Doppler effect in the oscillator radiation process in the medium

The purpose of this paper is to investigate the radiation process of the charged particle passing through an external periodic field in a dispersive medium. In the optical range of spectrum we will consider two cases: first, the source has not eigenfrequency, and second, the source has eigenfrequency. In the first case, when the Cherenkov radiation occurs, the non-zero eigenfrequency produces a paradox for Doppler effect. It is shown that the absence of the eigenfrequency solves the paradox known in the literature. The question whether the process is normal (i.e. hard photons are being radiated under the small angles) or anomalous depends on the law of the medium dispersion. When the source has an eigenfrequency the Doppler effects can be either normal or anomalous. In the X-ray range of the oscillator radiation spectrum we have two photons radiated under the same angle- soft and hard. In this case the radiation obeys to so-called complicated Doppler effect, i.e. in the soft photon region we have anomalous Doppler effect and in the hard photon region we have normal Doppler effect.Comment: 6 pages, no figure

On the Possibility of Medium-Energy Compact X-ray Free-Electron Laser

The problem of X-ray Free-Electron Laser operating on self-amplified spontaneous emission in irregular microundulator is considered. The case when the spectrum width of spontaneous radiation is conditioned by the spatial distribution of sources creating the undulating field is considered. In this case gain function of the stimulated radiation is dozens of times higher than that of the conventional undulators. We propose a model of irregular microundulator, which can be used to construct a drastically cheap and compact X-ray free-electron laser operating on medium energy electron bunch.Comment: 6 pages, 5 figures, revtex4, accepted by Armenian Journal of Physic

Exact solutions of the Einstein equations for an infinite slab with a constant energy density

We find exact static solutions of the Einstein equations in the spacetime with plane symmetry, where an infinite slab with finite thickness and homogeneous energy (mass) density is present. In the first solution the pressure is isotropic, while in the second solution the tangential components of the pressure are equal to zero. In both cases the pressure vanishes at the boundaries of the slab. Outside the slab these solutions are matched with the Rindler spacetime and with the Weyl-Levi-Civita spacetime, which represent special cases of the Kasner solution.Comment: Final version, published in Physics Letters

Casimir densities for a plate in de Sitter spacetime

Wightman function, the vacuum expectation values of the field squared and the energy-momentum tensor are investigated for a scalar field with general curvature coupling parameter in the geometry of a plate in the de Sitter spacetime. Robin boundary condition for the field operator is assumed on the plate. The vacuum expectation values are presented as the sum of two terms. The first one corresponds to the geometry of de Sitter bulk without boundaries and the second one is induced by the presence of the plate. We show that for non-conformal fields the vacuum energy-momentum tensor is non-diagonal with the off-diagonal component corresponding to the energy flux along the direction perpendicular to the plate. In dependence of the parameters, this flux can be either positive or negative. The asymptotic behavior of the field squared, vacuum energy density and stresses near the plate and at large distances is investigated.Comment: 15 pages, 3 figures, figure 1 changed, figure 3 and references added, to appear in Class. Quantum Gra