Сorotating interaction regions of solar wind flows with different velocities have actively been magnetohydrodynamically simulated for many years. However, the main goal is to predict heliospheric characteristics in Earth’s orbit, and so calculations are performed to distances of 1–1.5 AU. In the last decade, systematic magnetohydrodynamic calculations of corotating interaction regions up to much larger distances have appeared, which are necessary for studying recurrent variations in the intensity of galactic cosmic rays. Based on one of these calculations, we previously showed that, at least for one rotation of the Sun (Carrington rotation 2066, January–February 2008), the effect of corotating interaction regions on large-scale characteristics of the heliosphere that are important for GCR modulation and, therefore, the intensity averaged over longitude is significant. We assumed that the main principles of this effect of corotating interaction regions on GCRs can be studied both by 3D modeling of the GCR intensity and in much simpler 2D models. In this paper, we discuss the results, prospects, and shortcomings of such a 2D description of the effect of corotating interaction regions on the GCR intensity.

The study of precipitation of high-energy electrons from the magnetosphere into the Earth’s atmosphere is important for studying the physical mechanisms of electron acceleration during interplanetary disturbances in near-Earth space, the processes of formation of trapped electron fluxes in the magnetosphere and their subsequent precipitation into the atmosphere. In addition, the precipitating electrons affect the spacecraft operation and often lead to significant destruction of mesospheric ozone, etc. Since 1957, the Dolgoprudny Scientific Station of the Lebedev Physical Institute has been conducting continuous measurements of cosmic ray fluxes at altitudes of 0–30 km in the atmosphere of polar latitudes (Murmansk oblast, Antarctica) and at middle latitude (Moscow oblast). During this time, almost 600 cases of electron precipitation were recorded, mainly from the Earth’s outer radiation belt near its polar boundary due to measurement in Murmansk oblast. At the same time, several cases of electron precipitation were recorded at mid-latitude (Moscow oblast) and at the Mirny station in Antarctica, in particular, in 2022–2023. The paper discusses interplanetary and geomagnetic conditions during these events. Analysis of measurement data in the stratosphere made it possible to establish the absorption spectra of secondary bremsstrahlung photons and, on their basis, using the method we developed, to determine the primary energy spectra of precipitating magnetospheric electrons.

Phenomena in the outer layer of the solar atmosphere, the heliosphere, including the supersonic solar wind, the heliospheric magnetic field (HMF) carried by it, and cosmic rays propagating in the heliosphere are important for many processes occurring in this layer. For some of these processes such as geomagnetic activity or propagation of cosmic rays, not only the strength, but also the direction of the field is significant. Nonetheless, if in this regard the situation during periods of low sunspot activity is quite clear - the heliosphere is divided into two hemispheres with opposite polarity (toward the Sun/away from the Sun), - during periods of high sunspot activity when the HMF inversion occurs, there is no simple model of this phenomenon. The paper is a sequel to the study of the HMF inversion phenomenon and associated effects in the intensity of galactic cosmic rays (GCR). Previously, general ideas about the 22-year cyclicity in the characteristics of the Sun, heliosphere, and cosmic rays have been formulated, and the effects observed in the GCR intensity, which we associate with the HMF inversion, have been discussed in detail. This paper deals with a model of HMF inversion, associated only with the evolution of the magnetic field in the layer between the photosphere and the base of the heliosphere due to changes in the distribution of photospheric fields from one solar rotation to the next one, and shows that this is not enough to explain the main effects in the GCR intensity. In this layer, the magnetic field is the main energy factor. A more complete model of HMF inversion, including the transformation of its characteristics due to the interaction of different-speed solar wind streams in the heliosphere itself, where the solar wind is the main energy factor, will be discussed in the next paper.

An analysis of the data of spacecraft that scanned large areas of the heliosphere, as well as the results of magnetohydrodynamic calculations, indicates that corotating interaction regions of solar wind (SW), which are almost always present in the low- and mid-latitude heliosphere, sometimes strongly change the large-scale characteristics of the heliosphere that are important for long-term variations in the intensity of galactic cosmic rays (GCRs). In particular, for Carrington rotation no. 2066 (January–February 2008), these regions enhance magnetic fields in the inner (r < 3–5 AU) heliosphere and weaken them in the middle and far heliosphere, as well as significantly changing the polarity distribution of heliospheric magnetic fields. The assumption is made that in this situation the influence of the corotating interaction regions should lead to an increase in the GCR intensity in many regions of the heliosphere. This paper discusses the process of changing the polarity distribution of heliospheric magnetic fields due to the interaction of SW streams for Carrington rotation no. 2066 of different speeds, the simple model of the heliospheric magnetic field without an interaction between the SW streams of different speeds, as well as the results of numerical two-dimensional finite-difference calculations of longitude-averaged GCR intensity with the use of this model in comparison with a three-dimensional Monte Carlo calculation based on three-dimensional magnetohydrodynamic simulation of the heliosphere.

Кратко формулируются наблюдаемые явления, результаты моделирования и представления об инверсии гелиосферного магнитного поля (ГМП) и связанных с ним эффектах в интенсивности галактических космических лучей (ГКЛ).Основное внимание уделено обсуждению моделей ГМП в периоды его инверсии и сравнению ожидаемого из этих моделей поведения ГКЛ с наблюдаемым.Обсуждаются также пути дальнейшего численного исследования эффектов.

The regions of interaction between solar wind streams of different speed, known as corotating interaction regions, form an almost constantly existing structure of the inner heliosphere. Using observational data on the main characteristics of the heliosphere, important for GCR modulation, and the results of 3D MHD modeling of corotating interaction regions, and Monte Carlo simulation of recurrent GCR variations, we analyze the importance of the corotating interaction regions for longitude-averaged characteristics of the heliosphere and GCR propagation, and possible ways for simulating long-term GCR intensity variations with respect to the corotating interaction regions.

The effects of the 22-year variation of solar magnetic fields in the galactic cosmic ray (GCR) intensity were first observed and interpreted as manifestations of inversion of the high-latitude solar magnetic field in properties of heliospheric magnetic fields by the Lebedev Physical Institute team in 1973. Since then, these effects have been studied already for 50 years. The situation with the heliospheric magnetic field is clear for periods of medium and low sunspot activity — the heliosphere consists of two unipolar “hemispheres” separated by a wavy global heliospheric current sheet and characterized by a general polarity A (unit quantity with the sign of the radial component of the heliospheric magnetic field in the northern hemisphere). Yet there is no consensus on what the inversion of the heliospheric magnetic field is and which effects in the GCR intensity are connected with this phenomenon. In this article, we briefly formulate general concepts of the 22-year variation in characteristics of the Sun, heliosphere, and GCR intensity and discuss the observed effects in the GCR intensity, which we attribute to the heliospheric magnetic field reversal. Models for this phenomenon and the results of GCR intensity calculations with these models will be discussed in the next article.

Lebedev Physical Institute, Russian Academy of Sciences, 119991 Moscow, Russia Polar Geophysical Institute, Russian Academy of Sciences, 184209 Apatity, Russia Centre for Space Research, North-West University, 2520 Potchefstroom, South Africa School of Physical and Chemical Sciences, North-West University, 2745 Mmabatho, South Africa Institute for Experimental and Applied Physics, CA University in Kiel, 24118 Kiel, Germany E-mail: kalinin273@sci.lebedev.ru, gvozdevsky@pgia.ru, mkrainev46@mail.ru,

The conditions in the heliosphere are considered during the minimum phase of the sunspot cycle when the intensity of galactic cosmic rays (GCRs) attains its maximum at the Earth. These times of maximum GCR intensity are determined for the last five sunspot minima, including the present one. From the quantitative correlation between the heliospheric factors important to the modulation of GCRs in the heliosphere and the index of high-latitude photospheric magnetic field (all determined corresponding to times of GCR intensity maxima) the conclusion is made that the poloidal magnetic field of the Sun is one of the main governing factors for these heliospheric characteristics. Following this up, the dependence of proton spectra near the Earth on the index as mentioned above for the last five sunspot minima, 21/22 to 24/25, is calculated, also taking into account the strength of the heliospheric magnetic field and the tilt of the heliospheric current sheet, the solar wind speed and the position of the termination shock as the observable factors depending on the high-latitude photospheric magnetic field. The calculations are discussed with special attention paid to the comparison of spectra for the current and previous sunspot minima. The conclusion is made on the general dependence of GCR spectra on the poloidal magnetic field of the Sun.

We compare the quasi-biennial variations and Rieger-type variations (on a timescale of less than 1 year) in solar activity, interplanetary magnetic field, and galactic cosmic-ray flux modulation. We show that, in comparison with the 11-year cycle, the quasi-biennial variations are less suppressed in the interplanetary medium than on the Sun. Although the Rieger-type variations are adjacent in frequency to the quasi-biennial variations, they differ noticeably from them in the degree of reproduction in the interplanetary medium and the influence on the cosmic-ray modulation.

В работе получено 2D уравнение путём редуцированного по долготе 3D уравнения модуляции для галактических космических лучей, которое, вследствие наличия дрейфового механизма, не сводится к обычному осесимметричному уравнению. В результате сформулировано осесимметричное уравнение со средней по долготе скоростью дрейфа, дополненное слагаемым, имеющим форму источника и пропорциональным дрейфовому коэффициенту. На примере численного решения 3D уравнения модуляции для галактических протонов делается оценка точности источника 2D уравнения. Проводится обсуждение результатов и перспективы более адекватного учёта в 2D уравнении вклада дрейфов вдоль гелиосферного токового слоя в 3D уравнении.

Energetic electron precipitation (EEP) into the atmosphere is one of the mechanisms of depleting the Earth’s outer radiation belt. Precipitating electrons generate bremsstrahlung that penetrates the stratosphere and is recorded by detectors on balloons. However, these observations can be carried out only when the balloon is located at altitudes higher than ~20 km. The near-Earth POES satellites are constantly recording the fluxes of precipitating electrons in the loss cone, but they move too quickly in the space. In this paper, EEPs are compared on the basis of observations in the stratosphere and on satellites during 2003 and estimates of a number of EEP events at Apatity are obtained, assuming that the radiosonde was continuously located at an altitude higher than 26 km.

A study is performed of phases of solar cycle minima in sunspots, the heliosphere, and the intensity of Galactic cosmic rays (GCRs). Times of maximum GCR intensity in the minima of the last five cycles (including the current one), corresponding main heliospheric factors, and relationships between them are determined. The dependence of the near-Earth GCR proton spectrum on heliospheric factors of their linear trend in the minima of solar cycles 21/22, 22/23, and 23/24 (1987, 1997, 2009) is calculated and analyzed with emphasis on the behavior of crossover energy for successive minima.

The effect the three-component heliospheric magnetic field has on the modulation of galactic cosmic rays is considered. Radial and longitudinal components of the model are associated by the familiar Parker ratio. The latitudinal component is proportional to the radial one and emerges if the dependence of the latter deviates from the law of inverse squares. The model is tested using the problem of galactic proton modulation.

In the Parker model of the heliospheric magnetic field, the ratio of the azimuthal field component $${{B}_{{{\varphi }}}}$$ to the radial component $${{B}_{r}}$$ depends only on the radial speed V of the solar wind and coordinates of the observation point ( $$r,\,\theta $$ ): $${{{{B}_{{{\varphi }}}}} \mathord{\left/ {\vphantom {{{{B}_{{{\varphi }}}}} {{{B}_{r}}}}} \right. \kern-0em} {{{B}_{r}}}} = {{ - \omega r\sin \theta } \mathord{\left/ {\vphantom {{ - \omega r\sin \theta } V}} \right. \kern-0em} V}$$ (at a distance from the Sun r > 1 AU). We checked this relationship near the ecliptic at radial distances up to 19 AU based on data from the spacecraft VOYAGER 1, VOYAGER 2 and ULYSSES and outside the ecliptic according to ULYSSES data. It is shown that the predictions of the Parker model are in good agreement with observations outside the sector zones in time periods close to the solar activity minima. Within the sector zones and during periods of maximal solar activity, there are significant discrepancies between the observational data and the predictions of this model.

Using measurements from the PAMELA and ARINA spectrometers onboard the RESURS DK-1 satellite, we have examined the 27-day intensity variations in galactic cosmic ray (GCR) proton fluxes in 2007-2008. The PAMELA and ARINA data allow for the first time a study of time profiles and the rigidity dependence of the 27-day variations observed directly in space in a wide rigidity range from ~300 MV to several GV. We find that the rigidity dependence of the amplitude of the 27-day GCR variations cannot be described by the same power-law at both low and high energies. A flat interval occurs at rigidity R = <0.6-1.0> GV with a power-law index gamma = - 0.13+/-0.44 for PAMELA, whereas for R >= 1 GV the power-law dependence is evident with index gamma = - 0.51+/-0.11. We describe the rigidity dependence of the 27-day GCR variations for PAMELA and ARINA data in the framework of the modulation potential concept using the force-field approximation for GCR transport. For a physical interpretation, we have considered the relationship between the 27-day GCR variations and solar wind plasma and other heliospheric parameters. Moreover, we have discussed possible implications of MHD modeling of the solar wind plasma together with a stochastic GCR transport model concerning the effects of corotating interaction regions.

Effects on galactic cosmic rays (GCRs) of several heliospheric factors during the minimum phases of the sunspot cycles are studied. Times of maximum GCR intensity are determined for the last five sunspot minima, including the present one, together with the corresponding main heliospheric factors important for the modulation of GCRs in the heliosphere. The quantitative relation between these factors and the solar magnetic field is studied with the poloidal magnetic field of the Sun considered as a governing factor for many heliospheric characteristics during sunspot minima. The dependence of GCR proton spectra on these heliospheric factors for the last five sunspot minima 21/22–24/25 is calculated and discussed. Special attention is paid to the energy at which spectral cross-overs occur for consecutive minima, related to the changing polarity of the heliospheric magnetic field. The long-term observational series on GCR proton modulation at the Earth are considered with respect to the energy of these cross-overs.