Interference effects in the coherent X-ray radiation of relativistic electrons in two- and three-layer targets

A dynamic theory of the coherent X-ray radiation of relativistic electrons in “amorphous medium–single-crystal” and “amorphous medium–free-space–single-crystal” targets is developed. Expressions for the spectral-angular distributions of diffracted transition radiation (DTR), parametric X-ray radiation, and a term describing their interference are obtained. The spectral-angular density of the DTR is represented as a sum of terms describing the diffracted transition radiation from various boundaries and a term describing the interference of these components. Interference effects in the spectral-angular and angular densities of radiation are studied.     

Diffracted transition radiation of relativistic electrons in an artificial periodic structure

A theory concerning the coherent X-ray radiation of relativistic electrons crossing an artificial periodic medium in Laue scattering geometry has been constructed. Expressions describing the spectralangular characteristics of radiation in the Bragg scattering direction have been obtained and studied. Radiation is considered in analogy with that in the crystal medium as a result of the coherent summation of the contributions of two radiation mechanisms, in particular, parametric X-ray radiation (PXR) and diffracted transition radiation (DTR). It is shown that the DTR yield from a layered target can exceed the particle radiation yield in a single-crystal radiator by one order or more under similar conditions.     

X-ray transition radiation of electrons with energy of 300 to 900 MeV in periodic multifoil radiators

Results of experiments conducted at the Tomsk synchrotron to study resonant X-ray transition radiation generated by relativistic electrons in periodic multifoil radiators are reviewed. Both the internal synchrotron beam and the external secondary electron beam from the pair magnetic γ-spectrometer with energies ranging from 300 to 900 MeV were used in the experiments. The radiators consisted of many thin amorphous foils of various materials. The generation of X-ray radiation in a compound radiator consisting of a multifoil radiator and a crystal is also studied. In this case, the resonant X-ray transition radiation generated in the multifoil radiator is diffracted in the crystal and emitted at Bragg angles, together with the parametric X-ray radiation generated in the crystal. Spectral and angular properties of the resonant X-ray transition radiation and diffracted resonant X-ray transition radiation are investigated. The ratio between the contributions from the diffracted resonant X-ray transition radiation and other types of radiation to the total coherent X-ray radiation flux generated by electrons in periodic structures and crystals is estimated.     

Coherent X-ray radiation from a relativistic electron in a combined medium

A theory of coherent X-ray radiation from a relativistic electron crossing a combined medium that consists of amorphous and crystal plates is constructed within the dynamic diffraction theory. The field reflection asymmetry relative to the target surface determined by the angle between the atomic planes and the target surface is taken into account in the theory. The expressions describing the spectral-angular densities of parametric X-ray and diffracted transition radiations in this medium are derived and investigated.     

Enhancement of spectral-angular density of parametric X-rays in Laue geometry due to change in the angle between a target surface and reflecting atomic planes

Coherent X-rays of a relativistic electron crossing a single crystal with a uniform velocity in the Laue scattering geometry are considered in the two-wave approximation of dynamic diffraction theory [1]. Analytical expressions for the spectral-angular distribution of parametric X-rays (PXR) and diffracted transition radiation (DTR) have been obtained. The case when the system of diffracting atomic planes of a crystal is located at an arbitrary angle δ to a crystal surface (asymmetric reflection) is considered. The value δ = π/2 corresponds to the symmetric reflection in the given scattering geometry. The dependence of the PXR and DTR spectral-angular density on the angle δ has been investigated. It has been shown that the PXR spectrum width depends substantially on the given angle, which, in particular, allows one to increase significantly the PXR angular density by decreasing the angle δ.     

Effect of mutual orientation of the lattice of a single-crystal radiator and its outer surface on X-ray transition radiation characteristics

X-ray transition radiation (TR) of relativistic electrons crossing a single crystal target in the Bragg scattering geometry is considered within the framework of a dynamic diffraction theory. Analytical expressions are obtained for the TR spectral-angular distribution taking into account crystal surface orientation with respect to atomic planes. It is shown that at a fixed angle of electron incidence onto a system of atomic planes of the crystal the TR spectral-angular characteristics in the region of Bragg frequencies strongly depend on the orientation of the entrance surface of the target. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 37–42, June, 2006.     

Spectral-angular distributions of radiation from relativistic electrons in a thin layer of matter

Expressions for the spectral-angular density of bremsstrahlung from a relativistic electron in a thin layer of matter are obtained. The effect that the multiple scattering of electrons by medium atoms exerts on the spectral-angular features of radiation in a thin amorphous target is studied. It is shown that, if the root-mean-square angle of multiple scattering is much larger than the characteristic angle of relativistic-electron radiation, there occurs the bremsstrahlung-suppression effect, which is similar to the Landau-Pomeranchuk-Migdal effect.     

Parametric X-ray radiation along relativistic electron velocity in asymmetric Laue geometry

An analysis is presented of the parametric X-ray radiation emitted by a relativistic electron at a small angle to its velocity as it passes through a single-crystal plate in asymmetric Laue geometry (including symmetric geometry as a particular case). Expressions describing the spectral-angular distributions of parametric X-ray radiation, transition radiation, and their interference are obtained. The effect of asymmetry on the spectral-angular distributions is examined.     

On the Effect of Anomalous Photoabsorption in Parametric X Radiation

The parametric X radiation of relativistic electrons passing through a monocrystal is considered. It is demonstrated that, contrary to widespread opinion, conditions for the effect of anomalous photoabsorption to show up can be realized in the Laue scattering geometry. It is expected that the predicted effect will increase the spectral-angular density of the radiation several times.     

Coherent X-ray diffraction radiation produced by microbunched beams passing close to the edge of a slab

With use of formulas for single-particle X-ray transition and diffraction radiation (XTR and XDR), we obtain expressions for spectral-angular distributions and total numbers of emitted quanta in coherent X-ray transition radiation (CXTR2) and coherent X-ray diffraction radiation (CXDR) arising when a microbunched beam of electrons, respectively, intersects the interfaces of a slab or flies at small distance from the edge of the slab. Comparison of obtained results with those known for CXTR from a single interface is performed. It is shown on the basis of numerical calculations that experimental study of CXDR is at present possible on the Linac Coherent Light Source (LCLS, SLAC).     

Parametric x-ray radiation along the velocity of relativistic electron in a Bragg scattering geometry

Based on the dynamic scattering theory, forward parametric x-ray radiation (FPXR) of a relativistic electron is investigated in a single crystal plate in a Bragg scattering geometry. Analytical expressions for the spectral-angular distribution of FPXR and transition radiation (TR) including the crystal surface orientation with respect to a system of diffracting atomic planes are derived, which allow one to identify the conditions under which a contribution from FPXR is considerable even in the case of a thick absorbing crystal. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 48–56, June, 2007.     

Multiple scattering effect on the line width of parametric X-ray relativistic electron radiation in a crystal

It is shown that multiple scattering is of significant importance in the formation of the line width of parametric X-ray “backward” radiation of relativistic electrons in a crystal. A theory of the line width of this radiation based on the functional integration method is suggested. The problem of multiple scattering effects on parametric X-ray radiation is shown to be similar to the problem of the Landau-Pomeranchuk-Migdal multiple scattering effect on the bremsstrahlung of high-energy electrons in an amorphous medium.     

On parametric x-ray radiation

The spectral-angular and angular distributions of parametric x-ray radiation generated in the vicinity of the maximum at small angles to the direction of charged-particle motion are studied under the conditions of Laue and Bragg diffraction geometries. Detector parameters at which the dynamical maxima of parametric x-ray radiation can be observed against the background of transition radiation are indicated. The spectral-angular and angular distributions of parametric x-ray radiation are analyzed for the case of backward geometry. The results of the present theoretical calculations are found to be in good agreement with experimental data.     

Effect of anomalous photoabsorption in parametric X-ray radiation under asymmetric reflection conditions

Parametric X-ray radiation (PXR) of a relativistic electron crossing a monocrystalline plate is considered in the Laue scattering geometry. Expressions describing the spectral-angular distributions of PXR and diffracted transient radiation (DTR), which are formed in atomic planes arranged at an arbitrary angle δ to the surface of a crystalline plane (asymmetric reflection), are derived in the two-wave approximation of the dynamic diffraction theory. The conditions under which the effect of anomalously weak photoabsorption (Borman effect) is manifested most clearly are determined. This effect can considerably enhance the intensity of the sources of tunable quasi-monochromatic X rays, which are based on the PXR mechanism.     

Parametric x-ray radiation of a relativistic electron under conditions of asymmetric reflection

Coherent x-ray radiation of a relativistic electron crossing a single-crystal plate in the Laue scattering geometry is considered in a two-wave approximation of the dynamic diffraction theory [1]. Analytical expressions describing the spectral-angular distribution of parametric x-ray radiation (PXR) and diffraction transition radiation (DTR) formed on the atomic planes located at an angle δ to the crystal plate surface (asymmetric scattering) are derived. Dependence of the spectral-angular density of PXR, DTR, and their interference term on the angle δ is investigated. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 80–89, August, 2008.     

Coherent X-ray radiation generated by a relativistic electron in an artificial periodic structure

A theory of coherent X-ray radiation from a relativistic electron crossing an artificial periodic layered structure in the Laue scattering geometry is constructed. The expressions describing the spectral-angular radiation parameters are obtained. It is shown that the radiation yield in such a medium may substantially exceed the radiation yield in a crystal under analogous conditions.     

Contributions of transition and parametric X-ray radiation along the relativistic electron velocity in the 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.     

Feature of kinematic diffraction of nonmonochromatic divergent X-ray beams in a crystal with a periodically strained lattice

Coherent scattering of a nonmonochromatic divergent beam of X-ray quanta in a crystal excited by an acoustic wave is described using a kinematic approach. The possibility of manifestation of a peculiar effect of amplification of the diffracted X-ray beam by the acoustic wave is predicted using this approach.     

Quantum theory of laser cooling: Statistical description of the process dynamics

A dynamic theory of coherent X-ray radiation generated in a periodic layered medium by a relativistic electron multiply scattered by target atoms has been developed. The expressions describing the spectral–angular characteristics of parametric X-ray radiation and diffracted transition radiation are derived. Numerical calculations based on the derived expressions have been performed.     

Tunable source of parametric X-ray radiation

A new design of an X-ray source with a radiation energy controllably varying from 2 to 130 keV and a radiation intensity exceeding >10^?5 photon/e^?/sr is suggested. The source is based on parametric X-ray radiation (PXR) generated by moderately relativistic electrons in an original geometry. In this geometry, kinematic bunching of PXR reflections is used, which makes it possible to increase the intensity of the source. A model to calculate the PXR characteristics that takes into account absorption of radiation, beam parameters, multiple scattering, and energy loss is developed. The monochromaticity of the source lines is estimated.