A simple and robust method of reconstruction of the geomagnetically trapped proton fluxes detected with the PAMELA spectrometer is proposed. Instead of multiple calculations of the effective area for different pitch-angles and different orientations of the instrument relative to the geomagnetic field vector, a value of an effective geometrical factor (GF) is estimated using one simulation sample with additional information about the instrument’s orientation relative to the vector of the Earth magnetic field. In this procedure, the additivity of the geometrical factor for different parts of the instrument’s field of view (FOV) is used. The simulation data sample is obtained in a standard way using Monte Carlo calculations of the isotropic flux. The method was tested on the task of reconstruction of the angular distribution of the Galactic proton flux. The fluxes in the Earth’s Inner Radiation Belt (IRB) recovered with this method were compared with the measurements of the NOAA-17 experiment and showed a good agreement.

High anisotropy of geomagnetically trapped particles’ fluxes requires utilization of a complex methodology for their reconstruction from in-flight measurements. For precise position-sensitive instruments operating in the event-by-event mode, a standard approach is the one originally developed for the SAMPEX/MAST experiment. It consists in calculation of the instrument’s effective areas averaged over gyro-phase angle as a function of pitch angle of detected particles for detector’s different orientations relative to the geomagnetic field vector. This orientation normally changes as the instrument moves in space. Moreover, some space vehicles bearing a measuring instrument may and do change their orientation during flight by rotation of the instrument or as a whole. Each possible orientation needs an independent calculation of effective areas for each possible pitch angle, which is usually done by means of Monte-Carlo simulation. Therefore, especially for sophisticated devices, the calculation of an accurate and representative response function (consisting of a set of effective areas) may involve a vast amount of computation.In this paper, we propose a simplified approach, which is based on the assumption that for an anisotropic flux, the angular sphere the particles come to the detector from can be split into solid angle domains, within which the flux can be treated as isotropic. This allows one to use much easier computed geometrical factor or acceptance of the instrument as the proportionality factor. This method suggests that it can be calculated with respect to registration of the particles from these domains (we call it partial acceptance). The main advantage of the presented method is that the whole set of partial acceptances for each instrument orientation relative to the geomagnetic field vector and for all available values of (equatorial) pitch-angle for this orientation can be obtained from one simulation sample (for the given energy) of isotropic flux.

Forbush decreases are sudden drops of cosmic ray intensity recorded by ground based and satellite detectors. This effect is strongly connected with coronal mass ejections from the Sun. Those are the massive eruptions of plasma material from the Sun atmosphere into interplanetary space. Coronal mass ejections affect cosmic ray particles while moving through interplanetary space causing Forbush decrease. In this work, we have studied the behavior of time profiles of cosmic ray intensity during Forbush decreases using data on cosmic proton fluxes recorded by the AMS-02 from 2011 to 2019.

The research of the electron and positron spectrum of galactic cosmic rays is an important task of high-energy astrophysics. The necessity of using new methods of electron and positron registration is caused by insufficient statistical reliability of data from modern experiments in the TeV energy range. In the present work, one of the possible registration methods based on the use of synchrotron radiation of electrons and positrons in the Earth’s magnetic field is investigated. Using modeling of trajectories of high-energy electrons, positrons, and synchrotrons photons emitted by them, the detector count rate for the ISS and ROS orbits has been estimated. The possibility of separation of electrons and positrons using this method is shown.

The future space-based GAMMA-400 scientific observatory is being developed under the Federal Space Program of Russian Federation in the period from 2016-2025. This observatory includes a γ-ray telescope, which will detect gamma rays in the energy range from ~20 MeV to several TeV with high angular and energy resolutions and cosmic-ray electrons + positrons up to several tens of TeV using main and lateral appertures. Recent experimental observations indicate a possible existence of a break in the electrons + positrons spectrum at around TeV energies. A number of speculations to explain this phenomenon have arisen. This article presents the method of high-energy electrons detection from the lateral aperture of the GAMMA-400 gamma-ray telescope. This method implements the machine learning analysis and provides the high-energy proton background rejection at the level of 10$^4$ in the energy range from 100 GeV to 10 TeV. The effective acceptance for electron detection with such proton rejection is about 0.52 m$^2$×sr for the four lateral sides of the GAMMA-400 gamma-ray telescope. This effective acceptance exceeds by several times that of CALET and DAMPE experiments. This capability of our instrument will allow to improve significantly the measurements of electron + positron flux above 1 TeV and, hence, understand better the debatable spectrum break.

The GAMMA-400 gamma-ray telescope is the successor of Soviet and Russian gamma-ray telescopes. GAMMA-400 is being developed for cosmophysical research in accordance with the Russian Federal Space Program 2016–2025. The GAMMA-400 experiment will be implemented aboard the Russian astrophysical space observatory in a highly elliptic orbit during 7 years to provide new data on gamma-ray emission mainly from the Galactic plane, Galactic Center, the Sun and cosmic-ray electron + positron fluxes. The main mode of observations will be the continuous point-source mode with the duration of up to ∼ 100 days. The GAMMA-400 gamma-ray telescope will study high-energy gamma-ray emission up to several TeV and cosmic-ray electrons + positrons up to 20 TeV. GAMMA-400 will have the never-achieved angular resolution, the high-energy and time resolutions, as well as very good separation efficiency of gamma rays from cosmic-ray background and of electrons + positrons from protons. The distinctive features of GAMMA-400 are the excellent angular resolution of ∼0.01^∘ at E_γ=100 GeV that exceeds resolutions of the space-based and ground-based gamma-ray telescopes by a factor of 5–10, as well as high-energy resolution of ∼2% at E_γ=100 GeV. GAMMA-400 studies can discover gamma-ray emission from annihilation or decay of dark matter particles, identify many unassociated discrete sources, explore the structure of extended sources, search for gamma-ray bursts and solar gamma-ray flares, improve the data on cosmic-ray electron + positron spectra for energies of >50 GeV.

The space observatory GAMMA-400 is processed currently in accordance with the Federal Space Program of the Russian Federation for 2016–2025. The observatory includes a gamma-ray telescope for experimental studies of gamma rays in the energy range from ~20 MeV to ~1 TeV with high angular and energy resolution, as well as for research of electrons + positrons at energies above 100 GeV in both the main (top-down), and lateral apertures. At present time, there are experimental indications concerning the possibility of existing of spectrum break in electrons + positrons intensities about TeV energies. This point stimulates several speculations to explain such phenomena. In this paper we examined capabilities of GAMMA-400 telescope to explore this problem. The methods for electron detection in the energy range from 100 GeV up to 10 TeV from the lateral aperture of a gamma-ray telescope are presented. Also, the results of calculation for proton rejection factor and for electron acceptance are revealed.

A Forbush decrease (FD) is a sudden drop of cosmic-ray intensity arising as an effect of coronal mass ejection (CME) propagation in interplanetary space. The different physical properties of each CME cause variability in the FDs observed by scientific instruments. A comprehensive study of both phenomena is required to properly understand the processes involved in FDs. Most of the current studies in this field use experimental data obtained by ground-based apparatus that measure the flux of cosmic rays via their interaction with Earth’s atmosphere. Direct measurements in space of FDs are rather rare. In this work, we present the results obtained by the spacecraft-borne experiment Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics (PAMELA). The experiment took data from 15 June 2006 until January 2016. A series of FDs during the period 2006 – 2013 were studied. Only significant events with amplitude ≥ 10 R = 1.1 – 2.9 GV were taken into account. The dependencies of the recovery times on the particle rigidity were obtained for FD events generated by halo-type CMEs.

A new processing of the data obtained with the PAMELA spectrometer in the under-cutoff area and particularly at the lower edge of the Earth’s Inner Radiation Belt (IRB) is presented. For the reconstruction of anisotropic fluxes, a new method has been developed. The method is based on the division of the instrument’s field of view (FOV) into segments within which the flux could be treated as isotropic. For such an approach one single simulation data set is required. Using this method, distributions of proton fluxes measured with the PAMELA spectrometer over equatorial pitch angle, L-shell, and energy were reconstructed in a new way. Additionally, high energy (E>50 MeV/n) trapped 3He nuclei were found and analyzed.

The upcoming GAMMA-400 experiment will be implemented aboard the Russian astrophysical space observatory, which will be operating in a highly elliptical orbit over a period of 7 years to provide new data on gamma-ray emissions and cosmic-ray electron + positron fluxes, mainly from the galactic plane, the Galactic Center, and the Sun. The main observation mode will be a continuous point-source mode, with a duration of up to ~100 days. The GAMMA-400 gamma-ray telescope will study high-energy gamma-ray emissions of up to several TeV and cosmic-ray electrons + positrons up to 20 TeV. The GAMMA-400 telescope will have a high angular resolution, high energy and time resolutions, and a very good separation efficiency for separating gamma rays from the cosmic-ray background and the electrons + positrons from protons. A distinctive feature of the GAMMA-400 gamma-ray telescope is its wonderful angular resolution for energies of >30 GeV (0.01° for Eγ = 100 GeV), which exceeds the resolutions of space-based and ground-based gamma-ray telescopes by a factor of 5–10. GAMMA-400 studies can reveal gamma-ray emissions from dark matter particles’ annihilation or decay, identify many unassociated, discrete sources, explore the extended sources’ structures, and improve the cosmic-ray electron + positron spectra data for energies of >30 GeV.

Machine learning is used to obtain ratios of 100–500-MeV positron-to-electron and electron-to-proton fluxes with rigidities of 1–1.7-GV from the PAMELA experimental data for 2006–2016 in order to study the solar modulation of cosmic-ray fluxes with energies below 1 GeV. Observed features of the data and a comparison to AMS-02 experimental results allow study of the charge–sign dependence of modulation around the sunspot minimum in 2009 and the maximum in 2015.

The anomalous effect found in the PAMELA experiment is an increase of the fraction of positrons in the total electron–positron flux of galactic cosmic rays. To study the nature of this effect, it is necessary to measure the positron flux with energies above 1 TeV. In this work, we model the process of detecting positrons and electrons by registering their synchrotron radiation in the geomagnetic field. In our calculations, we used the international model of the Earth’s magnetic field IGRF. The positrons’ detection efficiencies in the TeV energy range for the polar and equatorial regions at an altitude of 400 km above the Earth are compared. According to estimates, the operation of the detector in the polar regions is preferable as it provides ∼ (5–35) % greater efficiency.

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.

The isotopic composition of Li and Be nuclei in the 1–5 GV range of rigidities (nuclear energies of 0.1–1.5 GeV/nucleon) is analyzed using PAMELA flight data from 2006–2014 on the rigidity of detected nuclei and their velocities (time-of-flight analysis and ionization losses in the detector’s multilayer calorimeter). The new PAMELA data expand the range of energies in earlier measurements, are consistent with scarce results, and indicate correlated deviations of Li and Be isotope ratios from the GALPROP data for GCRs, which can be interpreted as evidence of contributions from several nearby local sources against the GCR background. Analysis of precision AMS-02 data on the spectra of positrons, antiprotons, and secondary nuclei of Li, Be, and B also indicates correlated increases in intensity at rigidities of ~50–1000 GV, which could also be due to local sources. The contribution from local sources against the GCR background is estimated at levels of tens of percents for rigidities of 1–5 GV and several percent at rigidities of 50–1000 GV.

The global features of the modulation of galactic cosmic ray protons and helium nuclei are studied in the heliosphere from minimum to maximum solar activity with a comprehensive, three-dimensional drift model and compared to observations measured by PAMELA and AMS02 taken between 2006 and 2017. Combined with accurate very local interstellar spectra (VLIS) for protons and helium nuclei, this provides the opportunity to study in detail how the proton to helium (p/He) ratio at different rigidities behaves with increasing solar activity, through solar maximum conditions and afterward. In particular, the effects at the Earth of the difference in their VLIS's, mass-to-charge ratio (A/Z) and those caused by the main modulation mechanisms are investigated. We find that the rigidity slopes of the parallel and perpendicular diffusion coefficients below 4 GV should change differently before solar maximum than afterwards to reproduce the observed p/He ratio, in addition to scaling down (up) the values of the diffusion and drift coefficients towards (after) solar maximum. The compatibility between the model computations and observations indicate that the PAMELA and AMS02 measurement of p/He above similar to 5 GV precisely reveals the difference in the rigidity slopes of their VLIS's at these rigidities.

The currently developing space-based gamma-ray telescope GAMMA-400 will measure the gamma-ray and electron + positron fluxes using the main top-down aperture in the energy range from ~20 MeV to several TeV in a highly elliptic orbit (without shading the telescope by the Earth and outside the radiation belts) continuously for a long time. The instrument will provide fundamentally new data on discrete gamma-ray sources, gamma-ray bursts (GRBs), sources and propagation of Galactic cosmic rays and signatures of dark matter due to its unique angular and energy resolutions in the wide energy range. The gamma-ray telescope consists of the anticoincidence system (AC), the converter-tracker (C), the time-of-flight system (S1 and S2), the position-sensitive and electromagnetic calorimeters (CC1 and CC2), scintillation detectors (S3 and S4) located above and behind the CC2 calorimeter and lateral detectors (LD) located around the CC2 calorimeter. In this paper, the capabilities of the GAMMA-400 gamma-ray telescope to measure fluxes of GRBs from lateral directions of CC2 are analyzed using Monte-Carlo simulations. The analysis is based on off-line second-level trigger construction using signals from S3, CC2, S4 and LD detectors. For checking the numerical algorithm the data from space-based GBM and LAT instruments of the Fermi experiment are used, namely, three long bursts: GRB 080916C, GRB 090902B, GRB 090926A and one short burst GRB 090510A. The obtained results allow us to conclude that from lateral directions the GAMMA-400 space-based gamma-ray telescope will reliably measure the spectra of bright GRBs in the energy range from ~10 to ~100 MeV with the on-axis effective area of about 0.13 m2 for each of the four sides of CC2 and total field of view of about 6 sr.

The observation of various cosmic ray particles at the Earth had been done with the PAMELA space detector for almost 10 years, from June 2006 to January 2016. The AMS-02 space experiment provides similar cosmic ray data. The purpose of this work is to utilize the available state-of-the-art numerical modulation model for the transport of cosmic rays in the heliosphere to compute the modulation of galactic protons from minimum to maximum solar activity. These modeling results, which simulate realistic heliospheric conditions, are compared to proton observations from PAMELA taken between 2006 and 2010 and to similar AMS-02 observations after 2011. It will be shown how differently modulation mechanisms influence the time-evolution of the proton spectra when modulation conditions change from minimum to maximum, including a reversal of the polarity of the heliospheric magnetic field.

Time-dependent energy spectra of galactic cosmic rays (GCRs) carry fundamental information regarding their origin and propagation. When observed at the Earth, these spectra are significantly affected by the solar wind and the embedded solar magnetic field that permeates the heliosphere, changing significantly over an 11 yr solar cycle. Energy spectra of GCRs measured during different epochs of solar activity provide crucial information for a thorough understanding of solar and heliospheric phenomena. The PAMELA experiment collected data for almost 10 years (2006 June 15–2016 January 23), including the minimum phase of solar cycle 23 and the maximum phase of solar cycle 24. In this paper, we present new spectra for helium nuclei measured by the PAMELA instrument from 2010 January to 2014 September over a three-Carrington-rotation time basis. These data are compared to the PAMELA spectra measured during the previous solar minimum, providing a picture of the time dependence of the helium-nuclei fluxes over a nearly full solar cycle. Time and rigidity dependencies are observed in the proton-to-helium flux ratios. The force-field approximation of the solar modulation was used to relate these dependencies to the shapes of the local interstellar proton and helium-nuclei spectra.

The PAMELA experiment had operated almost ten years on board of the Resurs DK1 satellite. The satellite was launched on the 15th of June 2006 and placed in orbit with an inclination of 70 degrees and an altitude of 350 to 610 km. The experiment had continuously measured electron and positron fluxes of Galactic cosmic rays in a wide energy range from about 50 MeV to hundreds of GeV. The spectra of electrons have been analysed from the end of 23rd until the beginning of 24th solar cycle including the prolonged deep solar minimum period from 2006 to the end of 2009 and the solar magnetic polarity reversal period in 2012-2014. Here, we present updated annual electron spectra from 2006 to 2015.

The future space-based GAMMA-400 gamma-ray telescope will operate onboard the Russian astrophysical observatory in a highly elliptic orbit during 7 years to observe Galactic plane, Galactic Center, Fermi Bubbles, Crab, Vela, Cygnus X, Geminga, Sun, and other regions and measure gamma- and cosmic-ray fluxes. Observations will be performed in the point-source mode continuously for a long time (~100 days). GAMMA-400 will measure gamma rays in the energy range from ~20 MeV to several TeV and cosmic-ray electrons + positrons up to several tens TeV. GAMMA-400 instrument will have very good angle and energy resolutions, high separation efficiency of gamma rays from cosmic-ray background, as well as electrons + positrons from protons. The main feature of GAMMA-400 is the unprecedented angular resolution for energies >30 GeV better than the space-based and ground-based gamma-ray telescopes by a factor of 5-10. GAMMA-400 observations will permit to resolve gamma rays from annihilation or decay of dark matter particles, identify many discrete sources, clarify the structure of extended sources, specify the data on cosmic-ray electron + positron spectra.