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.     

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.     

X-ray scattering in the presence of a strong laser field

Remarkable modifications of electron scattering in the presence of a strong, low frequency radiation field have been found by Kroll and Watson several years ago. It is shown that these modifications have their exact counterparts in the corresponding X-ray scattering by free and bound electrons. In view of the rapid development towards coherent X-ray sources, such induced radiation processes may become accessible to experimental verification in the near future.     

Multiple scattering and intensity fluctuations in optical coherent tomography of randomly inhomogeneous media

An expression for signal intensity fluctuations in optical coherent tomography has been obtained for the first time in the framework of the theory of the multiple scattering of low-coherent optical radiation in a random medium. The contribution of the multiple scattering of low-coherent radiation backscattered from a randomly inhomogeneous layer, as well as the speckles of the interference component in optical coherent tomography, has been calculated.     

Coherent X-ray radiation generated by a relativistic electron beam in a periodic layered medium in the Bragg scattering geometry

A dynamic theory is developed for coherent X-ray radiation generated when a diverging beam of relativistic electrons crosses a periodic layered target. Expressions describing the spectral–angular characteristics of coherent X-ray radiation are obtained and analyzed in the Bragg scattering geometry.     

第三代同步辐射光源X射线相干性测量研究

随着高性能第三代同步辐射光源的建成开放,基于X射线相干特性的实验方法得到了快速发展和广泛应用.作为一个典型的例子,X射线相位衬度成像已经成为常规的X射线实验方法并向用户开放.相干散射、相干衍射成像、光子关联谱等X射线实验方法正日益受到重视,在高空间分辨、时间分辨等研究领域已显示出其独特的优越性.因此,研究和测量第三代同步辐射的空间相干特性对进一步发展这些新的实验方法具有重要意义.基于Talbot自成像原理成功测量了上海光源X射线成像线站发射的X射线的空间相干长度,并进而测得了相应光源的空间尺度.光子能量为33.2 keV时,测得的X射线光束垂直方向空间相干长度为8.84μm,对应的光源尺寸为23μm,测量结果与理论分析相符.     

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.     

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.     

Similarity effects in multiple scattering of coherent radiation: Phenomenology and experiments

Based on phenomenological concepts of statistics of effective optical paths for multiple scattering of coherent radiation, an analysis is carried out of similarity effects observed for the dependences of statistical moments of the scattered field on the relaxation parameters with a dimension of reciprocal length. Within the framework of the diffusion approximation, expressions are obtained that describe the autocorrelation function of fluctuations of the scattered-field amplitude, the degree of polarization, and the normalized intensity of scattered light for media with a finite absorption length in the case of forward scattering of coherent radiation in a plane layer of an isotropic scattering medium. The results of the analysis show the similarity of the dependences of these quantities on the corresponding spatial scales. Experiments with model scattering media (aqueous suspensions of polystyrene spherical particles) supported the existence of similarity effects in multiple scattering. An experimental study was made of the relation between the characteristic depolarization length and the transport length for multiple scattering of coherent radiation in a plane layer. The effective value of the radiation diffusion coefficient providing the best agreement between the experimental and the calculated values of parameters of the scattered field is shown to be independent of the absorption coefficient of a medium.     

Concept of formation length in radiation theory

The features of electromagnetic processes are considered which connected with finite size of space region in which final particles (photon, electron–positron pair) are formed. The longitudinal dimension of the region is known as the formation length. If some external agent is acting on an electron while traveling this distance the emission process can be disrupted. There are different agents: multiple scattering of projectile, polarization of a medium, action of external fields, etc. The theory of radiation under influence of the multiple scattering, the Landau–Pomeranchuk–Migdal (LPM) effect, is presented. The probability of radiation is calculated with an accuracy up to “next to leading logarithm” and with the Coulomb corrections taken into account. The integral characteristics of bremsstrahlung are given, it is shown that the effective radiation length increases due to the LPM effect at high energy. The LPM effect for pair creation is also presented. The multiple scattering influences also on radiative corrections in a medium (and an external field too) including the anomalous magnetic moment of an electron and the polarization tensor as well as coherent scattering of a photon in a Coulomb field. The polarization of a medium alters the radiation probability in soft part of spectrum. Specific features of radiation from a target of finite thickness include: the boundary photon emission, interference effects for thin target, multi-photon radiation. The theory predictions are compared with experimental data obtained at SLAC and CERN SPS. For electron–positron colliding beams following items are discussed: the separation of coherent and incoherent mechanisms of radiation, the beam-size effect in bremsstrahlung, coherent radiation and mechanisms of electron–positron creation.     

Diffracted transition radiation of an ultra-high-energy relativistic electron beam in a thin single-crystal wafer

We consider diffracted transition radiation (DTR) emitted by high-energy relativistic electrons crossing a thin single-crystal wafer in the Laue geometry. The expression describing the DTR angular density is derived for the case where the electron path length in the target is much smaller than the X-ray wave extinction length in the crystal and the kinematic nature of this expression is demonstrated. It is shown that the DTR angular density in a thin target is proportional to the target thickness.     

X-ray radiation toward relativistic electrons incident on a flat target

Features of X-ray radiation emitted toward the velocity vector of relativistic electrons incident on a flat target are discussed. The contribution of polarization bremsstrahlung (PB) considered as scattering of the intrinsic field of a fast charge by electrons of the medium is estimated taking into account its dispersion properties. Spectral-angular characteristics of coherent and incoherent PB are analyzed for unstructured and structured targets. Such PB feature not only different intensities, but also different angular dependences reaching a maximum near the velocity direction of a fast charge. It is shown that coherent PB emitted from the target surface layer is characterized by an extraordinary, i.e., inversely proportional to the squared frequency, intensity dependence.     

Coherent X-ray radiation generated by a beam of relativistic electrons in a single crystal under conditions of multiple scattering

The dynamic theory of the coherent X-ray radiation of a divergent beam of relativistic electrons generated in a single-crystal wafer under conditions of the multiple scattering of incident particles is developed. Radiation cross sections are averaged over the divergent beam of rectilinear trajectories of electrons. Expressions describing the spectral-angular characteristics of parametric X-ray radiation and diffracted transition radiation under conditions of multiple scattering are obtained. Conditions under which the contribution of diffracted brehmsstrahlung can be disregarded are shown, and the spectral-angular characteristics of parametric X-ray radiation and diffracted transition radiation are calculated numerically for such conditions.     

Coherent radiation diagnostics of parameters of nanostructures at electron accelerators

The possibility of observing and diagnosing parameters of nanoobjects in a substance by using coherent X-ray radiation arising from the direct interaction of accelerated electrons with the object of interest is discussed. It is analytically shown that analysis of the generated radiation allows the microstructural features of the nanoobject to be studied. To illustrate the main conclusions, coherent radiation generated by relativistic electron scattering on fullerene is considered.     

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.     

Bremsstrahlung spectrum of nonrelativistic electrons scattered in metallic target: Theory and experiment

This work is devoted to theoretical and experimental investigation of the bremsstrahlung (BrS) spectrum of electrons with an energy of 10–30 eV scattered in a copper plate. Modeling of the photon yield from a target has been carried out taking into account the polarization BrS channel, elastic and inelastic electron scattering by medium atoms, photon absorption in the target material, and coherent effects when electrons interact with a polycrystalline structure of metal. An FEI Quanta 200 scanning electron microscope with a supplement for X-ray microanalysis was used. Good agreement between experimental and theoretical results has been obtained.     

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.     

Diffracted Transitive Radiation as a Means for Indicating the Divergence of an Ultrarelativistic Electron Beam

Russian Physics Journal - Diffracted transition radiation (DTR) emitted by a beam of relativistic electrons traversing a thin single-crystal plate in the Laue scattering geometry is considered. An...     

Spectrum broadening effect in coherent x-ray radiation of a relativistic electron crossing a single-crystal plate

Based on the dynamic diffraction theory [1], coherent x-ray radiation of a relativistic electron crossing a single-crystal plate at a constant velocity is considered in the Bragg geometry. In the general case of asymmetric reflection of the radiation from the target, expressions are derived for the spectral-angular distribution of parametric x-ray radiation (PXR) and diffraction transition radiation (DTR). For a fixed angle between the electron trajectory and the system of parallel atomic planes of the crystal (Bragg’s angle) it is shown that a decrease in the angle of electron incidence on the crystal plate gives rise to a significant increase in the PXR and DTR spectra, and the causes for spectral broadening for each of these radiation mechanisms are different. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 74–83, March, 2009.     

Incoherent properties of induced radiation

The evolution of a quantized electromagnetic field in a thermally excited dispersion medium is determined by two scattering channels. The coherent channel is formed exclusively by the elastic scattering of quanta. The incoherent channel, along with elastic scattering processes, necessarily contains inelastic scattering processes, including induced radiation. Interference between the channels is absent because of the orthogonality of the wave functions of the medium in its final states, which correspond to different scattering channels. Therefore, in an excited medium, interference processes that are not described by its refractive index may arise. An interference pattern of this kind can be formed, in particular, as a result of the superposition of the resonance radiation incident on an excited medium and the radiation reflected from this medium. In this case, the conventional perturbation theory proves to be inadequate.