The article develops a method for determining the geomagnetic cutoff rigidity based on tracing of charged particles in Earth’s magnetic field using the particle-in-cell method implemented in the Buneman–Boris scheme. In order to test the method, the geomagnetic cutoff rigidity in the field of an ideal dipole and in the field given by the IGRF model are calculated. In the first case, the obtained data are compared with analytical values. The calculation accuracy in this case is 3 MV. In the second case, the penumbra pattern is reproduced in different geographical locations, for different periods, and the stability of the method to small perturbations of the initial parameters is investigated. As the main results, the article constructs and analyzes geomagnetic cutoff rigidity maps at low-orbit satellite altitudes for different directions in space as well as their variations from 1900 to 2015.

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.

A model is created of the motion of galactic cosmic ray particles in the Earth’s magnetosphere, as defined by the IGRF and CHAOS models of the magnetic field. A second model contains a lithospheric field component that is missing from the first model. Power spectra are obtained for the flux of galactic cosmic rays at a fixed height above the Earth’s surface, and a difference is discovered at high orders of multipole expansion l > 7 . When l > 20 , the result can be explained by the contribution from the lithospheric component of the magnetic field in the CHAOS model, relative to the IGRF. When l ⩽ 20 , it can be explained by the difference in the accuracy of describing the main field, since the IGRF is limited to the 13th order of expansion.

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.

The method for determining the geomagnetic cutoff rigidity is presented, based on tracing charged particles in the Earth’s magnetic field using the particle-in-cell model implemented in the Buneman–Boris method. The method verification results are given, along with comparisons to theoretical calculations in the ideal dipole field and existing calculations in the real field. The developed procedure shows high reliability through the replication of known effects. In a dipolar approximation, it is much more accurate than theoretical calculations. A typical pattern of the geomagnetic cutoff penumbra is reproduced.

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.

Very high accuracy and sensitivity have become attainable by modern instruments for experimental measurements of physical quantities in various scientific fields. Yet it is still impossible to completely eliminate the influence of instrumental effects on the result. The measured values of a physical quantity inevitably differ, sometimes significantly, from the true ones. The question therefore arises of restoring the true distributions from the measured ones, taking the specific features of the experiment and the characteristics of scientific instruments into account. Different approaches are in use based on a mathematical model of the instrument and the formulation of the deconvolution problem. We describe this problem, key ideas and methods for its solution, and features and implementation details using the example of elementary particle physics and space physics experiments.

We review the development of modern models of the magnetic field of Earth's inner magnetosphere, from the selection of experimental results to the approximation and presentation of the model output data. In particular, we discuss all principal sources of the magnetic field, their description in various models, and approaches to parameterizing the field. We briefly recall the history of the study of Earth's magnetic field and discuss modern-day and earlier experimental data used in model building and the underlying core mathematical tools. The main features of the majority of modern models describing Earth's magnetic field in the inner magnetosphere are discussed.

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.

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.

Unfolding is currently an important stage of processing experimental data, reducing the effect of errors and reconstructing approximately real distributions of quantities. Numerous approaches exist to solve this problem; in particular, they are widely used in the modern physics of atomic nuclei and elementary particles, space physics, and other related areas. However, many algorithms are not designed or are poorly adapted to reconstruct multidimensional distributions corresponding to, e.g., several characteristics of particles measured simultaneously. In this work, a method has been proposed to adapt the singular value decomposition (SVD) unfolding algorithm to the multidimensional case. The proposed modified method has been tested in application to simulation data for the cosmic ray spectrum measured in the PAMELA space experiment. This method not only makes it possible to estimate the real distribution of a multidimensional quantity (momentum and two angles specifying the direction of entering a particle into an instrument) but also provides a better result compared to the classical SVD approach in the one-dimensional case (only the momentum of the p-article).

This paper presents examples that characterize various aspects of the possibility of determining the phase composition of solid multielement substances and materials containing nanostructured forms of their components by a differential dissolution stoichiographic method. The use of stoichiography makes it possible to detect and quantitatively determine both known and unknown crystalline and amorphous phases of constant and variable composition without standards of solid phases. The use of stoichiographic methods and ideas of nonequilibrium thermodynamics allows one to gain fundamentally new data on solid-state transformations of multielement, multiphase substances and materials.

The PAMELA magnetic spectrometer on board the Resurs-DK1 spacecraft measured the fluxes of charged particles and antiparticles in cosmic radiation from June 2006 to January 2016. Based on the results from measurements, secondary antiprotons were first detected in near-Earth space in 2011, and the energy spectra of the albedo and captured components were determined in the 60 to 750 MeV range of energies. This work presents the results from measuring the antiproton flux in the Earth’s radiation belt according to the data of the PAMELA experiment, obtained over the period of the experiment, using improved algorithms for data processing and event selection.

A way of calculating a directional flux of charged particles in near-Earth space under conditions of high anisotropy of the flux is developed. It can be used for telescope-type spectrometers capable of measuring the direction of incident particle arrival.

We present a study of the east–west anisotropy of trapped-proton fluxes in low-Earth orbit based on the measurements of the Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics (PAMELA) experiment. The differential intensities of eastward- and westward-traveling protons detected in the South Atlantic Anomaly region were estimated as a function of equatorial pitch angle and drift shell, for six energy bins between 80 MeV and 2 GeV. We found that, as a consequence of the strong atmospheric gradient coupled with the large gyroradius in this energy range, the intensities of eastward fluxes exceed those of westward fluxes by a factor of ∼10–20. However, the reported directional asymmetry also depends on the sign of the local flux gradient, resulting in more intense westward fluxes beyond the radial distances where the inner belt peaks. PAMELA observations can be used to improve the description of the near-Earth radiation environment at lowest altitudes and highest trapping energies, where current theoretical and empirical models are affected by the largest uncertainties.

In this paper, we present an overview of antiproton fluxes measured in modern spectrometer-type experiments PAMELA (2006–2016) and AMS-02 (2011–present). These experiments provided important data on the fluxes of antiprotons of galactic origin and contributed towards the discovery of secondary antiprotons in the near-Earth space. We discuss the impact of the scientific discovery made in the PAMELA experiment as well as the confirmation of these results in the AMS-02 experiment, which was done with high statistical accuracy and additional extension of measurements into the high energy region. An outline of the existing theoretical models that attempt to describe the newly obtained spectra by introducing additional sources of galactic antiprotons is provided.

We present a study of the solar-cycle variations of >80 MeV proton flux intensities in the lower edge of the inner radiation belt, based on the measurements of the Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics (PAMELA) mission. The analyzed data sample covers an 8 year interval from 2006 July to 2014 September, thus spanning from the decaying phase of the 23rd solar cycle to the maximum of the 24th cycle. We explored the intensity temporal variations as a function of drift shell and proton energy, also providing an explicit investigation of the solar-modulation effects at different equatorial pitch angles. PAMELA observations offer new important constraints for the modeling of low-altitude particle radiation environment at the highest trapping energies.