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According to the data of ground-based measurements of cosmic rays (CRs) from the world network of stations, the behavior of CR intensity during the geomagnetic disturbance in January 2015 has been studied using the spectrographic global survey method. The spectra of CR variations and spectrum indexes of these variations are presented, when approximating the spectrum by the power function of the particle rigidity in the rigidity range from 10 to 50 GV, as well as pitch-angular anisotropy of CRs. It is shown that the spectrum indexes of CR variations at its approximation by the power function of the particle rigidity in the phase of maximum modulation are greater than in the phases of decay and recovery of CR intensity.

The data from terrestrial observations of cosmic rays at the global network of stations by the method of spectrographic global survey were used to analyze two Forbush decreases during the geomagnetic storms in March and June 2015. The spectra of cosmic ray variations, pitch angle anisotropy of cosmic rays at different phases of Forbush decrease development, and the changes in the planetary system of geomagnetic cutoff rigidities are presented. It is shown that, during the approximation of the spectra of variations by the power function of particle rigidity in the interval of 10–50 GV, the spectrum index is softer at the maximum modulation phase than during the phases of cosmic ray intensity decline and recovery. In the axisymmetric model of the bounded magnetosphere of the Earth, which takes into account the currents at the magnetopause and the ring current, the distance to the subsolar point and the radius of the ring current, as well as the contribution of the ring current to the changes in geomagnetic cutoff rigidity and to the Dst index during the studied events, are determined.

Using data from ground-based observations of cosmic rays (CRs) on the worldwide network of stations and spacecraft, we have investigated the proton spectra and the CR anisotropy during the ground level enhancements of CRs on May 17, 2012 (GLE71) and January 6, 2014 (GLE72) occurred in solar cycle 24 by the spectrographic global survey method. We provide the CR rigidity spectra and the relative changes in the intensity of CRs with a rigidity of 2 GV in the solar–ecliptic geocentric coordinate system in specific periods of these events. We show that the proton acceleration during GLE71 and GLE72 occurred up to rigidities R ~ 2.3−2.5 GV, while the differential rigidity spectra of solar CRs are described neither by a power nor by an exponential function of particle rigidity. At the times of the events considered the Earth was in a loop-like structure of the interplanetary magnetic field.

We propose a mechanism for proton propagation from the Sun to Earth orbit in the electromagnetic field presented, in the simplest case, through the Parker model. Within this model, proton ingress on the Earth is shown possible in the case when the Earth is in the surroundings of the heliospheric current sheet neutral line (HCSNL), at the distance from the latter that is smaller than the Larmor radius of the protons drifting along the HCSNL. Based on that model, we analyzed the paths of the protons with energies characteristic of solar proton events. As a result of such an analysis, solar proton events on the Earth appear to be observed only in the case when energetic protons eject from an active region (AR) located in the northern (southern) hemisphere of the Sun, at the positive (negative) polarity of the solar global magnetic field in that AR. There is a minimal value for the proton energy below which solar proton events on the Earth are not observed. This energy value is proportional to the value for the angle of the latitude at which the flare AR is located.

Variations in the cosmic ray intensity (specifically, Forbush effects) and in the geomagnetic cutoff rigidity planetary system during powerful geomagnetic disturbances in cycle 23 were studied based on worldwide station network data by the global spectrographic survey method. The cosmic ray variation spectra during these periods and the spectral indices of these variations when the spectrum was approximated by the power function of the particle rigidity varying from 10 to 50 GV during different Forbush effect development phases are presented. It was indicated that the spectral indices of cosmic ray variations during spectrum approximation by the power function of the particle rigidity are larger during the maximal modulation phase than during the cosmic ray intensity decline and recovery phases. The fact that the amplitude of the second harmonic of the cosmic ray pitch angle anisotropy did not increase on November 20, 2003, confirms that the Earth fell into a Sun-independent spheromark magnetic cloud. The increased amplitudes of the second harmonic of the cosmic ray pitch angle anisotropy during other Forbush effects in July 2000, March–April 2001, October 2003, and November 2004 indicate that the Earth was in the coronal mass ejection region, in which the interplanetary magnetic field structure was loop-like during these periods.

Using data from a worldwide network of neutron monitors, we have investigated the cosmicray (CR) energy spectra and anisotropy during the CR increases attributable to the solar events of June 11 and 15, 1991, by the spectrographic global survey method. By jointly analyzing ground-based and satellite measurements, we have determined the parameters of the CR rigidity spectrum reflecting the electromagnetic characteristics of the heliospheric fields in each hour of observations within the framework of the model of CR modulation by regular heliospheric electromagnetic fields. The CR spectra and relative CR intensity variations in the solar—ecliptic geocentric coordinate system are presented at specific times of these events.

Using ground-based cosmic-ray (CR) observations on the worldwide network of neutron monitors, we have studied the variations in CR rigidity spectrum, anisotropy, and planetary system of geomagnetic cutoff rigidities during Forbush decreases in March-April 2001 by the global spectrographic method. By jointly analyzing ground-based and satellite measurements, we have determined the parameters of the CR rigidity spectrum that reflect the electromagnetic characteristics of the heliospheric fields in each hour of observations within the framework of the model of CR modulation by the heliosphere’s regular electromagnetic fields. The rigidity spectra of the variations and the relative changes in the intensity of CRs with rigidities of 4 and 10 GV in the solar-ecliptic geocentric coordinate system are presented in specific periods of the investigated events.

We propose a model for the modulation of cosmic rays (CRs) based on changes in the CR energy in different regular electromagnetic fields of the interplanetary medium. Within the framework of the elaborated concept, an analytical expression for the CR rigidity spectrum has been obtained. It allows us to describe variations in proton intensity observed in the energy range from several MeV to several tens of GeV per hour of observation. We give a description of a method for determining parameters of the model spectrum that reflect the electromagnetic characteristics of the interplanetary medium with a different nature. Using ground-based and satellite measurements of the CR intensity, we have examined variations in the CR rigidity spectrum and anisotropy and variations in the planetary system of geomagnetic cutoff rigidities during different manifestations of solar activity. A whole set of phenomena under observation has been interpreted.

Using the spectrographic global survey method, variations in the rigidity spectrum and anisotropy of galactic cosmic rays (March 1991) have been studied using data from ground-based observations of cosmic rays (CR) at the worldwide network of stations. Variations in geomagnetic cutoff rigidity (GCR) have been calculated. The paper also presents latitudinal GCR variations at certain moments of the considered period for different geomagnetic field disturbance levels. Calculation results of GCR variations have been compared with those of effect of the westward current flowing with a strength proportional to the latitude cosine along parallels on the sphere, for different radii of the current ring in the dipole field.

Dynamic processes in the interplanetary space have been investigated using time variations in time parameters of the cosmic-ray rigidity spectrum. Change of heliosphere electromagnetic characteristics has been found out to precede sporadic phenomena on the Sun. In particular, it is shown that sporadic phenomena are followed by generation of local polarization electric fields, decrease of the magnetic-field strength in small-scale heliospheric structures, and increase of the potential difference between the pole and the plane of the ecliptic. These features allow prediction of solar proton events in advance (from several hours to several tens of hours) with a high degree of confirmation.

The Forbush decrease (Fd) of the Galactic cosmic ray (GCR) intensity and disturbances in the Earth’s magnetic field generally take place simultaneously and are caused by the same phenomenon, namely a coronal mass ejection (CME) or a shock wave created after violent processes in the solar atmosphere. The magnetic cut-off rigidity of the Earth’s magnetic field changes because of the disturbances, leading to additional changes in the GCR intensity observed by neutron monitors and muon telescopes. Therefore, one may expect distortion in the temporal changes in the power-law exponent of the rigidity spectrum calculated from neutron monitor data without correcting for the changes in the cut-off rigidity of the Earth’s magnetic field. We compare temporal changes in the rigidity spectrum of Fds calculated from neutron monitor data corrected and uncorrected for the geomagnetic disturbances. We show some differences in the power-law exponent of the rigidity spectrum of Fds, particularly during large disturbances of the cut-off rigidity of the Earth’s magnetic field. However, the general features of the temporal changes in the rigidity spectrum of Fds remain valid as they were found in our previous study. Namely, at the initial phase of the Fd, the rigidity spectrum is relatively soft and it gradually becomes hard up to the time of the minimum level of the GCR intensity. Then during the recovery phase of the Fd, the rigidity spectrum gradually becomes soft. This confirms that the structural changes of the interplanetary magnetic field turbulence in the range of frequencies of 10−6 – 10−5 Hz are generally responsible for the time variations in the rigidity spectrum we found during the Fds.