Annotation of the results obtained in 2023
TeV observations of the gamma-ray burst GRB 221009A obtained last year provided the project participants with a unique opportunity to study the earliest phase of the afterglow, when it is observed simultaneously with the main pulse. To describe this phase, we have proposed and developed a local model of a blast wave as a two-element structure with intermittent energy pumping. The central source supplies energy to the internal part (the ejected matter heated in the reverse shock wave). When matter in this region expands, its internal energy is transferred to external matter heated in the bow shock wave. The model takes into account the inertia of the raked external substance - the pressure drop in the outer part of the blast wave determines the derivative of the Lorentz factor of the blast wave. When applied to GRB 221009A, the model shows very good agreement with observations for the entire TeV light curve, with the exception of three regions where there are excesses of the observed flux relative to the model. These regions correlate with the three most powerful episodes of activity from the central source, so we interpret them as emission from the reverse shock wave. The best agreement with observations for GRB 221009A is provided by a model with an extremely narrow jet with an opening angle of about 0.07 degrees, extending into the stellar wind. Interestingly, photon annihilation does not play a decisive role in the parameters that provide the best agreement with observations. The properties of nonequilibrium distributions of particles arising on relativistic shock waves were studied. The characteristics of these distributions were determined by calculating the radiation of their constituent particles and comparing the resulting spectral and temporal characteristics with observational data. In particular, the research was aimed at calculating the observational manifestations of two extreme radiation mechanisms - coherent radiation detected at radio frequencies and inverse Compton radiation observed in the gamma range. A new scenario for fast radio bursts is proposed, taking into account the initial anisotropy of the stimulating photon field. Taking this effect into account made it possible to construct a model for the formation of millisecond radio bursts on shock waves with a characteristic radius of 10^15 cm, which can be formed by magnetar flares. Based on a statistical analysis of magnetic flares on a cosmological scale, it has been established that the parameters and frequency of magnetic flares correspond very well to the frequency of recorded fast radio bursts. The study of the fraction of particles with high and ultra-high energies was carried out by modeling gamma radiation from the afterglows of gamma-ray bursts and comparing it with observational data obtained on the H.E.S.S., MAGIC and LHAASO telescope systems. The study of radiation from gamma-ray burst afterglows included (1) the development of a new model for the formation of hard gamma-ray radiation, taking into account the influence of shock wave front inhomogeneities; (2) development of a new approach to the analysis of gamma-ray spectra from relativistic sources characterized by a bright X-ray component; (3) study of the process of formation of the light curve of gamma-ray bursts, taking into account the effect of shifting the reference point of time in the self-similar mode, which significantly affects the determination of the parameters of the relativistic outflow responsible for the formation of the gamma-ray burst. The dispersion properties of the Weibel-type instability are analytically determined, taking into account the magnetic field and particle collisions, and the patterns of its nonlinear stage and the evolution of the emerging magnetic turbulence in an anisotropic magnetoplasma are qualitatively indicated. In particular, it is shown that in a wide range of plasma parameters, collisions of particles in it contribute to the development of Weibel instability, leading to filamentation of currents under conditions under which this is impossible in the case of a strictly collisionless plasma. A physical interpretation and consistent description of the stages of transient processes of filamentation of currents and the generation of strong small-scale magnetic fields during the injection of high-energy particles or the decay of a strong discontinuity in the presence of an inhomogeneous background plasma and an external magnetic field are given. A scenario for a solar (stellar) flare in a separate coronal arc is proposed, which explains a large number (up to a billion or more) of simultaneous nanoflares initiated by Weibel-type instability. A multi-satellite analysis of current sheets has been carried out, which is the most extensive statistical study of the applicability of single-satellite methods for determining the properties of current sheets in the solar wind. The results of this analysis made it possible to estimate the error of single-satellite methods for determining the main parameters (width and current density) of current sheets. It has been established that the single-satellite method, in which it is assumed that current sheets are frozen into the local plasma flow, and the normal is determined by the vector product of magnetic fields at the boundaries of the layer, makes it possible to determine the main parameters of current sheets with high accuracy. The most extensive statistical study of 18,000 current sheets at a distance of 5 AU from the Sun has been carried out using Ulysses satellite measurements. For each current sheet, the main parameters (width, current density, and rotation angle of the magnetic field) were determined and the properties of current sheets observed at distances of 0.2, 1, and 5 AU from the Sun were compared. A comparative analysis of current sheets observed at different radial distances made it possible to establish that the difference in the parameters of the current sheets is due solely to the difference in the background parameters of the plasma. With proper normalization, current sheets observed at different distances from the Sun have almost identical parameters. This result is the strongest argument in favor of the hypothesis about the local generation of current sheets and practically excludes the alternative hypothesis about the origin of current sheets in the solar corona and the passive transport of these structures in the heliosphere. The local generation of these structures is also indicated by the scale-invariant properties of current layers that we discovered. A detailed study of the generation of discrete chorus emissions was carried out using a numerical model developed by us based on the EPOCH code, which implements the particle-in-cell method. In our model, unlike the source code, it is possible to use an arbitrary distribution function of energetic electrons, including one that has a feature in the form of a finite width difference in velocity along the geomagnetic field. Based on calculations, it is shown that the generation mode in the system is determined by the degree of exceeding the generation threshold: when the threshold is slightly exceeded, stationary generation takes place, when the threshold is higher, periodic or quasiperiodic generation of discrete chorus elements occurs, and when the threshold is even higher, stochastic generation of elements with a fine structure takes place. The generation threshold, which can be characterized by an integral value proportional to the absolute height of the drop on the distribution function, increases quadratically with increasing width of the drop and weakly depends on its relative height. It was found that the threshold electron concentration increases by an order of magnitude if the relative width of the drop increases from zero (a sharp drop) to 8%. This result indicates the important role of the presence of a sufficiently sharp drop in the particle distribution function for the generation of chorus VLF emissions. Based on the analytical solution of model problems of scattering of electromagnetic waves by strongly conducting inhomogeneities in a cold magnetoplasma, it is shown that under conditions typical of near-Earth plasma, quasi-isotropic scattering of waves in the resonant frequency range is realized (the ratio of the squares of the electric field at the maximum and minimum of the radiation pattern is on the order of 1, and in in extreme cases does not exceed 5).

 

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Annotation of the results obtained in 2021
1. A numerical model of a relativistic shock wave is developed and analyzed. It is based on a new algorithm for calculating the observed wide-range spectrum taking into account (a) synchrotron and inverse Compton radiation, as well as (b) the formation of electron-positron pairs due to the absorption of high-energy photons inside the emitting region and the radiation of the resulting secondary pairs (in a one-zone approximation using exact quantum electrodynamic cross sections of the processes). It is shown that information on the optical flux of shock wave radiation in combination with TeV observation data eliminates the degeneracy in the parameter space of the model. A numerical model is developed and a set of physical parameters of the emitting region of the cosmic gamma-ray burst GRB 190114C is calculated. It makes it possible to explain its observations in all ranges, from optical to sub-TeV, under the assumption that electrons emit in the fast cooling mode. The calculated parameters of the emitting region, found for two different instants of time, significantly deviate from a number of previously generally accepted assumptions, but at the same time they agree well with the predictions obtained in the framework of the self-consistent modified shock wave model (that takes into account the balance between the processes of creation and acceleration of electrons and positrons). The results are published in The Astrophysical Journal. Based on a theoretical analysis of the acceleration and wide-range radiation of high-energy particles in relativistic shock waves, a description of a number of radiation processes occurring in them is given. They are compared with observational data for cosmic gamma-ray bursts, and the key factors influencing the formation of gamma radiation are identified. The conditions for the occurrence of maser radio emission during the passage of a relativistic shock wave through the interstellar medium are determined. It is shown that its properties are extremely sensitive to certain physical parameters, in particular, to the density of a relativistic plasma. Therefore, detection of maser radiation will provide important information on the processes occurring in relativistic shock waves. 2. Using a three-dimensional numerical simulation of the initial value problem of the development of electron-ion Weibel instability in a non-magnetized homogeneous anisotropic plasma, a spectral-correlation analysis of quasi-magnetostatic turbulence is carried out at a deeply nonlinear stage of the process. It is shown that, after an exponential increase in currents as a result of electron Weibel instability, there is a long stage of their quasilinear decay with a simultaneous forced increase in ion currents, which is subsequently replaced by saturation and dominance of the latter, as well as the adjustment of electron currents to them at a late stage of instability development. The features of bounce oscillations of particles in a self-consistent small-scale inhomogeneous magnetic field and their energy redistribution in an inductive electric field are indicated. The typical duration of bounce oscillations of particles and the characteristic scales of changes in the local anisotropy of their distribution over velocities are estimated, and the role of partial electrons magnetization in limiting the possible development of ion Weibel instability in the presence of a sufficiently high residual anisotropy of the ion velocity distribution is determined. As a result, new properties of the nonlinear dynamics of two-component (electron-ion) Weibel instability are established, largely due to the effects of an inductive electric field acting on one of the particle fractions due to the growth or decay of the magnetic field of currents of the other fraction and affecting the consistent evolution of various spatial harmonics of quasi-magnetostatic turbulence with a significant shift in the spectrum from small to large scales. Within the framework of the quasilinear approximation using the created program for the numerical simulation of two-dimensional inhomogeneous TM-quasi-magnetostatic turbulence, a number of characteristic properties of electron Weibel instability (neglecting slowly moving ions) at the stages of successive saturation, slow decay, and relay evolution of the spatial harmonics of the current density and magnetic field is found. The features of the evolution of the velocity distribution function of particles are clarified, and the dependence of the saturating magnetic field on its initial anisotropy is found. As a result of an analytical study of the linear stage of the general case of electron-ion instability of the Weibel type in the presence of an external uniform magnetic field for a number of mutual orientations of the wave vectors of unstable perturbations and directions of the external magnetic field and the axis of anisotropy of the particle velocity distribution, the growth rates of instability depending on the wave numbers are found and the optimal scales of this instability are determined. It is shown that, under certain conditions, the parameters of a nonequilibrium plasma and an external magnetic field necessary for its development can be achieved in the region of the boundaries of magnetic clouds of the solar wind, planetary magnetopauses, and the upper parts of coronal arches. An analysis of 17043 proton kinetic-scale current sheets is presented. They are selected on the basis of magnetic field measurements with a resolution of 11 Hz for 124 days on board the Wind spacecraft at a distance of 1 au from the Sun. Current sheets have thicknesses from several tens to thousands of kilometers with the most typical value of the order of 100 km, which corresponds to scales from 0.1 to 10 proton inertial lengths with the most typical value of the order of the proton inertial length. The analysis shows that the current density is higher in current sheets with a smaller scale, but does not exceed the critical value, which corresponds to the relative drift of ions and electrons with a velocity of the order of the Alfvén velocity. In dimensionless units (the current is normalized to the critical value, the thickness to the proton inertial length), the current density, the amplitude of the magnetic field and the shear angle of the current sheet (the angle between magnetic fields at the boundaries of the current sheet) depend on its thickness according to power laws that are expected for turbulent fluctuations with a magnetic field turbulence spectrum typical for the solar wind. The observed dependences unambiguously indicate that local plasma turbulence leads to the formation of thin current sheets in the solar wind; analysis of the mechanisms limiting the current density in current sheets requires further research. A statistical analysis of 11200 proton kinetic-scale current sheets observed on the Parker Solar Probe during 10 days of motion near the first perihelion (at a distance of 0.17 – 0.24 au from the Sun) is presented. Current sheet thicknesses range from a few to 200 km with the most typical value of about 30 km, while current densities range from 100 to 10000 nA/m^2 with a typical value of about 700 nA/m^2. These thin current sheets were resolved thanks to high-resolution (73-290 Hz) measurements of the magnetic field. The thickness of the current sheets ranges from about 0.1 to 10 proton inertial lengths with the most typical value of about 2 proton inertial lengths. The magnitude of the magnetic field does not change significantly when passing through the current sheet, so that the component parallel to the magnetic field prevails in the current density. Current sheets are generally asymmetric, that is, the values of the magnetic field at the boundaries of the current sheet are statistically different. Analysis of the variation of the plasma beta parameter and the shear angle across the current sheets showed that the magnetic reconnection in the solar wind cannot be controlled by the diamagnetic effect. As for the Wind observations, the current density is higher for current sheets of a smaller scale (thickness), but statistically does not exceed the critical limit, which corresponds to the relative drift of ions and electrons with a velocity of the order of the Alfvén velocity; in this case, the same power-law dependences of the current density, magnetic field amplitude, and shear angle on the thickness of the current sheet take place. From the observations of the Parker Solar Probe at a distance of 0.17 – 0.24 au from the Sun and their comparison with observations at a distance of 1 au, it can be argued that current layers of the proton kinetic scale in the solar wind near the Sun are formed during the development of a turbulent cascade and violate the condition of diamagnetic suppression (reconnection of magnetic field lines cannot be suppressed due to the diamagnetic effect) because of their geometry, dictated by local plasma turbulence. 3. The properties of VLF chorus emissions obtained within the framework of four numerical models describing the nonlinear process of generation of chorus emissions (including a simplified model of the backward wave oscillator mode in a magnetospheric cyclotron maser created earlier by the project participants) are compared with the statistical properties of these emissions obtained from Van Allen Probes observations. It is shown that all models reproduce the observed parameters of wave packets quite well. In particular, the calculations generate both frequently observed short wave packets with a high frequency drift up or down and more rare long packets, mainly with an increasing frequency. The calculations quantitatively reproduce both an increase in the length of the observed chorus elements with an increase in their maximum amplitude and a rapid decrease in the frequency drift velocity with an increase in length. The results are published in the Journal of Geophysical Research: Space Physics. 4. From the numerical simulation of target ablation by a cylindrically focused beam of a femtosecond ultra-high-power laser in the presence of an external magnetic field, a theoretical description of the expansion of a magnetized weakly collisional plasma, which initially uniformly fills a half-space and contains a semicylindrical region of heated electrons elongated along the surface of the plasma boundary, is given. It is found that the decay of the inhomogeneous discontinuity "magnetized plasma - vacuum" is strongly influenced by an external magnetic field parallel to its boundary and significantly affecting small- and large-scale currents in an expanding nonequilibrium plasma cloud. It is shown that small-scale transient phenomena in it are largely determined by the anisotropic cooling of electrons and the accompanying Weibel-type instability, as a result of which magnetic fields (comparable in magnitude to the external magnetic field or significantly exceed it) are generated. The estimates made indicate that such phenomena are possible not only in laser but also in space plasma, including explosive processes in planetary magnetospheres and stellar coronal arches. http://arxiv.org/abs/2112.04879

 

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Annotation of the results obtained in 2022
For an expanding spherical relativistic shock wave, relations are obtained between the parameters of the radiating zone in the outgoing flow, which are input values in numerical models, and the values measured by a remote observer. These relations are formulated in terms of dimensionless effective coefficients combined with obvious dimensional estimates. The calculations performed take into account the evolution of the Lorentz factor of the shock wave, the geometric delay due to the curvature of the shock wave front, and the angular dependence of the Doppler factor for frequency and brightness. These relations are primarily intended for use in the studies of the afterglow of gamma-ray bursts, although they may have wider applications. A two zone model is proposed to describe the gamma radiation detected from the afterglow of gamma-ray bursts. Spectral properties of synchrotron and Compton radiation arising in such models are analyzed. Compared to standard one zone models widely used to describe the afterglow of gamma-ray bursts, two zone models are characterized by a much harder gamma-ray spectrum. For parameters typical for the afterglow of gamma-ray bursts, the most noticeable differences from the standard description occur in the TeV range. It is shown that this approach makes it possible to naturally explain the matching of the spectral indices of X-ray and gamma radiation, which was revealed during the observation of the afterglow of the GRB 190929A gamma-ray burst. Calculations were carried out based on a quasi-linear approach to describing the spectrum of developed Weibel turbulence within the framework of the initial problem (using the created original code). As a result of these calculations, the following hypothesis expressed earlier by the project authors was confirmed: the time dependence of the characteristic spatial scale of this turbulence is close to the root law. Patterns for the formation of an anisotropic electron velocity distribution function and the appearance of the Weibel instability due to it were established, as well as patterns for the formation of small-scale current filaments and the associated magnetic field under conditions of injection of a plasma with hot electrons into a vacuum, including in the presence of an external magnetic field. The possibility of a significant influence of this field, parallel to the hot plasma boundary and much smaller in magnitude than the formed small-scale formed, on the spatial structure of the latter is revealed. The growth rates, characteristic wave numbers, and the magnitude of the saturating magnetic field for Weibel-type instability in the presence of an external magnetic field parallel to the axis of greatest anisotropy of the particle distribution function (this is typical for the problem of injection of energetic electrons into the background plasma of a coronal loop), are estimated analytically. For all considered problems, the corresponding estimates were made under conditions typical for target ablation by a femtosecond pulse of a superhigh-power laser, and the possibility of using the obtained theoretical results for planning experimental work in the laboratory astrophysics of explosive coronal processes was proved. The parameters of more than 1200 thin current sheets, which were observed sequentially by four Cluster mission satellites in the mode when the magnetic field is measured with a 25 Hz resolution, are analyzed. The area of applicability and error of single-satellite methods for determining the normal, propagation velocity, and other current sheet parameters is determined. The multi-satellite measurements analysis made it possible to reliably determine these parameters. Comparative analysis showed the following. 1) The most accurate single-satellite method for estimating the normal is the vector product of magnetic fields at the boundaries of the current sheet; this method provides a current sheet normal within 20 degrees of true normal. On the contrary, the method of minimum variation, quite often used to this day, is not a satisfactory method for determining the normal, even in a statistical sense. 2) The current sheet propagation velocity coincides within 10% accuracy with the ion velocity along the normal (the validity of the Taylor hypothesis), which is often assumed to be true in current sheets analysis by using single-satellite measurements. 3) It was possible to establish a fairly high statistical accuracy of single-satellite methods for estimating the current density and thickness of the current sheet; the error of single-satellite methods for determining the current density and layer thickness does not exceed 30% with a probability of more than 90%. Data on more than 2000 thin current sheets observed by four Magnetospheric Multiscale satellites in the mode of ultrafast plasma (30-150 Hz) and magnetic field (128 Hz) is analyzed. An analysis of plasma measurements made it possible to identify about 10% of current sheets with signs of magnetic reconnection (the presence of plasma jets). It is shown that reconnection is suppressed in 90% cases due to the presence of an ion velocity jump across the current sheets, the magnitude of which is on the order of the local Alfvén velocity. In current sheets with signs of magnetic reconnection (10% of the total number of sheets), the ion velocity jump across the current sheet is less than 0.3 of the local Alfvén velocity, and reconnection is possible. These results indicate the most probable mechanism for suppression of reconnection in a turbulent plasma. The dependence of the dynamic spectra on the position of the observer inside the generation region in the presence of sinusoidal disturbances of the geomagnetic field with a modulation amplitude of up to 2% and a characteristic scale of 2000–4000 km is studied. It is shown that under these conditions, various combinations of rising and falling tones can be observed at the exit from the generation region. Using a numerical model based on the particle-in-cell method and the EPOCH code and modified after the test simulations, the dependence of chorus VLF emissions parameters on the hot plasma density and the width of the velocity distribution function gradient region is systematically studied. It is shown that even at a finite width of the drop in the longitudinal velocity distribution function with respect to the external magnetic field, the dependences of the instability growth rate and wave amplitude at the nonlinear stage are in good agreement with the laws established (both numerically and analytically) on the basis of an approximate model that assumes a sharp drop in the velocity distribution function. Calculations have been performed for parameters corresponding to observations in Jupiter's inner magnetosphere. According to the results of calculations, the wave energy density in chorus elements is consistent with the published Juno data obtained in the equatorial region of Jupiter's magnetosphere at distances of 8-11 planetary radii from its center.

 

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