Alexander Igorevich Podgorny

The primary release of solar flare energy in the corona at altitudes of 15,000 — 70,000 km is explained by the physical mechanism of S.I. Syrovatsky, based on the rapid release of energy accumulated in the magnetic field of the current layer. The observed manifestations of the solar flare are explained by its electrodynamic model proposed by I.M. Podgorny. The model uses analogies with the electrodynamic model of a substorm, previously developed by its author. Since it is impossible to obtain the magnetic field configuration in the corona from observations, it is necessary to conduct MHD modeling. When setting the problem, no assumptions were made about the mechanism of the solar flare. For the numerical solution, an upwind absolutely implicit finite-difference scheme, conservative with respect to magnetic flux, was developed. The scheme is realized in the PERESVET computer program. A detailed study of the pre-flare state over the active region AR 10365 was conducted. The study revealed the emergence of an extended current sheet 50,000 km wide, which is a surface of magnetic lines passing through a chain of closely spaced current density maxima. The magnetic lines of the surface are in the form of arches located in the bright region of the flare emission. At the center of such a current sheet, a 3D maximum of current density does not necessarily have to be achieved. An appearance of a flare in such an arcade is explained by the fact that the main part of the surface of the magnetic arcs has properties that contribute to the development of flare instability.

Solar cosmic rays (SCRs) are generated during the primordial energy release in solar flares. This explosive process takes place in the solar corona above the active region. It represents the fast release of the magnetic field energy of the current sheet, which is formed near a singular magnetic field line. Solar cosmic rays appear as a result of the acceleration of charged particles, mainly protons, by an inductive electric field in the current sheet equal to the field E = V × B/c (with V the speed of plasma and B the magnetic field near the current sheet, and c the speed of light). To study the mechanism of solar flares and obtain conditions for studying SCR acceleration, it is necessary to carry out magnetohydrodynamic (MHD) simulations of flare situations in the solar corona above a real active region. Methods of stabilization were developed which made it possible to partially solve the problem of numerical instabilities. MHD simulations shows complicated configurations near the singular line. Comparison of the results of the MHD simulations with observations showed the general agreement of the positions of the current sheets with regions of intense flare radiation. However, there are some problems with the details of such coincidences. The results obtained in this paper show the possibility of improving the methods of MHD simulation in order to solve the problems that arise during solving of MHD equations.

Solar cosmic rays (SCR) are generated during the primordial energy release in solar flares. This explosive process takes place in the solar corona above the active region. It represents fast release of the magnetic field energy of the current sheet, which is formed near a singular magnetic field line. Solar cosmic rays appear as a result of acceleration of charged particles, mainly protons, by an inductive electric field in the current sheet, equal to the field E=V´B/c near the current sheet. To study the mechanism of solar flares and obtain conditions for stydy SCR acceleration it is necessary to carry out magnetohydrodynamic (MHD) simulation of a flare situation in the solar corona above a real active region. The methods of stabilization were developed which made it possible to solve partially the problem of numerical instabilities. MHD simulations showed complicated configuration near the singular line. Comparison of the results of MHD simulations with observations showed a general agreement of the positions of the current sheets with regions of intense flare radiation. However, there are some problems with the details of such coincidences. The results show the possibility of improving the methods of MHD simulation in order to solve the arisen problems.

An Erratum to this paper has been published: https://doi.org/10.3103/S1062873822220014

As shown in the first results of MHD simulations in the real scale of time, above the active region (AR) 10365, during the first flare M 1.9 (05/26/2003 05:34) at a height of 16–18 mm (lower corona), a singular line of magnetic field appears. The local maximum of the current density is situated on this singular line. The magnetic field in the vicinity of this singular line is the superposition of an X-type magnetic configuration and a divergent magnetic field. The accumulation of magnetic energy for solar flare with current sheet creation takes place near this singular line due to magnetic field deformation by disturbances in the X-type configuration in spite of the presence of overlaid diverging magnetic configuration. The magnetic configuration is so complicated that the singular line can be found only by using specially developed graphical system of search. The position of singular line coincides with position of source of flare radio emission at the frequency 17 GHz above AR 10365 measured by Nobeyama Radioheliograph (NoRH). Also, MHD simulation shows appearance of the singular line, in the vicinity of which X-type configuration dominates. However, apparently due to small disturbance, propagating from the photosphere, sufficient magnetic energy was not accumulated in this configuration, so the NoRH does not show the flare source of emission at the frequency 17 GHz in the place, where this singular line is situated.

An electrodynamic model of a solar flare is proposed by I.M. Podgorny that explains its main observed manifestations. Solar cosmic rays are accelerated alo

The use of parallel computations on Nvidia Tesla GPUs allows the magnetohydrodynamic (MHD) simulation of preflare situations in the solar corona above an active region in the real scale of time. The MHD simulation for AR 10 365 shows a significantly smaller number for the current density maxima, which mask real current sheets, i.e., the places of the primordial release of solar flare energy, as compared to previous MHD simulation on a reduced scale of time, where strong instabilities appeared near the photospheric boundary of the computational domain under the effect of an unnaturally rapid change in the photospheric magnetic field (the time scale was reduced by 10⁴ times). A more than 100× speedup of the numerical solution of a set of MHD equations is attained in comparison with successive calculations. The new results make it possible to determine a more precise magnetic configuration near current sheets, which can be used to improve the prediction of the appearance of charged particle fluxes accelerated to relativistic energies under the action of the Lorentz electromagnetic field, i.e., solar cosmic rays, which carry radiation dangerous for people and equipment in space and Earth’s polar latitudes.

The generation of solar cosmic rays occurs during explosive energy release in a solar flare, so in order to understand this phenomenon it is necessary to study both the mechanism of the solar flare and the process of particle acceleration by the generated electric field. During a solar flare in the solar corona above the active region (AR), the energy stored in the magnetic field of the current sheet is released. Using the results of numerical simulation and observations, I.M. Podgorny proposed an electrodynamic model of a solar flare, explaining its main observational manifestations, in particular, the appearance of X-ray emission on the surface of the Sun. The acceleration of protons occurs along a singular line of the magnetic field of the current sheet by the electric field E = -V×B/c. To obtain accurate results it is necessary to carry out MHD simulation in the real scale of time, which is only be done using parallel calculations. The parallelization of the program PERESVET carried out using graphics card (GPU), the calculations were accelerated by ~ 120 times. As a result of optimization of the approximation of the boundary conditions of free exit at the non-photospheric boundary, instability near the boundary was stabilized. The first results of MHD simulation in the real scale of time above the AR 10365 showed the appearance of a plasma flow near singular X-type lines, which have to cause to the formation of a current sheet.

Solar flares take place in the solar corona due to release of magnetic energy accumulated in the magnetic field of current sheet during instability of the current sheet.Solar cosmic rays are accelerated in the inductive electric field of the current sheet. The magnetic field of the solar wind forms the shape of an Archimedes spiral and affects the propagation of solar cosmic rays in interplanetary space. The modern detection of giant flares on the class G star dwarfs with the energy significantly exceeding the energy of the solar flares indicates the possibility of proton acceleration beyond the boundary of the solar system to energies significantly greater than the energy of solar cosmic rays. The recent experimental data shows that the energy of the stellar flares can exceed energy of 10³⁶ erg. It is by 3-4 orders greater than the energy of a large solar flare, and, apparently, the energy of the protons accelerated in these stellar flares can significantly exceed the energy of the particles registered from flares on the Sun. Thus, the flare can be a universal astronomical process responsible for proton acceleration on the Sun and on the stars.