June solstice is considered as a period with the lowest probability to observe typical equatorial plasma bubbles (EPBs) in the postsunset period. The severe geomagnetic storm on 22-23 June 2015 has drastically changed the situation. Penetrating electric fields associated with a long-lasting southward IMF support favorable conditions for postsunset EPBs generation in the dusk equatorial ionosphere for several hours. As a result, the storm-induced EPBs were progressively developed over a great longitudinal range following the sunset terminator. The affected area has a large longitudinal range of~100°in the American sector and a rather localized zone of~20°in longitude in the African sector. Plasma depletions of equatorial origin were registered at midlatitudes (30°-40°magnetic latitude) of both hemispheres in the African and American longitudinal sectors. We examine global features of the large-scale plasma depletion by using a combination of ground-based and space-borne measurements-ground-based Global Positioning System/Global Navigation Satellite System (GPS/GNSS) networks, Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) GPS Radio Occultation (RO), Swarm upward looking GPS data, and in situ plasma density observations provided by Swarm, Communications/Navigation Outage Forecasting System (C/NOFS), and Defense Meteorological Satellite Program (DMSP) missions. Joint analysis of the satellite observations revealed that these storm-induced EPBs structures had extended over 500 km in altitude, at least from~350 to~850 km. These irregularities caused strong amplitude and phase scintillations of GPS/GNSS signals for ground-based and space-borne (COSMIC RO) measurements and seriously affected performance of navigation-based services.

On the basis of the Landau kinetic equation a generalized Lorentz model is proposed, which contrary to the standard model, considers ion system as an equilibrium one. For electron system kinetic equation of the Fokker-Planck type is obtained. In the Bogolyubov method of the reduced description, which is based on his idea of the functional hypothesis, basic equations for electron hydrodynamics construction with account for temperature and macroscopic velocity relaxation processes (kinetic modes of the system) is elaborated. The obtained equations are analyzed near the end of the relaxation processes when the theory has an additional small parameter. The main in small gradients approximation is studied in details, it corresponds to the description of relaxation processes in a spatially uniform case. The obtained equations are approximately solved by the method of truncated expansion in the Sonine polynomials. The velocity and temperature relaxation coefficients are discussed in one- and two-polynomial approximation. As a result the relaxation coefficients are calculated in one-polynomial approximation.

In the framework of the Bogoliubov method of reduced description of nonequilibrium states, which is based on his functional hypothesis, we obtain a kinetic equation for arbitrary inhomogeneous electron states in a polar crystal in the presence of a strong electric field. Using the reduced description method, we study the equalization of velocities and temperatures of the polaron gas with a small density and the phonon subsystem in the presence of a weak electric field in the spatially homogeneous case. We establish that the nonequilibrium distribution function of a polaron differs from the Maxwell distribution even in the approximation that is linear in small differences between the subsystem velocities and temperatures. We calculate the corresponding relaxation times and polaron mobility.

The process of self-ordering in the famous Dicke model was studied in the framework of eliminating the boson variables. But the reduced description method enables us to obtain also the picture of electromagnetic field evolution provided field amplitudes and correlation functions are included into the number of reduced description parameters. In the Dicke Hamiltonian structure the interaction term includes the operators of emitter dipole moments or dipole moment density (polarization) since a spatial system is under consideration. Thus operator evolution equations are based on using such operators and their derivatives. The chain of evolution equations for averaged field amplitudes and binary correlation functions are obtained with using the statistical operator calculated in a perturbation theory in quasispin-photon interaction assumed to be small. The problem of chain decoupling does not arise since at any step we have a closed set of equations. The sets should be solved on the basis of material equations for current density and their generalizations for more complicated correlation functions. The way to constructing such equations and estimating the material parameters which are necessary for the numerical modeling of the development of correlations is discussed in the paper.

Kinetics of electromagnetic field in noneqilibrim medium of atoms is studied on the basis of the Dicke model. The field is described by average electric and magnetic fields and their binary correlations. The atoms are considered in two-level approximation and assumed to be fixed in the space. States of the medium are described by the energy density. Nonresonant atom-field interaction is accounted phenomenologically. The theory is built on the Bogolyubov idea of the functional hypothesis that is the basis of his method of the reduced description of nonequilibrium processes. The investigation of the system is carried out in the framework of the Peletminsky–Yatsenko model. Atom-field interaction is assumed to be small and is taken into account up to the second contributions in the interaction included. Average electric and magnetic fields satisfy the Maxwell equations. Material equations for them express average current and charge densities through the average field. Evolution equations for the binary correlation of the field are constructed. Material equations for these equations express correlations field-current trough correlations field-field. The time equation for energy density of the medium is obtained. Density evolution is governed by the average field and field correlations. All material coefficients of the system are found.