X-ray free electron lasers (XFELs) provide several orders of magnitude brighter x-rays than 3rd generation sources. However, the electron beamlines and undulator magnets required are on the scale of kilometers, costing billions of dollars with only a half dozen or so currently operating worldwide. One way to overcome these limitations is to prebunch the electron beam on the scale of the x-ray wavelength. In this paper one such scheme is discussed, which uses a nanopatterned grating called a dynamical beam stop. This uses diffraction from crystal planes of the etched portion of a grating to impart a transverse modulation which becomes a temporal modulation via an emittance exchange (EEX). To expand upon this topic, dynamical electron diffraction intensities for a 200 nm thick Si(001) unpatterned membrane are simulated via the multislice method and compared to experiment for various crystallographic orientations at MeV energies. From this as well as an analysis of the experimental inelastic plasmon diffuse scattering, it is determined that the optimal transverse modulation would be formed from a bright field image of the beam stop, with the nanopattern being etched all the way through the membrane. A model quantifying the quality of the modulation - the bunching factor - as a function of contrast and duty factor is formulated and the optimal modulation is determined analytically. A prototype beam stop is then imaged in a transmission electron microscope (TEM) at 200 KeV, with the measured bunching factor of 0.5 agreeing with the model and approaching a saturated XFEL. Using the angular spectrum method, it is determined that the spatial coherence of the MeV energy electron beam is insufficient for significant self-imaging to occur for gratings with pitches of hundreds of nanometers. Finally, the first-order EEX input requirements for the electron beam are examined in the transverse dimension as are newly proposed longitudinal requirements to compensate for lingering correlations between the initial and final longitudinal phase spaces.

With the advent of the X-ray free-electron laser (XFEL), an opportunity has arisen to break the nexus between radiation dose and spatial resolution in diffractive imaging, by outrunning radiation damage altogether when using single X-ray pulses so brief that they terminate before atomic motion commences. This dissertation concerns the application of XFELs to biomolecular imaging in an effort to overcome the severe challenges associated with radiation damage and macroscopic protein crystal growth. The method of femtosecond protein nanocrystallography (fsPNX) is investigated, and a new method for extracting crystallographic structure factors is demonstrated on simulated data and on the first experimental fsPNX data obtained at an XFEL. Errors are assessed based on standard metrics familiar to the crystallography community. It is shown that resulting structure factors match the quality of those measured conventionally, at least to 9 angstrom resolution. A new method for ab-initio phasing of coherently-illuminated nanocrystals is then demonstrated on simulated data. The method of correlated fluctuation small-angle X-ray scattering (CFSAXS) is also investigated as an alternative route to biomolecular structure determination, without the use of crystals. It is demonstrated that, for a constrained two-dimensional geometry, a projection image of a single particle can be formed, ab-initio and without modeling parameters, from measured diffracted intensity correlations arising from disordered ensembles of identical particles illuminated simultaneously. The method is demonstrated experimentally, based on soft X-ray diffraction from disordered but identical nanoparticles, providing the first experimental proof-of-principle result. Finally, the fundamental limitations of CFSAXS is investigated through both theory and simulations. It is found that the signal-to-noise ratio (SNR) for CFSAXS data is essentially independent of the number of particles exposed in each diffraction pattern. The dependence of SNR on particle size and resolution is considered, and realistic estimates are made (with the inclusion of solvent scatter) of the SNR for protein solution scattering experiments utilizing an XFEL source.