Том 61, № 3 (2023)

The interaction of the magnetospheric–ionospheric (MI) system surrounding the Earth with the environment (solar wind) occurs in the form of a series of transient processes at different scales. The largest of them, magnetic storms, are obviously triggered by disturbances in the solar wind (direct driving). The role of the internal dynamics of the MI system, which is caused to a large extent by the nonlinearity and temporal delays of the loading–unloading processes of energy and particle from the solar wind into the magnetosphere, becomes more significant at smaller scales (substorms, pseudobreakups, injections, and activations). A typical dynamic state of the MI system is characterized as self-organized criticality or turbulence, which are characterized by statistical scale invariance (scaling) in the fluctuation distributions of many characteristics. The dynamics of the MI system is projected into the region of the auroral oval, the very existence of which is due to this dynamics. The space–time structure of auroral disturbances largely reflects the structure of processes in the MI plasma. The description of this structure is important both for studying the fundamental study of plasma processes and for many topical applied problems related to the propagation of radio waves in the ionosphere and vital activity at high latitudes. The paper discusses approaches and developments for constructing a model of the space–time structure of the auroral oval, based on fractal and multifractal characteristics.

A new method is proposed for determining the electron density in rarefied plasma, based on simultaneous measurements of the Interball-2 satellite potential using IESP-2 (electric field instrument) and KM-7 (electron temperature sensor) probe devices. This makes it possible to estimate the photoelectron current density based on a procedure proposed earlier by the authors of this study. The electron concentration was determined only for the positive potential of the spacecraft. The balance equations for the satellite and the probe between the currents of the surrounding plasma electrons and photoelectrons emitted by the illuminated surface were compiled. In the magnetosphere, to bring the probe potential to the potential of the surrounding plasma, a bias current is directed into the probe, which was taken into account in the current balance equation for the probe. The electron energy used in the calculations was kTe = 1 eV. We analyzed data from ~350 orbits in the auroral region of the magnetosphere at altitudes of 2–3 RE from October 1996 to March 1998 during the period of low solar activity at the beginning of the 23rd cycle. Examples of the calculated electron density are given, which is in the range of 1–30 cm–3.

Solar protons in eruptive flares are stochastically accelerated in a wide spatial angle, and then they are effectively kept behind the expanding coronal mass ejection (CME) front, which can either bring protons to the magnetic-field line going to a remote observer or carry them away. We consider 13 solar proton events of cycle 24 in which protons with energy E > 100 MeV were recorded and were accompanied by the detection of solar hard X-ray (HXR) radiation with E > 100 keV by an ACS SPI detector and γ-radiation with E > 100 MeV by the FermiLAT telescope with a source in the western hemisphere of the Sun. The first arrival of solar protons into the Earth’s orbit was determined in each event by a significant “proton” excess over the ACS SPI background during or after the HXR burst. All events were considered relative to our chosen zero time (0 min) of parent flares. The “early” arrival of protons to the Earth’s orbit (<+20 min), which was observed in four events, corresponds to the “fast” acceleration of electrons (10 MeV/s). The “late” arrival of protons (>+20 min) corresponds to the “slow” acceleration of electrons (1 MeV/s) and was observed in six events. In three events, a “delayed” arrival of protons (>+30 min) was observed, when the CME propagation hindered the magnetic connection of the source with the observer. The direction of CME propagation is characterized in the catalog (SOHO LASCO CME Catalog) by the position angle (PA). The observed PA systematizes the times of the first arrival of protons and the growth rate of their intensity. The PA parameter should be taken into account in the analysis of proton events.

The problem of optimal control of the relative motion of a spacecraft with a finite thrust engine in arbitrary circumcircular orbits using the Pontryagin’s maximum principle is considered. Motion is studied in an orbital cylindrical coordinate system, using variables written in the form of secular and periodic components of relative motion in the orbital plane. The main attention is paid to the analysis of the optimal control structure with a free and transversal orientation of the thrust vector in the presence of passive areas on the trajectory. As a criterion for choosing the optimal control, the motor operating time of the corrective motors was considered. Characteristic control structures for various areas of initial driving conditions have been determined, and estimates of the marginal costs of motor time have been obtained.