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The article discusses the processes of designing, developing and launching an online course "The basics of programming for schoolchildren" for the center of pre-university training in a pandemic. The choice of the top-level design model SAM1 for courses that need to be developed and launched in a short time without complete data on the target audience is substantiated. The advantages of choosing a backward design model for developing the content of the target course are shown. Using the method of backward design, the course "The basics of programming for schoolchildren" was designed and developed. The program of the course is presented in the form of a sequence of modules and individual topics. The use of gamification elements based on the "VKontakte" social network has been substantiated. Examples of educational activities are given. A link is given to the developed course posted in LMS Moodle Donetsk Academy of Management and Public Administration.

Cerebral palsy is a group of developmental disorders affecting motor skills and postural maintenance, leading to motion defects due to non-progressive damage and/or a developing brain anomaly in the fetus or the newborn child. Leg muscle weakness and spasticity associated with cerebral palsy limit the range of motion in the ankle joint and negatively affect the childs motor ability. This article reviews scientific studies on an innovative method of functional electrical stimulation of walking in children with cerebral palsy. We searched for information in the Scopus, Web of Science, Medline, The Cochrane Library, PubMed, Pedro, Scholar, eLibrary, and CyberLeninka databases. The efficiency of remedial treatment of motion using functional electrical stimulators was assessed using biomechanical and neurophysiological methods of evidence-based medicine. When children are rehabilitated using electrical stimulation techniques such as functional electrical stimulation, the gait is restored significantly, dorsiflexion is improved, the gait pattern is normalized, stability when walking is increased, the number of falls is decreased, and the need for additional support is reduced. The effect of functional electrical stimulation on the normalization of walking speed, gait kinematics and symmetry, the ability to overcome obstacles, and the range of motion of the ankle joint and foot clearance during walking are discussed. In addition, the work analyzes the effect of functional electrical stimulation on reducing the patients energy consumption when walking, normalizing muscle tone, decreasing the risk of falls, and increasing confidence and comfort when walking. As part of this analysis, the speed of adaptation and patient tolerance of the devices for functional electrical stimulation are also discussed. A comparative characteristic of functional electrical stimulation using ankle joint orthoses is provided. CONCLUSIONS: For many years, movement dynamics have used functional electrical stimulation technologies to rehabilitate neurological patients after stroke and multiple sclerosis. It is only a matter of time before these technologies also become the standard treatment for children with cerebral palsy in rehabilitation programs.

The last decade has contributed to the rapid progress in the gyrotron development. Megawatt-class, continuous wave gyrotrons are employed as high-power millimeter (mm)-wave sources for electron cyclotron heating (ECH) and current drive in the tokamaks and stellarators. The progress in gyrotron development pushes ECH from a minor to a major heating method. Also gyrotron based technological complexes successfully applied in electron cyclotron resonance ion sources, for microwave ceramic sintering and diamond disk production. The paper describes the main features of high frequency gyrotrons. Some data about pulsed and CW tubes, working in the terahertz frequency range, are given. These gyrotrons operate (in some specific combinations) at very low voltage and beam current, demonstrate an extremely narrow frequency spectrum or wide frequency tuning. Although in comparison with the classical microwave tubes the gyrotrons are characterized by greater volume and weight due to the presence of bulky parts (such as superconducting magnets and massive collectors where the energy of the spent electron beam is dissipated) they can easily be embedded in a sophisticated laboratory equipment (e.g., spectrometers, technological systems, etc.). All these advantageous features have opened the road to many novel and prospective applications of gyrotrons.

We demonstrate selective excitation and coherent amplification in the multicore fiber of the out-of-phase supermode that has equal intensities but interleaved 0/π phases in the neighboring cores. The out-of-phase supermode is beneficial due to its stability at arbitrary high powers, whereas the fundamental supermode becomes unstable at relatively high powers. We fabricated a double-clad all solid silica fiber with six highly Yb-doped coupled cores arranged in a ring structure. We obtained amplification of 50 picosecond chirped pulses up to ∼1 μJ energy with measured content of the out-of-phase mode of >80%. The experimental results were supported by 3D numerical simulation demonstrating the possibility of the out-of-phase supermode amplification in the multicore fibers with real parameters without degradation of supermode composition for powers up to damage threshold in silica glass.

A method for generating subrelativistic laser pulses with a sharp leading edge is proposed, which is based on Raman backscattering of an intense short pump pulse by a counter-propagating long low-frequency pulse propagating in a thin plasma layer. A thin plasma layer serves both to attenuate parasitic effects and to effectively reflect the central part of the pump pulse when the field amplitude exceeds the threshold value. A prepulse with a lower field amplitude passes through the plasma almost without scattering. This method works for subrelativistic laser pulses with durations up to 100 fs. The contrast of the leading edge of the laser pulse is determined by the seed pulse amplitude.

We demonstrate selective excitation and coherent amplification in multicore fiber of the out-of-phase supermode that has equal intensities but interleaved 0/π phases in the neighboring cores. The out-of-phase supermode is beneficial due to its stability at arbitrary high powers, contrary to the fundamental supermode. We fabricated a double-clad all solid silica fiber with six highly Yb-doped coupled cores arranged in a ring structure. We obtained amplification of 50 picosecond chirped pulses up to ~1 µJ energy with measured content of the out-of-phase mode of >80%. We demonstrated in 3D numerical simulation the possibility of the out-of-phase supermode amplification for powers up to damage threshold in silica glass.

Coherent propagation of supermodes in a multicore fiber is promising for power scaling of fiber laser systems, eliminating the need for the active feedback system to maintain the phases between the channels. We studied the propagation of broadband pulsed radiation at a central wavelength of 1030 nm in a multicore fiber with coupled cores arranged in a square array. We designed and fabricated a silica multicore fiber with a 5 × 5 array of cores. For controllable excitation of a desired supermode, we developed a beam-forming system based on a spatial light modulator. We experimentally measured intensity and phase distributions of the supermodes, in particular, the in-phase and out-of-phase supermodes, which matched well the numerically calculated profiles. We obtained selective excitation and coherent propagation of broadband radiation with the content of the out-of-phase supermode of up to 90% maintained without active feedback. Using three-dimensional numerical modeling with allowance for a refractive index profile similar to those of the developed fiber, we demonstrated stable propagation of the out-of-phase supermode and collapse of the in-phase supermode at a high signal power.

The propagation of laser pulses in multicore fibers (MCFs) made of a central core and an even number of cores located in a ring around it is studied. Approximate quasisoliton homogeneous solutions of the wave field in the MCF considered are found. The stability of the in-phase soliton distribution is shown analytically and numerically. At low energies, its wave field is distributed over all MCF cores and has a duration that exceeds the duration of the nonlinear Schr\"odinger equation (NSE) soliton with the same energy by many (i.e., five to six) times. In contrast, almost all of the radiation at high energies is concentrated in the central core with a duration similar to the NSE soliton. The transition between the two types of distributions is very sharp and occurs at a critical energy, which is weakly dependent on the number of cores and on the coupling coefficient with the central core. The self-compression mechanism of laser pulses was proposed. It consists in injecting such MCFs with a wave packet being similar to the found soliton and having an energy larger than the critical value. It is shown that the compression ratio depends weakly on the energy and the number of cores and is approximately equal to six times with an energy efficiency of almost 100%. The use of longer laser pulses allows one to increase the compression ratio up to 30--40 times with an energy efficiency of more than 50%. The obtained analytical estimates of the compression ratio and its efficiency are in good agreement with the results of a numerical simulation.

The out-of-phase soliton distribution of the wave field was found for a multicore fiber (MCF) from an even number of cores located in a ring. Its stability is proved both with respect to small wave field perturbations, including azimuthal ones and to small deformations of the MCF structure. As an example of using this soliton distribution, the problem of laser pulse compression in an active MCF is studied. The optimal fiber parameters, the minimum duration of the output pulse, and the compression length have been found, which are in good agreement with the results of numerical simulation. In order to achieve high energies in the output laser pulse, the requirements for MCF deformations are determined.

The coherent propagation and amplification of high-power laser beams in a multicore fiber (MCF) of and lattices of weakly coupled cores is studied. Exact stable analytical nonlinear solutions are found in the form of the out-of-phase distribution that describe the coherent propagation of wave beams in such MCFs. The use of these distributions makes it possible to operate with laser radiation with a power of up to 2N times of the critical self-focusing power in homogeneous media. The analytical results are confirmed by the direct numerical simulation of the wave equation. The limitations on active fiber parameters for stable amplification of the found out-of-phase solution are determined.

Nonlinear spatiotemporal dynamics of femtosecond pulses in a hexagonal 7-core silica fiber pumped by a sub-uJ 370 fs Er:fiber CPA system was studied. Two orders of magnitude contrast enhancement of the pulses trapped in the central core of a multicore fiber was obtained. Further compression of pulses spectrally broadened in the multicore fiber down to 53 fs was demonstrated.

Analytical and numerical studies of the coherent propagation of laser radiation in a small-sized system of weakly coupled fibers are carried out. Configurations of the wave field in a multi-core fiber are found to ensure coherent propagation of radiation with a power exceeding the critical for self-focusing in a homogeneous medium. Analogous solutions in form of temporal solitons are found in such a small-sized discrete system for pulsed laser radiation.

The self-action features of wave packets propagating in a two-dimensional system of equidistantly arranged fibers are studied analytically and numerically on the basis of the discrete nonlinear Schr��dinger equation. Self-consistent equations for the characteristic scales of a Gaussian wave packet are derived on the basis of the variational approach, which are proved numerically for powers $\mathcal{P} < 10 \mathcal{P}_\text{cr}$ exceeding slightly the critical one for self-focusing. At higher powers, the wave beams become filamented, and their amplitude is limited due to nonlinear breaking of the interaction between neighbor light-guides. This make impossible to collect a powerful wave beam into the single light-guide. The variational analysis show the possibility of adiabatic self-compression of soliton-like laser pulses in the process of their three-dimensional self-focusing to the central light-guide. However, the further increase of the field amplitude during self-compression leads to the longitudinal modulation instability development and formation of a set of light bullets in the central fiber. In the regime of hollow wave beams, filamentation instability becomes predominant. As a result, it becomes possible to form a set of light bullets in optical fibers located on the ring.

A detailed theoretical analysis is carried out of the hose instability of relativistically strong laser pulses propagating in a plasma, whose duration is less than the period of a plasma wake wave. An analytic expression is obtained for the displacement of the mass center of a wave pulse, and the effect of this instability on the modification of the spectrum of laser radiation is analyzed for a wide range of initial parameters. It is shown that the development of instability is characterized by a power-law (rather than exponential) time dependence along the propagation path and does not deteriorate the self-compression of laser pulses.

The analytical and numerical study of the radiation self-action in a system of coupled light guides is fulfilled on the basis of the discrete nonlinear Schr\"odinger equation (DNSE). We develop a variational method for qualitative study of DNSE and classify self-action modes. We show that the diffraction of narrow (in grating scale) wave beams weakens in discrete media and, consequently, the ``collapse'' of the one-dimensional wave field with power exceeding the critical value occurs. This results in the ability to self-channel radiation in the central fiber. Qualitative analytical results were confirmed by numerical simulation of DNSE, which also shows the stability of the collapse mode.

Nonlinear spatiotemporal dynamics of femtosecond pulses in a hexagonal seven-core silica fiber pumped by a sub-μJ 370 fs Er:fiber chirped pulse amplification (CPA) system were studied. Nonlinear pulse shaping and compression in the central core and pedestal coupling to the outer cores were directly measured by frequency-resolved optical gating. Further compression of the pulses spectrally broadened in the multicore fiber down to 53 fs was demonstrated. Two orders of magnitude contrast enhancement of the pulses after compression was observed.

We show that a self-focusing mode for intense laser pulses comprising less than about ten optical cycles is resistant to the transverse modulational instability. For such pulses, a method of pulse self-compression based on adiabatic decrease of the duration of a solitonlike wave packet and transverse cumulating of energy during the self-focusing in Kerr-like media with anomalous dispersion is proposed. This method can be used for generation of high-quality, high-energy, few-cycle pulses down to a single-cycle duration.

Development of the gyrotron system for ITER is based on solution of many very difficult scientific and engineering problems. At present the main purpose of the system modification is an enhancement of the system reliability and implementation of all gyrotron systems into ITER machine and its control and safety system. Recently development of ITER gyrotron system in Russia came into completion phase.

The city is 100% aquifer dependent for potable, domestic, commercial and industrial water supplies, which are provided by both intraurban and periurban wellfields. A highly productive but much localized periurban valley fill wellfield located only 8 km south of the city center provides about half of the city’s water demand, the balance coming from boreholes of various depths distributed throughout the city. Surface water is used only for irrigation in the city. The majority of abstraction boreholes are operated by the municipal water supply utility Bishkekvodokanal, which provides water for both domestic and industrial purposes. There are two separate reticulation systems for domestic water: cold water for potable use, and hot water for nonpotable use and for district heating use, the last being a closed system (within each block of flats) which operates only during the winter. All come under the description of “public water supply.” Private urban water use is much less important both numerically and volumetrically; a small number of factories have private wells for potable or nonsensitive supply, and there are also a few private domestic and municipal irrigation wells in seasonal use. Owner-operated boreholes for commercial premises, hospitals, and large state administrative buildings appear to be insignificant.

The development of the spatiotemporal (filamentation) instability of a laser pulse upon excitation of a plasma wave is studied numerically and analytically. It is shown that first, as in a medium with inertialless cubic nonlinearity, the filamentation of radiation occurs and then filaments are attracted to each other. The following evolution differs weakly from the evolution of a smoothed wave beam in a medium with inertial nonlinear response.

Tests of the Russian ITER gyrotrons were continued after debugging of the test facility at Kurchatov Institute including the evacuated transmission line and power supplies capable to provide gyrotron CW operation. A new ITER gyrotron (V-10) with upgraded body insulation, liquid cooling system for the DC-break ceramic and improved design of the relief window has been manufactured and is currently under test. A maximal total efficiency near 55% at 1 MW power level was attained. The maximal pulse duration of 1000 s at 0.8 MW power was limited at that time by the test stand. At 1 MW power level the gyrotron V-10 up to now reached a pulse duration of 570 s. An advanced short-pulse (100 ms) gyrotron model operating in the TE28.12 mode demonstrated a very robust operation at relatively high electron energies (up to 100 keV) necessary to achieve 1.5-2 MW output power. Three double frequency gyrotrons have been delivered to ASDEX Upgrade. The development of a multi-frequency gyrotron with a broadband or tuneable synthetic diamond window is in progress.

Powerful gyrotrons with radiation frequencies in the range 0.33–0.65 THz were demonstrated at the IAP as early as in the 1970–1980s. This trend has recently been renewed in connection with a significant increase in interest in terahertz frequency range. In the course of new experiments, the radiation frequency of pulsed gyrotrons was increased up to 1.3 THz and 1 THz at the fundamental and third cyclotron harmonics, respectively. In addition, gyrotrons operated in CW regime with a frequency of 0.3 THz for technological applications (in collaboration with the University of Fukui, Japan) and 0.26 THz for the dynamic nuclear polarization at a high-field NMR were implemented. Designs of a pulsed fundamental-harmonic gyrotron with MW-level power at 0.3 THz and a CW kW-level third-harmonic gyrotron with a frequency of 0.4 THz are currently developed. Estimates show that modern techniques for the creation of strong magnetic fields now make it possible to realize gyrotrons with an operating frequency at least up to 1–1.5 THz. Such generators utilize a relatively low particle energy and can provide higher average power than the existing FELs.

A multifrequency electron cyclotron resonance heating (ECRH) system is currently under construction at the ASDEX Upgrade tokamak experiment. The system employs depressed collector gyrotrons, step tunable in the range of 105-140 GHz, with a maximum output power of 1 MW and a pulse length of 10 s. One two-frequency GYCOM gyrotron has been in routine operation at ASDEX Upgrade since 2006. A further extension of the system with three more gyrotrons is underway. An in situ calibration scheme for the broadband torus window has been developed. The system is equipped with fast steerable mirrors for real-time MHD control. The gyrotron and the mirrors are fully integrated into the discharge control system. The ECRH system turned out to be essential for the operation of H-modes after covering the plasma facing components of ASDEX Upgrade with tungsten. Deposition of ECRH inside rhotor < 0.2 is necessary to prevent accumulation of W in plasmas with high pedestal temperatures. With respect to the limited loop voltage available in ITER, the use of ECRH for neutral-gas preionization to facilitate plasma breakdown and its application during the current ramp-up to increase the conductivity in order to save transformer flux have been demonstrated successfully for 105 GHz, 3.2 T (O1-mode) and 140 GHz, 2.2 T (X2-mode), corresponding to 170 GHz at ITER with the full and half values of its foreseen toroidal field of 5.3 T.

To combine powers from a set of gyrotrons and to switch the combined wave beam between a number of output channels, various kinds of multiplexers can be used. Especially, narrow-band frequency diplexers in connection with small frequency-shift keying of gyrotrons can be used to switch the millimeter-wave power between two output channels. This technique can, for example, be used for fast beam steering for synchronous stabilization of rotating neoclassical tearing modes in tokamaks. Beam steering can be performed by a multistage multiplexer, provided that phase-controlled sources are available. In the paper, various concepts for fast directional switches as well as their integration into transmission lines are discussed. Calculations and low-power measurements of prototypes are presented. A resonant diplexer experiment is at present being prepared to be tested at high power in the electron cyclotron resonance heating (ECRH) system for Wendelstein 7X (W7-X). Requirements and techniques for frequency control of the gyrotrons are discussed, and the results of preliminary frequency modulation experiments are shown. Finally, future prospects for the application of diplexers in large ECRH systems are discussed.

Self-focusing dynamics of electromagnetic pulses of arbitrary duration is analyzed numerically and analytically. The wave-field evolution is considered by the wave equation in the reflectionless approximation under quite general assumptions about the dispersion of the medium. Methods for qualitative investigation of the self-focusing dynamics of quasimonochromatic radiation are generalized to the case of wave packets with the length of a few oscillation periods. In particular, sufficient conditions for collapse and many other integral relations are obtained by the momentum method. A self-similar-type transformation is used to show that new structural features are primarily associated with the nonlinear dispersion of the medium (with the dependence of the group velocity of a wave packet on its amplitude). Numerical analysis confirms that the self-focusing of radiation is preceded by an increase in the steepness of the longitudinal profile.

A regime of extreme self-compression of optical solitons to single-cycle duration with further shortening along with superbroad spectrum up-shifting is revealed when the Kerr nonlinearity and ionization process are independently controlled. This results in efficient optical-pulse compression as a whole towards extremely short single-cycle pulses at essentially shorter wavelengths, which may open a new way to generate optical pulses with durations of hundreds of attoseconds in the ultraviolet domain.

Design development of continuous-wave 240 GHz gyrotron and 300 GHz gyrotrons with output power about 200–1000 kW for fusion research at advanced plasmas with intense magnetic field is presented. Main goal of such gyrotrons is application for EC complexes of IGNITOR and DEMO tokamaks. This paper includes task motivation and existing technical basis, results of calculation, design, technical requirements and pre-prototype experimental tests for main subsystems of gyrotron.

We report an experimental observation of electromagnetically induced transparency (EIT) in Pr3+:LaF3 at liquid helium temperature at the 3H4(0)–1D2 (16 872 cm−1) transition. Transparency resonance at ground state hyperfine sublevels (in a Λ scheme) and a dispersion-shaped resonance due to excited state hyperfine coherences (in a V scheme) are detected. Theoretical analysis taking into account the six-level Pr3+ level structure gives qualitative agreement with the experiment.

We observed radio-frequency (rf) induced transparency for a probe optical field in an rf-optical double resonance experiment in a neon discharge. The origin of the transparency is coherent population trapping at Zeeman sublevels of the lower level of an optical transition of neon. Stokes and anti-Stokes optical fields were generated due to stimulated Raman scattering of both the radio-frequency field on the probe-induced optical coherence and the probe field on the Zeeman coherence.

The self-action dynamics of three-dimensional wave packets whose width is on the order of the carrier frequency is studied under fairly general assumptions concerning the dispersion properties of the medium. The condition for the wave field collapse is determined. Self-action regimes in a dispersion-free medium and in media with predominance of anomalous or normal group velocity dispersions are numerically investigated. It is shown that, for extremely short pulses, nonlinearity leads not only to the self-compression of the wave field but also to a “turn-over” of the longitudinal profile. In a dispersionless medium, the formation of a shock front within the pulse leads to the nonlinear dissipation of linearly polarized radiation and to self-focusing stabilization. For circularly polarized radiation, the wave collapse is accompanied by the formation of an envelope shock wave.

A groundwater residence time study of the deep fluvioglacial aquifer supplying Bishkek, capital of Kyrgyzstan, has found evidence of deep infiltration of recent recharge both in the main periurban wellfield and below the city. Commonly-employed hydrochemical markers detected urban influence in the city-centre to depths of 65–100 m, but gave no indication of the important role of induced river/canal bed leakage, either upgradient in the periurban wellfield or within the city. This was revealed by O and H stable isotope measurements, which showed that local rainfall/snowfall play little part in the aquifer water balance. More remarkably, the universal detection of CFCs and SF6, including in boreholes with 140–220 m deep upper screens, demonstrated that induced leakage of water just a few decades old had penetrated much deeper into the aquifer system than other hydrochemical markers indicated. A two-dimensional flow model set up to test whether such deep pumping-induced leakage could occur below the periurban wellfield confirmed its feasibility. The results imply vertical infiltration rates of 5–10 m/year and demonstrate that in this not-uncommon intergranular aquifer setting, deep boreholes with deep screen settings do not necessarily abstract old water. Hence, there are major implications for urban groundwater management and protection in such settings.

A solution to the problem of realizing the collapse of three-dimensional wave packets in nonlinear media with normal group velocity dispersion is proposed. Wave packets with pronounced hyperbolic topology are shown to collapse; i.e., the field increases infinitely near the system axis. In particular, wave collapse of the tubular axisymmetric packets occurs through the concentration of the compressed ring field distribution at the axis. The collapse is shown to stabilize due to the saturation of nonlinearity or nonlinear dissipation, which restrict the field increase and lead to the packet splitting in the transverse direction.

We study the possibility of efficient self-compression of femtosecond laser pulses in nonlinear media with anomalous dispersion of group velocity during the self-focusing of wave packets with a power several times greater than the critical self-focusing power. The results of qualitative analysis of the evolution of three-dimensional wave packets with the quasi-soliton field distribution are confirmed by the computer simulation. The simulation proves that the considered regime of compression of high-power laser pulses with initial durations of about ten optical cycles is stable relative to filamentation instability due to the influence of the nonlinear dispersion. We demonstrate the possibility of self-compression of laser pulses at a multi-millijoule energy level and up to one optical cycle with an energy efficiency of more then 50%.

A detailed theoretical investigation is performed for the self-compression of relativistically strong laser pulses under plasma wake wave excitation conditions. An analytical expression is obtained for the characteristic length of laser pulse self-compression in the one-dimensional case. A good agreement between the theoretical and numerical calculation of the dependence of the wave-packet compression length on both amplitude and plasma concentration is demonstrated. The influence of the wave beam self-focusing radiation process on the rate of shortening of the laser pulse duration is considered.

The features of the dynamics of the self-ffects of the wave field are considered for the case when the dynamics is described by the nonlinear Schrodinger equation (NSE) with a hyperbolic spatial operator. An analytical investigation of the characteristic regimes of the self-effects is carried out; these regimes are due to the spatial competition of the self-focusing compression of the wave packet in one direction and its defocusing in another. The initial distributions of the wave field are analyzed with the goal of using them in a numerical modeling for illustration of the features of the self-effects. It is shown that three stages can be discerned in the evolution of the localized distributions: self-focusing filamentation of the wave field in the transverse direction, and compression and subsequent fragmentation in the defocusing (longitudinal) direction. The strongest non-uniformities are excited in the self-similar collapse of the wave field to hyperbolas (to the characteristic curves of the hyperbolic operator of the NSE). The stabilization of the development of the fragmentation instability is discussed separately.