-before-destruction in crystallography. The effect from a varying temporal photon distribution within a pulse is also investigated. A well-defined initial front determines the quality of the diffracted signal. At lower intensities, the temporal shape of the X-ray pulse will affect the overall signal strength; at high intensities the signal level will be strongly dependent on the resolution. Water is routinely used to deliver biological samples into the X-ray beam. Structural dynamics in water exposed to intense X-rays were investigated with simulations and experiments. Using pulses of different duration, we found that non-thermal heating will affect the water structure on a time scale longer than 25 fs but shorter than 75 fs. Modeling suggests that a loss of long-range coordination of the solvation shells accounts for the observed decrease in scattering signal. The feasibility of using X-ray emission from plasma as an indicator for hits in serial diffraction experiments is studied. Specific line emission from sulfur at high X-ray energies is suitable for distinguishing spectral features from proteins, compared to emission from delivery liquids. We find that plasma emission continues long after the femtosecond pulse has ended, suggesting that spectrum-during-destruction could reveal information complementary to diffraction.