For the perturbative model of a plane gravitational wave on a flat background of Minkowski space-time, electromagnetic radiation from a charged cloud in the field of a gravitational wave, detected by a remote observer, was found. It is shown that the charge density in the cloud does not change, and the radiation is generated by currents induced by the gravitational wave. The angular distribution of the radiation is obtained. If the refractive index of the cloud medium is greater than unity, Cherenkov-type radiation is generated.

For the strong gravitational wave model, an explicit transformation is obtained from a privileged coordinate system with a wave variable to a synchronous reference frame with separation of time and space variables. In a synchronous reference frame, a general form of the gravitational wave metric, solutions to the equations of trajectories for test particles in the Hamilton-Jacobi formalism, a solution to the eikonal equation for radiation, and a form of equations for the light cone of an observer in a gravitational wave were found. Using the obtained relations, the form the retarded time of radiation in the gravitational wave was found. The general relations obtained can be applied both in Einstein general theory of relativity and in modified theories of gravity. The obtained relations were applied in the work for an exact model of a gravitational wave in the Bianchi type VI universe based on an exact solution of Einstein vacuum equations.

An exact non-perturbative model of a gravitational wave with pure radiation is constructed. It is shown that the presence of dust matter in this model contradicts Einstein’s field equations. The exact solution to Einstein’s equations for gravitational wave and pure radiation is obtained. The trajectories of propagation and the characteristics of radiation are found. For the considered exact model of a gravitational wave, a retarded time equation for radiation is obtained. The obtained results are used to construct an exact model of gravitational wave and pure radiation for the Bianchi type IV universe.

The angular momentum of radiation from an arbitrarily moving relativistic charge is studied. The angular momentum is presented as the sum of the angular momentum relative to the point where the charge is located at a retarded moment of time and the angular momentum relative to an arbitrary stationary center. In particular, the instantaneous center of curvature of the trajectory is considered as such a center. Explicit expressions for the angular distribution of these components of angular momentum fluxes are obtained and studied. It is shown that the angular momentum of the field relative to the position of the charge is determined only by the properties of the electromagnetic radiation field, and the angular momentum relative to an arbitrarily distant point is the vector product of the displacement of this point and the force corresponding to radiation pressure. It is shown that in the ultrarelativistic limit, the canonical angular momentum of the radiation coincides with the angular momentum following from the symmetrized energy-momentum tensor of the electromagnetic field.

For the perturbative model of a plane gravitational wave on a flat background of Minkowski space-time, electromagnetic radiation from a charged cloud in the field of a gravitational wave, detected by a remote observer, was found. It is shown that the charge density in the cloud does not change, and the radiation is generated by currents induced by the gravitational wave. The angular distribution of the radiation is obtained. If the refractive index of the cloud medium is greater than unity, Cherenkov-type radiation is generated.

We study theoretically by means of quantum electrodynamics the vortex radiation of a relativistic electron in a uniform magnetic field. The exact expressions for the probability of emission of a photon with a certain angular momentum are found. The classical asymptotics ħ→0 of this probability does not match the angular momentum flux density calculated by the classical method using the symmetrized energy-momentum tensor. Although the flux of angular momentum integrated over the radiation directions is the same in both cases. We found the angular momentum flux of the radiation field using the canonical (not symmetrized) energy-momentum tensor and showed that the flux obtained in this way coincides with the classical limit for the probability of photon emission.

We provide an explicit calculation to check that Newtown's third law holds for non-parallel currents if the field momentum is accounted for. In textbooks of electrodynamics, it is usually noted that in the interaction of non-parallel current elements, the action force is not balanced by the reaction force, though these forces are balanced in the interaction of two closed current-carrying loops. In the case of non-closed current segments the change in the momentum stored in the field should be taken into account. Using a simple model of two non-parallel straight current segments we show how it works. As such a model, two straight orthogonal to each other conductors are considered, with equal charges of opposite signs at the ends of each conductor. For some interval of time, a direct current is supported in the conductors. We show that the total momentum of the system is conserved.

Radiation of a charged particle moving in a cylindrical channel with elastic walls is studied. We assume that the particle in the channel is in free motion, periodically colliding with the channel wall. Explicit expressions for the spectrum and angular distribution of radiation are obtained. These results can be used to calculate the spectrum and radiation intensity of charged particles in carbon nanotubes of relatively great diameter. The emission spectrum is essentially a bremsstrahlung one, however, periodic collisions of the particle with the wall lead to coherent amplification of radiation at frequencies that are multiples of the collision frequency. If a beam of particles is channeled, then the multiple spectral lines merge into a continuous spectrum.

The flux of angular momentum of electromagnetic field of an arbitrarily moving point charge is investigated. General equations are obtained for the transfer of angular momentum at arbitrary distance from the charge, and corresponding equations in the far-field approximation. An explicit expression is obtained for the flux of angular momentum in the wave zone in terms of coordinates, velocity, and acceleration of the charge. The torque is calculated, that would act on an object if it absorbed all the radiation incident on it. It is shown that this torque is proportional to the curl of the stress tensor of the electromagnetic field; in the far field approximation the torque is proportional to the curl of the Poynting vector.

Dynamics and radiation of a relativistic charged particle moving in a linear restoring force field is studied. Solutions to the equations of motion are presented in a compact form in terms of Jacobi elliptic functions. The intensity of radiation, its angular distribution and radiation spectrum of a relativistic oscillator are investigated. It is shown that, unlike a non-relativistic oscillator, the maximum intensity is emitted not at the turning points, but at some intermediate points of the particle’s trajectory. The emission spectrum consists of lines at frequencies that are multiples of the oscillation frequency of the oscillator. As the oscillator energy increases, the number of harmonics in the spectrum increases. The maximum in the spectrum of highly relativistic oscillator occurs on high numbers of harmonics.

The angular momentum of radiation related to the passage of relativistic particles in a cylindrical channel is studied theoretically. To enhance the angular momentum of radiation, it is proposed to place the channel in a strong magnetic field parallel to the channel axis. The trajectories of the particles in the channel, the conditions for trapping particles in the channeling mode are investigated and equations for calculating the orbital angular momentum of radiation are obtained. It is shown that the angular momentum of radiation of a uniform beam of particles in the channel is not equal to zero only if the particles enter the channel at an angle greater than the critical angle. A significant difference between vortex radiation from a bunch of cylindrical channels (for example bunch of carbon nanotubes) from laser or undulator radiation is that the radiation beam of the latter has only one vortex axis. While the radiation from the beam of cylindrical channels has one vortex axis per each channel. Dependence of the angular momentum of radiation on the value of magnetic field and on the incident angle is studied.

We study theoretically the vortex radiation of a relativistic charged particle. General expressions for the spectral and angular distributions of angular momentum of radiation are derived for an arbitrary moving charge. Special attention is given to calculation of the angular momentum of synchrotron radiation. We obtain the spectrum and the angular distribution of angular momentum carried by synchrotron radiation. Similar expressions for the angular momentum of radiation of a charge moving on a spiral trajectory are derived by use of Lorentz transformations. It is shown that the main part of angular momentum in this case is emitted at a small angle to the vortex axis. Relativistic charged particles at spiral motion are effective source of the vortex photon beams at wave lengths ranging from radio waves to gamma rays. The obtained equations can be used for calculations of the angular momentum emitted by charged particles in the helical undulators and at axial channeling in solid crystal.

The effective potential energy of the particles in the field of rotating uniformly magnetized celestial body is investigated. The axis of rotation coincides with the axis of the magnetic field. Electromagnetic field of the body is composed of a dipole magnetic and quadrupole electric fields. The geometry of the trapping regions is studied as a function of the magnetic field magnitude and the rotation speed of the body. Examples of the potential energy topology for different values of these parameters are given. The main difference from the classical Størmer problem is that the single toroidal trapping region predicted by Størmer is divided into equatorial and off-equatorial trapping regions. Applicability of the idealized model of a rotating uniformly magnetized sphere with a vacuum magnetosphere to real celestial bodies is discussed.

We study theoretically the angular momentum of radiation emitted at axial channeling of the fast particles in a crystal or in a bunch of micro- or nanotubes placed in strong magnetic field. It is shown that high energy particles channeled in the presence of magnetic field are effective source of vortex radiation in the X-ray and gamma range of photons energies. We show that there are two factors that increase the angular momentum of emitted radiation in the presence of magnetic field. First, the magnetic field favours additional "twisting" of the channeled particles in a certain direction and, secondly, the particles that have the corresponding initial angular momentum are predominantly captured into the channeling mode. Dependence of the angular momentum of radiation on the value of magnetic field and on the incident angle is studied.

The mode of propagation of relativistic, positively charged particles through a system of mutually oriented and periodically arranged ultrathin crystals whose thicknesses are equal to the half-period of the particle trajectory during planar channeling in a thick crystal is considered. In the case of an incidence angle that is less than the critical channeling angle, a certain fraction of particles is specularly reflected from the atomic planes of the crystal. Therefore, passing through a stack of crystals, a particle moves along quasiundulator trajectories. The characteristics of the radiation of a particle passing through such a “multicrystal microundulator” are found. The radiation spectrum is discrete, and the first-harmonic frequency and the number of harmonics in the spectrum are dependent on the distance between the crystals, the particle energy, and the potential of atomic planes of the crystal. Radiation is concentrated in a narrow cone in the direction of the average velocity of particles and is mainly polarized in a plane that is orthogonal to the atomic planes of the crystal. The microundulator can be composed of separate crystals with micron thicknesses and can be fabricated using modern methods of microlithography and micromechanics with deep, for example, plasmochemical etching of the crystal surface.

The radiation at grazing incidence of relativistic positively charged particles on the crystal surface in the presence of magnetic field is studied theoretically. The magnetic field is supposed to be parallel to the surface. Dependent on the initial conditions the particle can be captured in the channeling mode and perform periodic oscillations along the surface of the crystal. The spectrum, angular distribution and polarization of radiation are calculated. The emission spectrum of a single particle is discrete and it extends up to very large numbers of harmonics. If the magnetic field is much weaker than the electric field of atoms, the frequency range of radiation of the particle beam does not depend on magnetic field and is defined solely by the energy of the particles and by the surface averaged potential, though the frequency of the first harmonic is defined only by the magnetic field. In case of channeled positrons the characteristic energy of the emitted photons is of order 10γ3/2 (eV), where γ is the particle relativistic factor. The main part of radiation is bound to a narrow cone and is polarized largely orthogonal to the surface of the crystal.

Radiation of positrons passing through a set of equidistant crystal plates is calculated. Each plate is of thickness of half of the particle trajectory period at planar channeling in a thick crystal. Positively charged particle entering the first plate at an angle smaller than the critical channeling angle is captured into channeling mode and changes the direction of its transversal velocity to reversed. Between the half wave plates the particle moves along a straight line. The proposed setup can be realized as a set of equidistant ridges on the surface of a single crystal. Passing through such set of half-wave crystal plates the particle moves on quasi-undulator trajectories. Properties of the particle radiation emitted during their passage through such "multicrystal undulator" are calculated. The radiation spectrum in each particular direction is discrete, and the frequency of the first harmonic and the number of harmonics in the spectrum depend on the distance between the plates, on energy of the particles and on the averaged potential energy of atomic planes of the crystal. The radiation is bound to a narrow cone in the direction of the average particle velocity and polarized essentially in a plane orthogonal to the atomic planes in the crystal. (C) 2016 Elsevier B.V. All rights reserved.

Although the electromagnetic field of a given distribution of charge and current is unambiguously defined by the Maxwell equations, there is no unique inverse correspondence between this field and point-like sources. We prove this statement for electric and magnetic dipoles and discuss two examples when the same field at some point or in some region is generated by either a dipole or an electric charge that are varying in different ways. The electric and magnetic fields of the charge depend on its speed and the distance between the charge and the observation point. It is shown that it is possible to find a law of motion for the charge in which the variation in the distance to the observer is compensated for by variation in the velocity of the charge. One particular example of the motion of a charge is discussed, wherein the electric and magnetic fields at a specific point of observation remain constant. The issues discussed could be of interest to both scientists and scholars.

The conditions of channeling of relativistic positively charged particles near the surface of a crystal in the presence of a magnetic field parallel to the surface are studied. It is shown that the emission spectrum of a single particle is discrete. The frequency of the first harmonic and the number of harmonics, making a significant contribution to the spectrum depend strongly on the initial coordinates and velocities of the particles. When averaged over the initial coordinate of the particle, the spectrum becomes continuous. The spectral range in which the radiation of parallel beam of particles is generated, does not depend on the magnetic field and is determined only by the energy of the particles and the averaged potential of the surface atomic layer. Radiation is concentrated in a narrow cone in the direction of the average velocity of the particles and polarized essentially in the plane orthogonal to the crystal surface. (C) 2015 Elsevier B.V. All rights reserved.

The field of a uniformly magnetized rotating sphere is studied with special attention to the surface where the electric and magnetic fields are orthogonal to each other. The equation of this surface, valid at arbitrary distances from the rotating magnetized sphere, is obtained. Inside the light cylinder this surface can be considered as a force-free surface, i.e. as a place where the particles with strong radiation damping can be trapped due to their energy loss. Outside the light cylinder this surface makes just a geometric locus which moves with a superlight velocity around the axis of rotation. The 2- and 3-dimensional plots of the force-free surface are constructed. Estimation of influence of the centrifugal force on the particle dynamics is made. It is shown, that in case of strong magnetic field the centrifugal force is negligible small everywhere except a narrow neighbourhood of the light cylinder.