The work based on a semiclassical description, presents the results of studying the processes of absorption and radiation of a field in the form of a standing wave in a waveguide filled with a two-level active medium. Under conditions of spatial inhomogeneity of the field intensity, interference of quasi-periodic oscillations of population inversion occurs in different local regions of the waveguide. A quasiperiodic change in population inversion is determined by the Rabi frequency, which is known to be associated with the probability of induced radiation with a positive population inversion, or induced absorption with its negative value. Since the population inversion change is accompanied by absorption or emission of field quanta, this leads to the exchange of energy between the field and the active medium located in the waveguide. It is shown that the attenuation of a large-amplitude field to a waveguide filled with an unexcited active medium is nonlinear. In the developed mode, this process has the character of energy exchange between the field and the active medium. In this case, the wave attenuation is replaced by its growth, just as it happens in the well-known case of Landau kinetic damping. Competition of the processes of radiation and absorption leads to the fact that the nature of the oscillations (nutations) of the population inversion at different points of the waveguide space is different. The interference of nonsynchronous spatially localized oscillations of the population inversion in the volume of the waveguide leads to changes in the field amplitude. The paper also discusses the process of field excitation in a waveguide with a pre-inverted two-level active medium, taking into account external mechanisms for the absorption of wave energy. Consideration of these problems is important for understanding the processes of generation of induced radiation, which, as noted by C. Towns, is to a large extent coherent radiation.

The development of one-dimensional parametric instabilities of intense long-wave plasma waves is considered in terms of the so-called hybrid models, when electrons are treated as a fluid and ions are regarded as particles. The analysis is performed for both cases when the average plasma field energy is lower (Zakharov's hybrid model -ZHM) or greater (Silin's hybrid model -SHM) than the plasma thermal energy. The efficiency of energy transfer to ions and to ion perturbations under the development of the instability is considered for various values of electron-to-ion mass ratios. The energy of low-frequency (LF) oscillations (ion-sound waves) is found to be much lower than the final ion kinetic energy. We also discuss the influence of the changes in the damping rate of the high-frequency (HF) field on the instability development.Reduced absorption of the HF field leads to the retardation of the HF field burnout within plasma density cavities and to the broadening of the HF spectrum. At the same time, the ion velocity distribution tends to the normal distribution in both ZHM and SHM.

In this paper, the self-consistent model was considered, consisting of a system of oscillators, the coupling between them was assumed to be integral (due to the fields formed as a result of their co-radiation). With the help of this model, the features of synchronization by waves of finite amplitude of a system of oscillators were refined, the initial phase values of which are random. The effect of nonlinearity, in particular, due to the change in the mass of the oscillator due to relativistic effects, was taken into account. It was shown that the nonlinearity does not violate the nature of the energy exchange between the wave and the oscillator system, leading only to a slight decrease in the efficiency of such an exchange. KEYWORDS: oscillator, nonlinearity, synchronization, energy exchange пл. Свободы 4, 61022, Харьков, Украина В данной работе была рассмотрена самосогласованная модель, состоящая из системы осцилляторов, связь между которыми предполагалась интегральной (за счет полей, формируемых в результате их совместного излучения). С помощью данной модели были уточнены особенности синхронизации волнами конечной амплитуды системы осцилляторов, начальные значения фаз которых являются случайными. Был проведен учет влияния нелинейности, в частности, обусловленной изменением массы осциллятора за счет релятивистских эффектов. Было показано, что нелинейность не нарушает характер обмена энергией между волной и системой осцилляторов, приводя лишь к небольшому снижению эффективности такого обмена. КЛЮЧЕВЫЕ СЛОВА: осциллятор, нелинейность, синхронизация, обмен энергией Synchronization of systems of oscillators which drew the attention of C. Huygens as early as in the seventeenth century, was discussed by many researchers [1,2]. The influence of external periodic force is able to adjust the parameters of the oscillator and its phase. Therefore, synchronization is often referred to as "locking" of frequency and/or phase [3,4].The most efficient synchronization of a large number of oscillators occurs under the influence of a strong external force or under the impact of already synchronized oscillators.The coupling between the oscillators can be local due to their mutual non-linear influence or have integral nature due to the fields generated by their joint radiation. Of great interest are the various parametric mechanisms affecting the efficiency of interaction of oscillators [5,6], although in this work, we neglect their direct interaction. Instead, we focus on the case when independent oscillators interact via the common field (generated by them and influencing them).An important factor of interest to this case is the apparent self-consistency of the described systems and the great practical importance of such problems. The considered models are able to clarify some useful properties of oscillators' synchronization by the finite-amplitude waves when initial phases of oscillators are random. Also, we studied nonlinear effects, particularly caused by the change of the oscillator's mass due to the relativity effects.So, ...

The paper considers the development of the process of superradiance of radiating oscillators interacting with each other by means of an electromagnetic field. The interaction of oscillators occurs both with the nearest neighbors and with all other oscillators in the system. In this case, the possibility of longitudinal motion of oscillators along the system, due to the action of the Lorentz force, is taken into account. It is shown that, regardless of the motion of the oscillators, for example, due to their different masses, the maximum attainable amplitude of the generation field changes little. However, the radiation efficiency depends on how this field is distributed in the longitudinal direction. In the case of a shift of the field maximum towards the ends of the system, the radiation efficiency can noticeably increase. In addition, the direction of the phase velocity of the external initiating field is important, which accelerates the process of phase synchronization of the oscillators. This can also affect the ejection of particles outside the initial region, and here the total number of ejected particles and their speed turn out to be important. It is discussed how the density of oscillators and the size of the region occupied by oscillators will change.

The paper presents the results of the study of the models of convective instability near its threshold of thin layers of liquid and gas bounded by poorly conducting walls. These models single out one spatial scale of interaction, leaving the possibility for the evolution of the system to choose the symmetry character. This is due to the fact that the conditions for the realization of the modes of convective instability near the threshold are chosen. All spatial perturbations of the same spatial scale, but of different orientations, interact with each other. It turned out that the presence of minima of the interaction potential of the Proctor-Sivashinsky equation modes, the absolute value of the wave number vectors of which is unchanged, determines the choice of symmetry and, accordingly, the characteristics of the spatial structure. In the case of a more realistic model of convection described by the Proctor-Sivashinsky equation, it was possible to observe both the first-order phase transition and the second-order phase transition and detect the form of the state function, which is responsible for the topology of the resulting convective structures: metastable rolls and stable square cells. In this paper, it is shown that the nature of the structural-phase transition in a liquid when taking into account the dependence of viscosity on temperature in the Proctor-Sivashinsky model is similar to the case of the absence of such a dependence. The transition time turns out to be the same, despite the fact that a different structure is formed -hexagonal convective cells. As in the Swift-Hohenberg model, a hard mode for the formation of hexagonal cells in a gas medium is possible only for a sufficiently noticeable dependence of its viscosity on temperature. The phase transition times are inversely proportional to the difference in the values of this function for two consecutive states. A similar description of phase transitions did not use phenomenological approaches and various speculative considerations, which allows for a closer look at the nature of transients.

The paper shows that the waves of anomalous amplitude are long-lived formations. They drift in the direction of the wave motion with the group velocity of the wave packet, which is half the phase velocity of the main wave. The swing of the wave (the distance from the hump to the trough) of the anomalous amplitude is more than three times the average value of the sweep of the wave motion. The modulation instability of this wave form a perturbation spectrum, the energy of which is twice the energy of the main wave in the developed process mode. The spatial size of the wave packet practically does not change, the amplitude of the swing in the maximum first increases, then gradually decreases. The number of such waves in areas of strong wind exposure is much larger than the statistics of random interference processes allow. This is due to the influence of the main wave (its amplitude remains noticeably greater than the amplitudes of each of the modes of the wave packet) on the behavior of each pair of modes from the wave packet of the perturbation. In the laboratory system, the duration of the anomalous wave coincides qualitatively with the time of existence of the Peregrin autowave. Although the Peregrin autowave corresponds to a different physical reality, where the dispersion of the wave is weak. Gravitational surface waves have a strong dispersion, and the NSE equation in this case is noticeably modified. However, in rest system of the wave packet (moving relative to the laboratory system) the abnormal amplitude wave lifetime is much longer. The distance that the wave packet travels with a persisting anomalous sweep is at least equal to several hundred wavelengths and can reach hundreds of kilometers. A simple calculation of such waves by means of space monitoring due to the small viewing area (frame) may be inaccurate. Once formed, such waves are able to drift over considerable distances. However, they may well get into the next frame of view. That is, estimates of the number of such waves can be overestimated.

The consequences of the development of the modulation instability of an intense wave field in a waveguide filled with plasma are considered. It is shown that in the mode of developed instability, the amplitude of the main wave under conditions of its weak absorption decreases by three to four times. The average energy density of the instability spectrum is almost twice the energy density of the main wave. The amplitude of the modulation envelope is three times the average amplitude of the main wave. The frequency of occurrence of anomalous modulation bursts is estimated.

In the article, for limited system conditions that form the spatial structure of the field, the attenuation processes of wave packets of finite amplitude are considered. The line width of the wave field may be the result of the dissipative processes (in a quantum system it is inverse of the lifetime of energy levels) or the result of reactive processes (in classical waveguide systems this is the spectral width of the packet). In the case of filling the waveguide with an active two-level medium, a description is possible using a quasiclassical model of the interaction of the field and particles. In this case, the quantum-mechanical description of the medium is combined with the classical representation of the field. Here, the Rabi frequency plays an important role, which determines the probabilities of induced radiation or absorption of field quanta and the oscillatory change in population inversion (nutation). Depending on the relationship between the Rabi frequency and the line width of the wave packet, the process can change the nature of the field behavior. In strong fields or with a significant population inversion, the line width can be neglected, while the field energy density is quite high. In this case, one should expect noticeable nutations of population inversions with different frequencies corresponding to the local Rabi frequency in different regions of the waveguide, the interference of which will determine the oscillatory behavior of the wave field. At a low level of electric field intensity or a slight population inversion, the mode of changing the field amplitude becomes monotonic. Plasma field damping (Landau damping) is considered. The role of population inversion is assumed by a quantity proportional to the derivative with respect to velocity of the electron distribution function. If the spectral width of the packet is small, the process of wave attenuation acquires a characteristic oscillatory form due to the exchange of energy between the wave and the plasma electrons captured by its field. The attenuation of wide packets is almost monotonic with the formation of a characteristic “plateau” in the vicinity of the phase velocity of the wave on the electron velocity distribution function.