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This paper describes a theory of transverse coherence properties of Undulator Radiation. Our study is of very practical relevance, because it yields specific predictions of Undulator Radiation cross-spectral density in various parts of the beamline. On the contrary, usual estimations of coherence properties assume that the undulator source is quasi-homogeneous, like thermal sources, and rely on the application of van Cittert-Zernike (VCZ) theorem, in its original or generalized form, for calculating transverse coherence length in the far-field approximation. The VCZ theorem is derived in the frame of Statistical Optics using a number of restrictive assumptions: in particular, the quasi-homogeneous assumption is demonstrated to be inaccurate in many practical situations regarding undulator sources. We propose a technique to calculate the cross-spectral density from undulator sources in the most general case. Also, we find the region of applicability of the quasi-homogeneous model and we present an analytical expression for the cross-spectral density which is valid up to the exit of the undulator. For the case of more general undulator sources, simple formulas for the transverse coherence length, interpolated from numerical calculations and suitable for beamline design applications are found. Finally, using a simple vertical slit, we show how transverse coherence properties of an X-ray beam can be manipulated to obtain a larger coherent spot-size on a sample. This invention was devised almost entirely on the basis of theoretical ideas developed throughout this paper.

This article is from Journal of Synchrotron Radiation , volume 21 . Abstract X-ray scanning microscopy greatly benefits from a reduced emittance of synchrotron radiation sources, especially from a diffraction-limited storage ring. Nanofocusing is discussed in view of focus size, flux and coherence.

This open access book collects the contributions of the seventh school on Magnetism and Synchrotron Radiation held in Mittelwihr, France, from 7 to 12 October 2018. It starts with an introduction to the physics of modern X-ray sources followed by a general overview of magnetism. Next, light / matter interaction in the X-ray range is covered with emphasis on different types of angular dependence of X-ray absorption spectroscopy and scattering. In the end, two domains where synchrotron radiation-based techniques led to new insights in condensed matter physics, namely spintronics and superconductivity, are discussed. The book is intended for advanced students and researchers to get acquaintance with the basic knowledge of X-ray light sources and to step into synchrotron-based techniques for magnetic studies in condensed matter physics or chemistry.

This open access book collects the contributions of the seventh school on Magnetism and Synchrotron Radiation held in Mittelwihr, France, from 7 to 12 October 2018. It starts with an introduction to the physics of modern X-ray sources followed by a general overview of magnetism. Next, light / matter interaction in the X-ray range is covered with emphasis on different types of angular dependence of X-ray absorption spectroscopy and scattering. In the end, two domains where synchrotron radiation-based techniques led to new insights in condensed matter physics, namely spintronics and superconductivity, are discussed. The book is intended for advanced students and researchers to get acquaintance with the basic knowledge of X-ray light sources and to step into synchrotron-based techniques for magnetic studies in condensed matter physics or chemistry.

The paper describes a new concept of visible pump/X-ray probe/slow detector experiments that could be performed at third-generation synchrotron light sources. We propose a technique that would allow time resolution up to femtosecond capabilities to be recovered from a long (100 ps) X-ray probe pulse. The visible pump pulse must be as short as the desired time resolution. The principle of operation of the proposed pump-probe scheme is essentially based on the statistical properties of the synchrotron radiation. These properties are well known in statistical optics as properties of completely chaotic polarized light. Our technique utilizes the fact that, for any synchrotron light beam there exist some characteristic time (coherence time), which determines the time-scale of the random fluctuations. The typical coherence time of soft X-ray synchrotron light at the exit of monochromator is in the femtosecond range. An excited state is prepared with a pump pulse and then projected with a probe pulse onto a final ion state. The first statistical quantity of interest is the variance of the number of photoelectrons detected during synchrotron radiation pulse. The statistics of concern are defined over an ensemble of synchrotron radiation pulses. From a set of variances measured as a function of coherence time (inversely proportional to monochromator bandwidth) it is possible to reconstruct the femtosecond dynamical process.

We investigate thermal synchrotron radiation at semi-relativistic and relativistic temperatures. We find an analytic expression for the angle-averaged emission coefficient, and show that it is significantly more accurate that those derived previously. We also present analytic approximations to the synchrotron turnover frequency. Then, we treat Comptonization of the synchrotron radiation, and give simple expressions for the spectral shape and the emitted power. We also consider modifications of the above results by bremsstrahlung. The importance of Comptonization of synchrotron radiation in compact X-ray sources is then studied. We consider emission from hot accretion flows and from active coronae above optically-thick accretion discs in black-hole binaries and AGNs. Synchrotron Comptonization is found to be, in general, negligible in luminous sources, except for those with hardest X-ray spectra and stellar masses. Increasing the black-hole mass results in a strong reduction of the maximum Eddington ratio possible from to this process. X-ray spectra of intermediate-luminosity sources, e.g., low-luminosity AGNs, can be explained by synchrotron Comptonization only in the case of hot accretion flows. Then, bremsstrahlung emission always dominates X-ray spectra of very weak sources. Finally, we consider weakly-magnetized neutron stars and find that synchrotron Comptonization can account for the power-law X-ray spectra observed in their low states.

This article describes a complete theory of spatial coherence for undulator radiation sources. Current estimations of coherence properties often assume that undulator sources are quasi-homogeneous, like thermal sources, and rely on the application of the van Cittert-Zernike theorem for calculating the degree of transverse coherence. Such assumption is not adequate when treating third generation light sources, because the vertical(geometrical) emittance of the electron beam is comparable or even much smaller than the radiation wavelength in a very wide spectral interval that spans over four orders of magnitude (from 0.1 Angstrom up to 10^3 Angstrom). Sometimes, the so-called Gaussian-Schell model, that is widely used in statistical optics in the description of partially-coherent sources, is applied as an alternative to the quasi-homogeneous model. However, as we will demonstrate, this model fails to properly describe coherent properties of X-ray beams from non-homogeneous undulator sources. As a result, a more rigorous analysis is required. We propose a technique, based on statistical optics and Fourier optics, to explicitly calculate the cross-spectral density of an undulator source in the most general case, at any position after the undulator. Our theory, that makes consistent use of dimensionless analysis, allows relatively easy treatment and physical understanding of many asymptotes of the parameter space, together with their region of applicability. Particular emphasis is given to the asymptotic situation when the horizontal emittance is much larger than the radiation wavelength, and the vertical emittance is arbitrary. This case is practically relevant for third generation synchrotron radiation sources.

The spectrum of electromagnetic emission generated by relativistic electrons scattered on small-scale random magnetic fields, implied by current models of the magnetic field generation in the gamma-ray burst sources, is considered. The theory developed includes both perturbative and non-perturbative versions and, therefore, suggests a general treatment of the radiation in arbitrary small-scale random field. It is shown that a general treatment of the random nature of the small-scale magnetic field, as well as angular diffusion of the electrons due to multiple scattering by magnetic inhomogeneities (i.e., non-perturbative effects), give rise to a radiation spectrum that differs significantly from so-called "jitter" spectrum. The spectrum of diffusive synchrotron radiation seems to be consistent with the low energy spectral index distribution of the gamma-ray bursts.

1Lendas dos Vegetaes

By Eduardo Sequeira

Nesta obra, o naturalista e botânico Eduardo Sequeira apresenta lendas e contos e significados, de diferentes povos do mundo, de 63 vegetais, frutas e legumes da flora portuguesa. - Summary by Lucas Oliveira