We show that a free-electron laser oscillator generating x rays with wavelengths of about 1 A is feasible using ultralow emittance electron beams of a multi-GeV energy-recovery linac, combined with a low-loss crystal cavity. The device will produce x-ray pulses with 10{9} photons at a repetition rate of 1-100 MHz. The pulses are temporarily and transversely coherent, with a rms bandwidth of about 2 meV, and rms pulse length of about 1 ps.
The problem of forward resonant scattering of x rays by an ensemble of nuclei is being solved directly in time and space. The wave equation describing the propagation of the radiation through the nuclear ensemble is derived. It is a first-order integrodifferential equation. Its kernel is a double time function K(t, t) that represents a coherent single scattering response of the nuclear system at time t to excitation at t. The explicit form of the kernel is defined by the character of interactions, the nuclei experience with the environment and by the character of their spatial motion. A general procedure of the solution of the wave equation is introduced that is independent of the type of the kernel. Examples for various kernels are presented and discussed for some particular cases: collective or diffusive motion of nuclei in space, thermal lattice vibrations, time-independent hyperfine interactions, and time-dependent hyperfine interactions due to atomic spin fluctuations or external magnetic-field switching.
Owing to the depth to which hard X-rays penetrate into most materials, it is commonly accepted that the only way to realize hard-X-ray mirrors with near 100% reflectance is under conditions of total external reflection at grazing incidence to a surface. At angles away from grazing incidence, substantial reflectance of hard X-rays occurs only as a result of constructive interference of the waves scattered from periodically ordered atomic planes in crystals (Bragg diffraction). Theory predicts that even at normal incidence the reflection of X-rays from diamond under the Bragg condition should approach 100%-substantially higher than from any other crystal. Here we demonstrate that commercially produced synthetic diamond crystals do indeed show an unprecedented reflecting power at normal incidence and millielectronvolt-narrow reflection bandwidths for hard X-rays. Bragg diffraction measurements of reflectivity and the energy bandwidth show remarkable agreement with theory. Such properties are valuable to the development of hard-X-ray optics, and could greatly assist the realization of fully coherent X-ray sources, such as X-ray free-electron laser oscillators [1][2][3] . Diamond is a material with superlative physical qualities: high mechanical hardness, high thermal conductivity, high dispersion index, high radiation hardness, high hole and electron mobilities, low thermal expansion and chemically inert 4 . Technological applications of diamond crystals are increasing not only in the traditional fields of cutting, grinding and polishing tools, but also in high-tech applications, such as diamond-based electronic devices, wide-bandgap radiation detectors, ultraviolet-emitting diodes, biochemical sensors, high-pressure cells and thermal sinks, to name only a few. Very recently, diamond crystals have been identified as indispensable for the realization of X-ray free-electron laser oscillators (XFELOs), next-generation hard-X-ray sources of the highest average and peak brightness and extremely narrow bandwidth 1,2 . The special role of diamonds in the feasibility of the XFELOs is due to their outstanding reflectivity for hard X-rays in Bragg diffraction, thus far only predicted in theory (Fig. 1a).The high reflectivity of crystals in Bragg diffraction is intimately connected with the perfect crystal structure. Progress in fabrication, characterization and X-ray optics applications of synthetic diamonds was substantial in the past decade [5][6][7][8][9][10][11][12][13] . Still the diamond crystals available commercially as a rule suffer from defects: dislocations, stacking faults, inclusions, impurities and so on. Synthetic high-purity (type IIa, low nitrogen content) crystals grown with a high-pressure, high-temperature technique are generally considered to have the highest crystal quality and the lowest density of defects among commercially available diamonds 10,13 . X-ray topography studies have demonstrated crystals with relatively large 4×4 mm 2 defect-free areas 13 . However, critical outstanding questions remain o...
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