Vol 163, No 4 (2023)

The integral over time of an electric or magnetic field in infinite limits (Bessonov integral) is considered; it is shown that it is equal to zero for any configuration of the free electromagnetic field with zero total energy. The connection between zero Bessonov integral and the impossibility of emission or absorption of a photon by a free charged particle is investigated. Exact expressions for the radiation field as well as its Fourier transform are obtained for an electric charge with an abrupt change in the velocity; it is shown that the Bessonov integral of such a radiation field equals zero as follows from the general statement. In conclusion it is shown that a nonzero Bessonov integral of the radiation field produced by an electric charge moving with acceleration, which has been reported in a number of publications, appears because of the incorrect decomposition of the total field of the accelerated charge into the radiative and nonradiative components.

To consider the evolution of current distribution in inhomogeneous thin conductive layers or foils, we apply an integrodifferential equation, which reduces the three-dimensional problem for the magnetic field to a two-dimensional problem, and, for the current distribution across the width of inhomogeneous conductive sheets or foils, this equation reduces the two-dimensional problem for the magnetic field to a one-dimensional problem. For homogeneous conductive layers with constant conductivity, the spatial scale of current distribution, initially concentrated in a limited area, increases proportionally to time at a rate of u = c2/4πσΔ, where σ is the conductivity of the layer material and Δ is its thickness. As an application to the problems of current transfer through electroexplosive opening switches, a current distribution across the width of a foil is considered for a periodic serpentine-type system of flat foils. It is shown that initially a current distribution corresponding to the perfect conductivity of foils is established in this system. Then, in a time on the order of s/u (2s is the width of a foil), the current distribution in the foil relaxes to a uniform distribution. Estimates show that if the foils are used as opening switches, then currents through the foils during the current transfer to the load are expected to have time to get uniformly distributed across their width; therefore, corrections for the nonuniformity of the current distribution in the switches should be small.

The main objective of this article is to examine some physically viable solutions through the Noether symmetry technique in f ( R, T 2) theory. In order to investigate Noether equations, symmetry generators and conserved quantities, we use a speci c model of this modi ed theory. We nd exact solutions and examine the behavior of various cosmological quantities. It is found the behavior these quantities is consistent with current observations indicating that this theory describes the cosmic accelerated expansion. We conclude that generators of Noether symmetry and conserved quantities exist in this theory.

The properties of nonlinear parametric resonance are investigated using the example of the low-mode Parker dynamo model. This model is a system of four ordinary differential equations and in the simplest approximation describes the processes of generation and oscillation of large-scale magnetic fields in stellar systems. In the absence of nonlinear effects, the problem under consideration, by analogy with a system of harmonic oscillations, admits an asymptotic division of multiple resonant frequencies. However, despite the fact that at first glance at these frequencies it is reasonable to expect an amplification of the amplitude in the nonlinear case, it is demonstrated that in the presence of nonlinear terms, the behavior of the system is significantly more complex. In particular, generation suppression can be observed at resonant or low frequencies, while amplification occurs in the immediate vicinity of the resonance or at sufficiently high frequencies. The reasons are discussed for this behavior, as well as the possibility of the influence of parametric resonance on the establishment of planetary dynamo cycles.

An isotopic effect arising from the substitution of superheavy water molecules for normal water molecules in ice (Ih) has been studied by the lattice dynamics method in a quasi-harmonic approximation using a rigid three-point potential modified to reproduce the superheavy water properties. It has been shown that the considerable variation of the vibrational state density upon substituting 12.5, 50, and 100% of water molecules takes place only in the range of libration. The temperature dependence of the superheavy ice density has been calculated, and the density maximum for this ice near 60 K has been predicted. A relationship between the melting point of (T2O + H2O)-ice Ih and the T2O molecule concentration in its structure has been constructed, and this relationship has been found to be linear.

The appearance of a thermogravitational convective flow in the bulk of a layer of normal liquid helium He-I h ≈ 1–3 cm deep in a wide cylindrical cell, which is heated from above in the gravity field in the temperature range Tλ ≤ T ≤ Tm, is accompanied by the excitation of a vortex flow on the free surface of the liquid. Here Tλ = 2.1768 K is the temperature of transition of liquid 4He from the superfluid He-II to the normal He-I state at the saturated vapor pressure, and Tm ≈ 2.183 K is the temperature at which the He-I density passes through a maximum. Bulk convection serves as a source of energy pumped into the vortex system on the surface of He-I. The nonlinear interaction of vortices on the surface with each other and with convective vortex flows in the bulk of the layer leads to the formation of two large-scale vortices (vortex dipole) on the surface of He-I, and their sizes are limited to the diameter of the working cell and several times exceed the layer depth. This behavior corresponds to the transition from the vortex flow mode on “deep water” (vortices on the surface of a three-dimensional liquid layer) to vortices on the surface of “shallow water” (vortices on the surface of a two-dimensional layer) in time. When the layer is heated further above Tm, the convective flows in the bulk decay quickly, but the vortex motion on the surface of a two-dimensional He-I layer is retained. In the absence of energy pumping from the bulk, the total energy of the vortex system on the surface of a shallow water layer decreases in time according to a near-power law because of the nonlinear interaction of large-scale vortices with each other and friction against the cell walls. As a result, during long-term observations, small-scale vortices with sizes comparable to or less than the layer depth again begin to prevail on the surface of He-I, which corresponds to the transition from a two-dimensional to a three-dimensional liquid layer. The energy of the vortex flow on the surface of a deep water layer decreases according to a near-exponential law. Thus, long-term observations of the dynamic phenomena on the free surface of an He-I layer several centimeters deep in a wide temperature range above Tλ allowed us, for the first time, to study the excitation, evolution, and decay of the vortex flows on the surface of a deep or shallow water layer in one experiment.

The injection of a pure spin current into a conducting helimagnet is investigated. The characteristic decay lengths for the spin current injected into the helimagnet are determined, and their physical meaning is described. It is shown that instead of the spin diffusion length, helimagnets are characterized by the decay length that is always smaller than the spin diffusion length, the difference in these lengths being determined by the ratio of the helimagnet spiral period to the spin diffusion length. We predict the existence of the “effect of the chiral polarization of a pure spin current,” i.e., the emergence of the spin current with longitudinal (transverse) polarization, which depends on the spiral chirality, upon the injection of a pure spin current with the transverse (longitudinal) polarization relative to the spiral axis.

The known methods for measuring the spin transport parameters in spin-valve structures are based on the Hanle effect, viz., electron spin precession in an external magnetic field and a decrease in the magnetoresistive signal. These methods make it possible to determine the spin relaxation time in the paramagnetic layer and the relative current polarization constant. We describe an alternative method of measuring in zero external magnetic field, which is based on the resonant increase in the magnetic susceptibility of the paramagnetic layer due to the paramagnetic resonance induced by the nonequilibrium magnetization due to the spin accumulation effect. The proposed method makes it possible to determine the absolute value of spin accumulation in a paramagnet, which can be used as a parameter for numerical solution of three-dimensional diffusion equations of spin transport.

Two chemical models of the plasma, which describe the mixture of free electrons, ions, and atoms, are derived using identity transformations based on the equation of state of the “physical” model of the plasma, in which an interacting mixture of electrons and nuclei (protons) us considered. These chemical models satisfy Onsager’s bookkeeping rule (the equation of state is independent on the position of the bookmark, viz., the boundary separating free and bound states). The effect of excited states of an atom on the equation of state and ionization equilibrium is analyzed. It is concluded that the contribution of the Debye attraction in traditional “chemical” models is overestimated. The relations obtained for the ionization potential lowering and the equations of state differ significantly from the generally accepted expressions and explain qualitatively the experimentally observed effect of “ideality” of a nonideal plasma.