Bragg Direction Research Articles

Emission of quasi-monochromatic ultrasoft X-ray of multilayer target in the Bragg direction under 5.7 MeV electron irradiation

Previously, it was experimentally shown that VUV radiation generated in a periodic structure of a multilayer X-ray mirror by relativistic electrons exhibits a quasi-monochromatic spectrum depending on the angle of inclination of the target and the direction of emission of radiation inside the radiation cone. Here, we present new experimental results regarding the properties of angular density of radiation. A comparison between the measured radiation intensity over a wide range of target inclination angles and theoretical calculations is provided.

Rocking Curves of X-ray Asymmetrical Laue Diffraction with Two-Dimensional Curvature of Wave Front

X-ray asymmetrical Laue diffraction in a perfect crystal with plane front surface was considered taking into account the two-dimensional curvature of a wave incident on the crystal. Using an appropriate Green function the dependences of rocking curves on deviation angles from selected exact Bragg direction were examined in the diffraction plane and in the direction perpendicular to the diffraction plane in locally plane wave approximation. The dependence of rocking curves on the degree of asymmetry of diffraction geometry was investigated. Analytical expressions for half widths of rocking curves in the diffraction plane and in the direction perpendicular to the diffraction plane are obtained. Some requirements to spatial and temporal coherence are estimated.

Angular distributions of parametric X-ray radiation from a diamond crystal

Angular distributions of parametric X-ray radiation (PXR) from 255MeV electrons incident on a 50μm thick diamond crystal are presented. Almost all experiments on the angular distributions of PXR have been performed using Si crystals. The purpose of the present work is to extend this research to diamond crystals. An imaging plate was adopted as a two-dimensional position-sensitive X-ray detector, and high-quality PXR angular distribution data were successfully obtained. The measured PXR angular distributions were compared with those predicted theoretically and good agreement was obtained. The cause of the slight difference observed around the center position (Bragg direction) is also discussed.

Spatial distribution of PXR generated by 855 MeV electrons: Comparison of simulation results with experimental data

The detailed data treatment of the experiment performed in MAMI-B microtron with the X-ray camera, taking into account the contribution of both diffracted transition radiation and bremsstrahlung, is presented. The X-ray camera efficiency was additionally considered. The simulated emission pattern in general agrees with the experimental one. However, along the Bragg direction where the influence of the beam size on the emission spatial distribution is most noticeable, a discrepancy between the model and the experiment is observed. Possible reasons of such discrepancy are discussed.

Comparison of DTR spectral-angular characteristics of divergent beam of relativistic electrons in scattering geometry of Laue and Bragg

Diffracted transition radiation (DTR) generated by a divergent beam of relativistic electrons crossing a single-crystal plate in different (Laue, Bragg) scattering geometry has been considered for the general case of asymmetric reflection of the electron coulomb field relative to the entrance target surface. The expressions for spectral-angular density of DTR and parametric X-ray Radiation (PXR) has been derived. Then DTR and PXR has been considered in case of a thin target, when multiple scattering of electron is negligibly small, which is important for divergence measurement in real time regime. Numerical calculation of spectral-angular density of DTR by a beam of relativistic electrons has been made using averaging over the bivariate Gauss distribution as angular distribution of relativistic electrons in the beam. It has been shown that in Bragg scattering geometry the angular density of DTR is bigger, than in Laue geometry, which can be explained by the existence of the frequency range, in which the incident wave propagation vector takes complex value even under absence of absorption. In this range, all of photons are reflected in Bragg direction. It means that the range of total reflection defines the width of DTR spectrum.

Quantum theory of X-ray radiation at Bragg angles at channeling

Abstract In the framework of quantum electrodynamics the theory of the new type of X-ray radiation from the channeled electrons in vicinity of the Bragg angle—Diffracted Channeling Radiation (DCR) is developed beyond the dipole approximation. The DCR occurs due to transitions of the channeled electrons from one transverse energy level to another with the diffraction of the emitted photon. It is demonstrated that dipole approximation is valid for the first order of diffraction DCR and not valid for higher orders of diffraction. On the basis of obtained equations for the first time it is theoretically shown that the angular distribution of the DCR is a system of very narrow ring-shaped peaks around of the Bragg direction. The calculations were performed taking into account the band structure of the transverse motion energy.

X-ray Laue diffraction with allowance for two-dimensional curvature of the wavefront: The concept a locally plane wave

Symmetrical Laue diffraction in a perfect crystal with a plane entance surface is considered. The two dimensional curvature of the wave front of the incident beam is taken into account. Using the corresponding Green function, a general expression for the amplitude of diffracted wave in the crystal is presented. Based on this expression, the concept of a locally plane wave is analyzed taking into account two-dimensional curvature of the wave front. This concept is used for obtaining the rocking curves depending on the angles of deviation from the chosen exact Bragg direction in both the diffraction plane and in perpendicular direction. The obtained result is compared with the result of the standard dynamical diffraction theory.

Comparison of the results of kinematic and dynamic approximations for parametric X‐ray radiation in the Bragg direction

AbstractA theoretical study on the kinematic and dynamic approximations of parametric X‐ray radiation (PXR) is presented. The results obtained are examined and compared. The ratio of the absolute maxima of kinematic and dynamic PXR can be obtained. The results are closer at lower energies and their correlation depends on the angle of incidence. These theoretical results indicate that in some energy regions and angle of incidence it may be necessary to apply the dynamic approximation of PXR for greater accuracy.

Acoustic "pumping effect" for quartz monochromators

There are investigations of dependences scattered at quartz crystals X-ray in Bragg direction of intensity on amplitude and frequency external alternating electromagnetic field, which initiates acoustic waves in crystal, in spectral mode.

Ratio of the parametric X-radiation yields in the Bragg direction and along the relativistic electron velocity in the Bragg geometry

Parametric X-radiation (PXR) and parametric radiation at a small angle to the relativistic electron velocity (FPXR) that arises from electron motion through a monocrystalline plate in Bragg scattering geometry are analyzed on the basis of the dynamic diffraction theory. The expressions for spectral-angular densities of these radiations have been derived in the general case of asymmetric field reflections from a target surface. They make it possible to reveal the noticeable dependence of the ratio of the PXR and FPXR yields on the angle between reflecting atomic planes and the surface of a monocrystalline plate, i.e., reflection asymmetry.

On the ratio of the relativistic electron PXR in the Bragg direction and in the forward direction in Laue geometry

Parametric X-ray radiation and parametric X-ray radiation at a small angle with respect to the velocity of a relativistic electron crossing a single crystal plate in Laue scattering geometry are studied based on the dynamic X-ray diffraction theory. Analytical expressions for the spectral-angular density of radiations are derived in the general case of asymmetric reflection. The ratio of the contributions of these radiation mechanisms is considered.

Modulation of x-ray line intensity emitted by a periodic structure under electron excitation

We report on the intensity modulation of a characteristic x-ray line emitted by a periodic structure, as a function of the observation angle. This intensity variation takes place around the Bragg direction corresponding to the diffraction of the x-ray line by the emitting structure. An enhancement of the emitted radiation is observed and interpreted on the basis of the reciprocity theorem. The enhancement remains unchanged by varying the number of emitting periods. Following Yariv and Yeh [J. Opt. Soc. Am. 67, 438 (1977)], a possible application as x-ray resonator to achieve a distributed feedback soft x-ray laser is envisaged.

Non-Rayleigh distribution of reflected speckle intensities from localized states inside the gap of disordered photonic crystals

The field distributions of reflected speckles arising from localized states inside the gap of disordered photonic crystals in two dimensions were studied through numerical simulations using the multiple-scattering method. The statistics of the Lyapunov exponent of the transmitted waves were also studied. Similar to the case of disordered photonic crystals in one dimension, two types of localized states were found depending on the degree of disorder and the frequency inside the gap. Our simulation results indicate that the reflection statistics depend on whether or not the localized states are of the normal type. They also depend on whether the reflected angles are in the Bragg direction or not. For the non-Bragg angles, we found that the intensity distribution arising from the normal-type localized states follows Rayleigh statistics, in agreement with random matrix theory. However, deviations from Rayleigh statistics were found for second type of localized states. The crossover behavior from non-Rayleigh to Rayleigh statistics was studied as a function of the degree of disorder. By separating the field into coherent and diffuse parts, we have studied the statistics of field and phase distributions for both diffuse and total fields as well as their speckle contrasts. It is found that the crossover behavior is very similar to behavior in ballistic to diffusive wave propagation for the transmitted waves and can be described by the random-phasor-sum model (RPS). For the Bragg angle, non-Rayleigh statistics were found for both kinds of localized states. The statisics are sensitive to the degree of disorder. It is found that both the RPS and K distribution have limited ranges of validity in this case.

Asymmetry of parametric x-ray radiation from polarized electrons (quantum approach)

The asymmetry of parametric x rays emitted by polarized electrons is considered on the basis of quantum theory. The asymmetry value is calculated for emission both in the Bragg direction and in directions different from the Bragg direction by an angle of order γ−1. The asymmetry is computed for the longitudinal and for the transverse polarization of the electrons.

Studies of coherent backscattering from opal photonic crystals

We studied the coherent backscattering (CBS) of light from synthetic opal photonic crystals with incomplete photonic gap. For incident angles far from the Bragg angle, we found that the CBS cones are similar to those observed in previous measurements of various random media and in excellent agreement with theory. However, for incident angles close to the Bragg angle, we observed a substantial broadening of the CBS cone. This broadening is due to the light intensity decay in course of propagation along the Bragg direction. We also measured the wavelength dependence of the CBS cone from opals and compare it to that of TiO 2 particle suspensions.

Examination of beam propagation in misaligned holographic gratings and comparison with the acousto-optic transfer function model for profiled beams

A transfer function formalism developed earlier for the propagation of profiled optical beams through acousto-optic Bragg cells is revisited and applied to a thick holographic grating. The results based on the holographic coupled wave model and the acousto-optic multiple scattering model are shown to be compatible, and equivalent parameters such as the Q and grating strength are defined for the two systems. Results for a Gaussian spatial profile are numerically computed and compared. For the holographic grating, a profiled beam may be interpreted as an angular misalignment or Bragg-angle mismatch problem. The case of Bragg-wavelength mismatch is also investigated for the case of a polychromatic READ beam with a uniform and a Gaussian amplitude spectrum. The resulting spatial amplitude distribution of the scattered order at the grating output is plotted as a function of the departure from the correct Bragg direction.

Parametric X-ray radiation from relativistic electrons in a crystal in the vicinity of and at angular distance from a Bragg direction

Investigations into differential yields of coherent radiation in a crystal at an angular distance from the Bragg and forward directions are presented for the first time. It is found that the radiation under study is due to the interaction of incident electrons with the electron subsystem of a crystal, i.e., the parametric X-ray radiation (PXR), and influence of coherent bremsstrahlung is not significant. The influence of the row effect on the PXR differential yields is also shown. The saturation of the PXR yield at angular distance θ 1 > 1 γ from the Bragg directions is observed with increasing incident electron energy. Some possible PXR applications and the origins of background in PXR spectra are considered.

Use of vector Bragg wave-number scattering condition in bistatic scattering experiments

Applying the Born approximation to a buoyant plume yields the Bragg scattering condition that determines along with knowledge of the scattering potential, the scattered wave at any given scattering angle. The Bragg scattering condition allows for information obtained from the same Bragg direction albeit different scattering angles to be pieced together to form an entire Bragg wave-number spectrum of the scatterer. Data are taken in a multiple bistatic configuration whose geometry is predetermined via knowledge of the bandwidth of the transducers and the desired overlap of the resulting Bragg phase space. Results are given for a buoyant axisymmetric laminar plume. As an aside of the Bragg scattering condition an empirical formula derived from the far-field expressions for the Green’s function solution to the Hemholtz equation given the scattering dimensionality of the plume, which is acoustically measured and shown to give expected results.

Time spectra of a nearly-single-line pure nuclear reflection excited by synchrotron radiation.

The time dependence of the coherent response of a $^{57}\mathrm{FeBO}_{3}$ single crystal excited by synchrotron-radiation (SR) pulses was studied in the pure nuclear (333) Bragg reflection near the N\'eel temperature, where the M\"ossbauer reflection spectrum consists of nearly a single line of almost natural linewidth. The time spectra revealed a delayed reemission of \ensuremath{\gamma} quanta into the Bragg direction starting at zero intensity. This behavior was determined by two factors: the coherent decay of the nuclear excited state and the interference of two nearly coinciding hyperfine components.

Wave-particle properties measured by neutron interferometry

Coherence phenomena of neutron waves have been investigated by means of perfect crystal interferometry. A perfect silicon phase shifter was used to obtain information on the longitudinal and transverse coherence lengths and to observe the strong variation of the phase shift near a Bragg direction. Interference experiments with pulsed beams displayed properties of the relative wave packet, and the self-interference character of experiments of this kind. Experiments with an absorber-detector in one coherent beam gave information about the unsharp particle-wave behaviour of neutrons.