Solar energetic particle (SEP) events are mostly generated by solar flares. They can be associated not only with flares that occur on the visible side of the Sun but also on the backside. It is noted that the shape of the time profiles of SEP events associated with flares on the back side of the Sun does not correspond to the typical impulsive or gradual time profiles. X-rays are the main source of information about the processes of energy release and particle acceleration in solar flares. For many years, information on this type of emission for flares on the back side of the Sun was rare. Nowadays, the ability to obtain this type of information is becoming more and more available. We present the results of testing numerical model realized as a code that makes it possible to reproduce the shape of the time profile of SEP events using simple assumptions about particle propagation into the interplanetary space. The time profiles of SEP protons with energies above 30 MeV have been modeled assuming that the particles were accelerated only in the solar atmosphere during the flare. Tests have been done for four impulsive flares that occurred in the western hemisphere of the Sun and in the center of the solar disk. We simulated the time profile of an SEP event, the source of which was a flare that possibly occurred on the backside of the Sun on October 21, 2003. The results, possibilities for model improvements, and the application of this method to the study of SEP events with no source on the visible side of the Sun are discussed.

The article presents the results of a comparative analysis of the solar proton event on March 30, 2022, which has an unusual time profile of solar proton fluxes, and the previous and subsequent solar proton events (March 28, 2022, and April 02, 2022). Increases in energetic proton fluxes in the interplanetary and near-Earth space are associated with successive solar X-ray flares M4.0, X1.3, and M3.9 and three halo-type coronal mass ejections. The study was based on experimental data obtained from spacecraft located in the interplanetary space (ACE, WIND, STEREO A, and DSCOVR), in a circular polar orbit at an altitude of 850 km (Meteor-M2) and in geostationary orbit (GOES-16, Electro-L2). An explanation has been proposed for the specific features of the energetic proton flux profile in the solar proton event on March 30, 2022: protons accelerated in the flare on March 30, 2022 were partially screened by an interplanetary coronal mass ejection, the source of which was the explosive processes on the Sun on March 28, 2022; late detection of maximum proton fluxes, simultaneous for particles of different energies, is due to the arrival of particle fluxes inside an interplanetary coronal mass ejection. The spatial distribution of solar protons in near-Earth orbit was similar to the distribution at the Lagrange point L1 but with a delay of 50 min.

The paper explores the possibilities of using data classification methods when forecasting time series of the geomagnetic Kp-index by machine learning methods. To classify categories of the Kp-index based on the degree of disturbance, linear and logistic regression, random forest, gradient boosting on top of decision trees, and artificial neural networks of various architectures are used. The results of these methods are compared with a trivial inertial forecast (the statistical indicators of which for problems of this type are always high) at horizons from 3 h to 1 day in 3-h increments. The problem of choosing a cross-validation scheme for selecting the model hyperparameters, ways to overcome the imbalance of categories, the relative importance of input features, as well as the dependence of the results on the test sample (beginning of the 25th solar activity cycle) on inclusion in the training sample of data from the 23rd and 24th cycles or only the 24th cycles are studied. Based on the results, conclusions are drawn about the preferred methods for classifying values of the Kp-index based on the level of geomagnetic disturbance. Ways for further research and possible improvement of the classification quality are outlined, including for determining the characteristic hidden states of Earth’s magnetosphere as a dynamic system in order to improve the quality of forecasting geomagnetic indices.

The results of studying the fluxes of solar protons with energies greater than 5 MeV in near-Earth space on March 13–23, 2023, are presented. The features of the period under study are no visible solar flare with which the beginning of the event could be associated and an untypical time profile of proton fluxes, as well as a long duration of the existence of solar proton fluxes in near-Earth space. An attempt was made to explain the sources of the observed different variations in particle fluxes and to understand what happened on the Sun and in the near-Earth space. The source of solar protons on March 13, 2023, was an explosive process on the back side of the Sun from the Earth, registered as a coronal mass ejection of very high power. The reason for the long and complex time profile of solar protons was the contribution of particle acceleration processes on the Sun and in the interplanetary medium, as well as the modulation of particle fluxes by the structures of the interplanetary magnetic field. A possible scenario has been proposed to explain the existence of increased fluxes of solar particles on March 15–23, 2023: the formation of a heliospheric structure, this being a closed trap region formed by two interplanetary coronal mass ejections and regions of interaction of high-speed and slow solar wind streams. The study uses experimental data obtained from the Solar Orbiter spacecraft and from spacecraft located near the L1 point of the Earth–Sun system (ACE and DSCOVR) and in geostationary orbit (GOES-16).

The authors demonstrate the possibility of using CubeSat nanosatellites to study solar cosmic rays (SCRs). SCR electron fluxes over the polar caps at altitudes of ∼550 km are detected. Measurements are made using scintillation detectors of cosmic radiation (DeCoR) mounted on several CubeSat nanosatellites of Moscow State University during an SCR event on September 6–21, 2022.

The paper applies the methods of information theory to the study of the interplanetary magnetic field and its variations as a result of solar activity. The statistical regularities of the projections of the vectors of the interplanetary magnetic field and the speed of the flow of solar wind particles do not carry information about the order of realization for the available states of the studied physical system. At the same time, such characteristics can be obtained from phase diagrams or phase portraits created on the basis of experimental samples in subspaces of the phase space, which display both the values of vector quantities and the sequence order in a particular time series. The paper proposes a method for synthesizing vector graphs in the phase subspace of the interplanetary magnetic field (IMF). Results are considered of the reconstruction and analysis of implemented graphs based on the time series of satellite monitoring of the state of the IMF, provided by the database of the NASA Goddard Space Flight Center since the beginning of 2023. The graph is constructed on the basis of experimental samples for projections of magnetic field vectors. Field vectors converge and diverge at the nodes of the graph, the edges of the graph allow one to control the analyzed trajectory of the system in the phase subspace and restore the transition tree for a particular vector field. The concept of a spherical reference surface of a vector graph is introduced, which allows one to bring the compared implementations of graphs to a single linear scale and a single curvature of the reference surface. Examples are considered under the action of various external factors associated with the solar magnetic field and coronal mass ejections.

Magnetic storms can cause disruptions in the operation of radio communications, pipelines, power lines, and electrical networks, and they may possibly cause human health problems. Therefore, prediction of geomagnetic disturbances is of great practical value. Geomagnetic disturbances are usually described with the help of geomagnetic indices, including the planetary index K_p which is provided at a 3-h interval. The approach used in this study implies classifying geomagnetic disturbances according to the level of the K_p index. To do so, the whole range of the index values is divided into several intervals according to the degree of disturbance. The input data are time series of parameters of solar wind and interplanetary magnetic field, measured onboard spacecraft at the L1 Lagrange point between the Sun and the Earth, aa well as the value of the K_p index itself. To account for the ‘‘memory’’ of the time series, delay embedding of all the parameters is used—for each of the parameters, its several preceding values are taken into account. Additional preprocessing of the parameters is performed by calculating moving averages and other statistical indicators of the time series. To perform classification, various machine learning methods such as gradient boosting and artificial neural networks are used. The optimal values of the parameters of each method are determined by cross-validation, and pattern misbalance among the classes is partially reduced using the SMOTE technique. It is demonstrated that the suggested approach outperforms the trivial inertial model for all the values of the prediction horizon from 3 to 24 h (with a 3-h step). The most efficient preprocessing methods are described, as well as the best machine learning models.

The problem of improving the neural network forecast of geomagnetic index Dst under conditions in which the input data for such a forecast are measured by two spacecraft, one of which is close to the end of its life cycle, and the data history of the other is not yet enough to construct a neural network forecast of the required quality. For an efficient transition from the data of one spacecraft to the data of another, it is necessary to use methods of domain adaptation. This paper tests and compares several data translation methods. Also, for each translated attribute, an optimal set of parameters for its translation were found, which further reduces the difference between domains. The paper shows that the use of domain adaptation methods with the selection of significant features can improve the forecast compared to the results of using untranslated data.

One of the promising approaches to predicting the values of geomagnetic indices is the use of machine learning methods. However, for the effective use of such methods, it is necessary to select essential input features of the problem in order to reduce its input dimension. In this paper, we consider an algorithm for obtaining the most efficient forecasting model based on lowering the input data dimension by gradually discarding input features based on the following machine learning methods: linear regression, gradient boosting, and a multilayer perceptron artificial neural network. The effectiveness of the listed methods is compared; the directions of further development of this work are considered.

— The first results of monitoring the radiation state of the near-Earth space on the Arktika-M no. 1 spacecraft in a high-apogee Molniya orbit are considered. The characteristics of the devices of the heliogeophysical instrumentation complex GGAK-HE are presented. The results of the comparative analysis of experimental and model distributions of energetic particle fluxes of the Earth’s radiation belts in the orbit of the Arktika-M no. 1 , as well as of some features of the dynamics of the outer electron radiation belt in 2021 and 2022 and the solar proton event of October 28, 2021, based on the experimental data from Arktika-M no. 1 , Meteor-M no. 2 , and Elektro-L no. 2 spacecraft are presented.

The use of the normalized range method for an analysis of the fast variability of electron fluxes in near-Earth space is proposed. This method makes it possible to conclude whether a uniform time series corresponds to a random process, or whether there are memory effects or excessive variability. This study analyzes the SiriusSat experiment data. We used data on the time of each particle interaction in the detector with an accuracy of ~20 μs, which makes it possible to study variations in electron fluxes of subrelativistic energies on subsecond time scales. In some cases, the value of the Hurst exponent indicates excessive flux variability in the gap region ( $$L\sim 2.3$$ ) east of the South Atlantic anomaly at characteristic times of 0.6–0.9 s.

The potential is investigated of predicting the time series of the Dst geomagnetic index using various adaptive methods: artificial neural networks (classical multilayer perceptrons), decision trees (random forest), gradient boosting. The prediction is based on the parameters of the solar wind and interplanetary magnetic field measured at the Lagrange point L1 in the ACE spacecraft experiment. It is shown that the best prediction skill of the three adaptive methods is demonstrated by gradient boosting.

The results of a comparative analysis from Russian satellite data on the radiation environment in the near-Earth space during September–November 2020 are presented. The source of variations in the fluxes and spectra of electrons in the Earth’s outer radiation belt during this period was the high-speed fluxes of the solar wind from the coronal hole. Differences in the response of the Earth’s outer radiation belt to recurrent geomagnetic disturbances at each solar revolution are discussed.

We studied 87 events of solar cosmic rays, i.e., solar energetic particle (SEP) emissions associated with solar flares of at least M5 class (according to the GOES classification) that occurred during solar cycle 23. A relationship between the spectral parameters of the SEP events and the microwave (MW) emission properties of the related solar flares was analysed. The peak frequency of the MW spectrum was used as an indicator of the acceleration processes during solar flares, which may characterize both the strength of magnetic field in the emission source and the intensity of the accelerated particle flux. The magneto-morphological classification (MMC) was applied to take into account the features of the magnetic topology of the active regions (ARs) that generated flares. Our analysis showed that most of ARs, associated with SEP events with large proton flux, violated at least one of the empirical laws established for sunspot groups (Hale’s law, Joy’s law, or another). The relationships between the spectral properties of electrons and protons and the properties of MW radiation were analyzed and discussed, taking into account the MMC of ARs generated flares associated with SEP events.

The possible use of artificial neural networks—classical multilayer perceptrons—with coupling functions to forecast time series of the Dst geomagnetic index is studied. The basic forecast is based on parameters of the solar wind and interplanetary magnetic field measured at the libration point L1 in an experiment on the ACE spacecraft. It is shown that the largest contribution to the improvement in forecast quality is made by the Bs and vBs functions, as well as the use of several coupling functions simultaneously.

The ways are studied to improve the quality of prediction of the time series of hourly mean fluxes and daily total fluxes (fluences) of relativistic electrons in the outer radiation belt of the Earth 1 to 24 hours ahead and 1 to 4 days ahead, respectively. The prediction uses an approximation approach based on various machine learning methods, namely, artificial neural networks (ANNs), decision tree (random forest), and gradient boosting. A comparison of the skill scores of short-range forecasts with the lead time of 1 to 24 hours showed that the best results were demonstrated by ANNs. For medium-range forecasting, the accuracy of prediction of the fluences of relativistic electrons in the Earth's outer radiation belt three to four days ahead increases significantly when the predicted values of the solar wind velocity near the Earth obtained from the UV images of the Sun of the AIA (Atmospheric Imaging Assembly) instrument of the SDO (Solar Dynamics Observatory) are included to the list of the input parameters.

The paper proposes a model for predicting the integral daily fluxes (fluences) of relativistic electrons (RE) (E > 2 MeV) of the Earth's outer radiation belt in a geostationary orbit using images of the Sun in the ultraviolet range. The results show that the accuracy of the forecast of the RE fluxes three or four days ahead increases significantly when adding the predicted values of solar wind speed at the Earth’s orbit, obtained by processing images of the Sun in the UV range from AIA instrument, SDO Observatory, to the input parameters of the forecasting model.

We present the results of a comparative analysis of the properties of a series of successive solar flares, which occurred in active region (AR) 10069 in August 2002, and the associated solar energetic particle (SEP) events. The active region was extremely flare productive during its evolution. The solar flare characteristics are based on X-ray and radio emission data: maximum detected photon energies and spectral index, delays between microwave, metric-radio and, hard X-ray emissions. The coronal mass ejections (CMEs) are characterized by their projected speed. The SEP properties are described by the relative electron to proton abundance as well as by the abundance of lower relative to higher energy particles. The analysis carried out supports some previous results obtained by large statistical studies, but at the same time refutes others. For example, the set of analyzed events that occurred in the AR did not show clear evidence of the big flare syndrome though the large proton events observed near Earth were always accompanied by CMEs. Some of the peculiar observations could be the result of the magnetic topology of the AR.