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X-ray Free-electron Lasers (X-ray FELs) give us for the first time the possibility to explore structures and dynamical processes of atomic and molecular systems at the Ångstrom-femtosecond space and time scales. They generate coherent photon pulses with time duration of a few to 100 femtosecond, peak power of 10 to 100 GW, over a wavelength range extending from about 100 nm to less than 1 Å. Using these novel and unique capabilities new scientific results are being obtained in atomic and molecular sciences, in areas of physics, chemistry and biology. In this paper we review the physical principles, the theoretical models and the numerical codes on which X-ray FELs are based, starting from a single electron spontaneous undulator radiation to the FEL collective instability of a high density electron beam, strongly enhancing the electromagnetic radiation field intensity and its coherence properties. We present also a short review of the main experimental properties of X-ray FELs, and discuss the results of the most recent research to improve their longitudinal coherence properties, increase the peak power and generate multicolor spectra.

We study the time structure, the frequency composition, and the shot to shot fluctuations of the radiation emitted by a free-electron laser starting from shot noise in the electron beam longitudinal distribution, taking into account slippage and finite bunch length effects. We find a very difkrent behavior when the bunch length, Eg, is much longer than the cooperation length, E"or of the order of a few 8,. The field evolution is dominated by slippage eÃects in both cases, and shows the presence of superradiant spikes.

Intense femtosecond x-ray pulses from free-electron laser sources allow the imaging of individual particles in a single shot. Early experiments at the Linac Coherent Light Source (LCLS) have led to rapid progress in the field and, so far, coherent diffractive images have been recorded from biological specimens, aerosols, and quantum systems with a few-tens-of-nanometers resolution. In March 2014, LCLS held a workshop to discuss the scientific and technical challenges for reaching the ultimate goal of atomic resolution with single-shot coherent diffractive imaging. This paper summarizes the workshop findings and presents the roadmap toward reaching atomic resolution, 3D imaging at free-electron laser sources.

Energy extraction efficiency of a free electron laser (FEL) can be greatly increased using a tapered undulator and self-seeding. However, the extraction rate is limited by various effects that eventually lead to saturation of the peak intensity and power. To better understand these effects, we develop a model extending the Kroll-Morton-Rosenbluth, one-dimensional theory to include the physics of diffraction, optical guiding, and radially resolved particle trapping. The predictions of the model agree well with that of the GENESIS single-frequency numerical simulations. In particular, we discuss the evolution of the electron-radiation interaction along the tapered undulator and show that the decreasing of refractive guiding is the major cause of the efficiency reduction, particle detrapping, and then saturation of the radiation power. With this understanding, we develop a multidimensional optimization scheme based on GENESIS simulations to increase the energy extraction efficiency via an improved taper profile and variation in electron beam radius. We present optimization results for hard x-ray tapered FELs, and the dependence of the maximum extractable radiation power on various parameters of the initial electron beam, radiation field, and the undulator system. We also study the effect of the sideband growth in a tapered FEL. Such growth induces increased particle detrapping and thus decreased refractive guiding that together strongly limit the overall energy extraction efficiency.

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the D!SfR:G' ; ' ; J : i United States Government or any agency thereof.

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