The Global Survey Method Applied to Ground-level Cosmic Ray Measurements

The global survey method (GSM) technique unites simultaneous ground-level observations of cosmic rays in different locations and allows us to obtain the main characteristics of cosmic-ray variations outside of the atmosphere and magnetosphere of Earth. This technique has been developed and applied in numerous studies over many years by the Institute of Terrestrial Magnetism, Ionosphere and Radiowave Propagation (IZMIRAN). We here describe the IZMIRAN version of the GSM in detail. With this technique, the hourly data of the world-wide neutron-monitor network from July 1957 until December 2016 were processed, and further processing is enabled upon the receipt of new data. The result is a database of homogeneous and continuous hourly characteristics of the density variations (an isotropic part of the intensity) and the 3D vector of the cosmic-ray anisotropy. It includes all of the effects that could be identified in galactic cosmic-ray variations that were caused by large-scale disturbances of the interplanetary medium in more than 50 years. These results in turn became the basis for a database on Forbush effects and interplanetary disturbances. This database allows correlating various space-environment parameters (the characteristics of the Sun, the solar wind, et cetera) with cosmic-ray parameters and studying their interrelations. We also present features of the coupling coefficients for different neutron monitors that enable us to make a connection from ground-level measurements to primary cosmic-ray variations outside the atmosphere and the magnetosphere. We discuss the strengths and weaknesses of the current version of the GSM as well as further possible developments and improvements. The method developed allows us to minimize the problems of the neutron-monitor network, which are typical for experimental physics, and to considerably enhance its advantages.     

On the magnitude and direction of the anisotropy of galactic cosmic rays

The results of measuring the diurnal cosmic-ray intensity variations in the energy range 1–100 TeV are discussed. Whereas the phase of the first harmonic of the sidereal daily wave directly determines the phase (right ascension) of the cosmic-ray anisotropy vector, the amplitude and declination of the true anisotropy cannot be reconstructed directly from the amplitude of the first harmonic. However, they can be determined by invoking data on the zero harmonic. The results of some recent experiments purporting to measure the cosmic-ray anisotropy with a particularly high accuracy are shown to be interpreted erroneously.     

On reproduction of long-term cosmic-ray modulation as seen by neutron monitor stations

The dependence of cosmic-ray intensity on 21st solar cycle phenomena has been studied using monthly cosmic-ray values from nine world wide Neutron Monitoring Stations.For this purpose the long-term cosmic-ray modulation is modelled by treating the most appropriate source functions among various solar, interplanetary and terrestrial activity indices as the input and the cosmic-ray intensity as the output of a linear system taking into account the corresponding time-lag. In this way the modulated galactic cosmic-ray intensity has been reproduced to a certain degree as the cosmic-ray variations follow the observations with a standard deviation of ~ 10%. Still remaining short-term variations in all stations with periods of 2.7 and 3.7 months can possibly be related to the galactic origin of cosmic-rays.The Simpson solar wind model improved by the spherically symmetric diffusion-convection theory can describe our proposed method.     

The role of the energy spectrum anisotropy in the variations of the cosmic-ray fluctuations power-spectrum before interplanetary medium disturbances

The variations in the form of the cosmic-ray fluctuation power spectrum as an interplanetary shock wave approaches the Earth have been calculated for different values of cosmic ray anisotropy. The relevant experimental estimates of the power spectra are inferred from the data of cosmic ray detection with the ground-based neutron monitors at cosmic-ray stations. A comparison between the theoretical and experimental estimates has demonstrated an important role of the cosmic ray anisotropy spectrum in the generation of the power spectrum as the latter is rearranged before the interplanetary medium disturbances.     

Analysis of Forbush decreases during strong geomagnetic disturbances in March–April 2001

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.     

Cosmic-ray anisotropy in interplanetary space

The kinetic equation describing cosmic-ray propagation in interplanetary space has been used to construct a consistent theory of cosmic-ray anisotropy including the second spherical harmonic of particle angular distribution. The amplitude and phase of semi-diurnal cosmic-ray variation have been calculated. Expressions describing the relationships of the semi-diurnal variation parameters to helio-latitude distribution of cosmic rays have been derived. The results obtained are compared with observational data.     

Diffusion of the galactic cosmic rays in the vicinity of the solar system

Cosmic-ray propagation in the vicinity of 1 kpc from the Sun is considered. The data on the 10¹²–10¹⁵ eV particle anisotropy, on 10¹² eV electron spectrum, and on temporal cosmic-ray variations are analyzed. The diffusion coefficientD(10¹²–10¹³ eV)=10²⁹–10³⁰ cm²s^–1 inferred from the analysis coincides with its standard value in the large-halo model withh=15 kpc. The total power of cosmic-ray generation, about 3×10⁴⁹ erg per SN in the proton component and about 10⁴⁸ erg per SN in the electron component, typical of the galactic diffusion model is in agreement with the obtained parameters of local sources.     

Heliolatitudinal dependence of cosmic-ray anisotropy

We analyze the heliolatitudinal dependence of the cosmic-ray anisotropy using data from the Yakutsk complex of muon telescopes on the ground and underground at depths of 7, 20, and 60 m w. e. for 1972–2002. The radial cosmic-ray anisotropy component during this period at all recording levels is shown to have been systematically enhanced southward from the helioequator irrespective of the polarity of the general solar magnetic field. The azimuthal anisotropy component depends on heliolatitude only at negative polarity of the general solar magnetic field; it increases northward from the helioequator. Such a situation can take place in the case of interaction of the fast solar wind from coronal holes with the slow wind in the northern part of the heliosphere and continuous particle removal in its southern part.     

Sector structure of the interplanetary magnetic field and anisotropy of 50–1000 GV cosmic rays

It is demonstrated that, at high rigidities (50 GV and beyond), all the main features of cosmic-ray anisotropy of solar origin can be explained in terms of regular particle motion —without diffusion being involved — in the large-scale interplanetary magnetic field (IMF). A simple model of the IMF is adopted with a corotating warped neutral sheet separating the regions of alternative polarities; the warped shape is indispensable for obtaining any form of anisotropy. Energy losses occurring along various computed trajectories are calculated to give the sidereal, solar and antisidereal intensity waves. The reliability of the variations obtained are checked by changing the parameters of the IMF model. Both the sense and amplitude of the polarity-dependent sidereal vector are compatible with those established experimentally. Also reproduced are the predictions of corotation in addition to the 3-hour phase of the semi-diurnal wave. The corotation is found to be near perfect at 50 GV, while it reduces at 100 GV. The model presented accounts for the change of solar daily vector that was observed in 1969.     

A search of cosmic-ray variations generated by pulsations of the heliosphere

Application of new statistical techniques to time series allow the investigation of cosmic-ray intensity variation in the periodicity range of 1 to 10 years. We can put significant levels to the existence of these oscillations and define their character as quasi-periodic and/or recurrent. Correlations between cosmic-ray intensity variations and solar activity changes during 1944–1979 are investigated. The two-year variation in cosmic rays is observed to be variable both in amplitude and phase, and not correlated with sunspot cyclic variations; but seems to depend on the magnetic polarity of the interplanetary medium. No significant evidence for the existence of longer period variations is obtained.     

Interplanetary Transients and Cosmic-Ray Anisotropy

Cosmic-ray intensity data recorded with the ground-based neutron monitor at Deep River have been investigated taking into account the associated interplanetary magnetic field and solar-wind plasma data during 1981 – 1994. A large number of days having abnormally high or low amplitudes for five or more successive days as compared to the annual average amplitude of diurnal anisotropy have been taken as high- or low-amplitude anisotropic wave-train events. The amplitude of the diurnal anisotropy of these events is found to increase on days with a magnetic cloud as compared to the days prior to the event, and it is found to decrease during the later period of the event as the cloud passes the Earth. The high-speed solar-wind streams do not play any significant role in causing these types of events. However, corotating solar-wind streams produce significant deviations in cosmic-ray intensity during high- and low-amplitude events. The interplanetary disturbances (magnetic clouds) are also effective in producing cosmic-ray decreases. Hα solar flares have a good positive correlation with both the amplitude and direction of the anisotropy for high-amplitude events, while the principal magnetic storms have a good positive correlation with both amplitude and direction of the anisotropy for low-amplitude events. The source responsible for these unusual anisotropic wave trains in cosmic rays has been proposed.     

Cosmic ray anisotropies observed late in the decay phase of solar flare events

Concurrent interplanetary magnetic field and 0.7–7.6 MeV proton cosmic-ray anisotropy data obtained from instrumentation on Explorers 34 and 41 are examined for five cosmic-ray events in which we observe a persistent eastern-anisotropy phase late in the event (t ? 4 days). The direction of the anisotropy at such times shows remarkable invariance with respect to the direction of the magnetic field (which generally varies throughout the event) and it is also independent of particle species (electrons and protons) and particle speed over the range 0.06 ? β ? 0.56. The anisotropy is from the direction 38.3° ± 2.4° E of the solar radius vector, and is inferred to be orthogonal to the long term, mean interplanetary field direction. Both the amplitude of the anisotropy and the decay time constant show a strong dependence on the magnetic field azimuth. Detailed comparison of the anisotropy and the magnetic field data shows that the simple model of convection plus diffusion parallel to the magnetic field is applicable for this phase of the flare effect. It is demonstrated that contemporary theories do not predict the invariance of the direction as observed, even when the magnetic field is steady; these theories need extension to take into account the magnetic field direction ψ varying from its mean direction ψ _o. It is shown that the late phase anisotropy vector is not expected to be everywhere perpendicular to the mean magnetic field. The suggestion that we are observing kinks in the magnetic field moving radially outwards from the Sun leads to the conclusion that the parallel diffusion coefficient varies as 1/cos² (ψ ? ψ _o). Density gradients in the late decay phase are estimated to be ≈ 700%∣AU for 0.7–7.6 MeV protons. A simple theory reproduces the dependence of the decay time constant on anisotropy; it also leads to a radial density gradient of about 1000%∣AU and diffusion coefficient of 1.3 × 10²⁰ cm² s^?1.     

Oscillatory cosmic-ray shock structures

A multiple scales analysis is used to derive a mixed Burgers-Korteweg-de Vries (BKdV) equation in the long wavelength regime for a two-fluid MHD model used to describe cosmic-ray acceleration by the first-order Fermi process in astrophysical shocks. The BKdV equation describes the time evolution of weak shocks in the theory of diffusive shock acceleration for all possible cosmic-ray pressures. Previous work on weak shocks in the cosmic-ray MHD model has assumed that dissipation alone is sufficient to balance nonlinearity, but, as cosmic-ray pressures become small, the weak shock becomes discontinous. By including Hall current effects into the MHD model, the low cosmic-ray pressure limit leads smoothly into solitary wave behaviour. For low cosmic-ray pressures, the shock has a downstream oscillatory precursor which is smoothed into the standard Taylor shock profile with increasing cosmic-ray pressure. As a by-product of the perturbation analysis, a dissipative KdV equation is derived. In conclusion, dispersive effects on Alfvén waves are discussed and a modulational stability analysis is presented.     

Precursor Effects in Different Cases of Forbush Decreases

Over the last few years, the pre-decreases or pre-increases of the cosmic-ray intensity observed before a Forbush decrease, called the precursor effect and registered by the worldwide neutron monitor network, have been investigated for different cases of intense events. The Forbush decreases presented in this particular study were chosen from a list of events that occurred in the time period 1967?–?2006 and were characterized by an enhanced first harmonic of cosmic-ray anisotropy prior to the interplanetary disturbance arrival. The asymptotic longitudinal cosmic-ray distribution diagrams for the events under consideration were studied using the “Ring of Stations” method, and data on solar flares, solar-wind speed, geomagnetic indices, and interplanetary magnetic field were analyzed in detail. The results revealed that the use of this method allowed the selection of a large number of events with well-defined precursors, which could be separated into at least three categories, according to duration and longitudinal zone. Finally, this analysis showed that the first harmonic of cosmic-ray anisotropy could serve as an adequate tool in the search for precursors and could also be evidence for them.     

Application of diffusion — Convection model to diurnal anisotropy data

The diurnal anisotropy of cosmic-ray intensity observed over the period 1970–1977 has been analysed using neutron-monitor data of the Athens and Deep River stations. Our results indicate that the time of the maximum of diurnal variation shows a remarkable systematic shift towards earlier hours than normally beginning in 1971. This phase shift continued until 1976, the solar activity minimum, except for a sudden shift to a later hour for one year, in 1974, the secondary maximum of solar activity.This behavior of the diurnal time of maximum has been shown to be consistent with the convective- diffusive mechanism which relates the solar diurnal anisotropy of cosmic-rays to the dynamics of the solar wind and of the interplanetary magnetic field. Once again we have confirmed the field-aligned direction of the diffusive vector independently of the interplanetary magnetic field polarity. It is also noteworthy that the diurnal phase may follow in time the variations of the size of the polar coronal holes. All these are in agreement with the drift motions of cosmic-ray particles in the interplanetarty magnetic field during this time period.     

Inversion of the Cosmic-Ray Solar Diurnal Variations

We have bounded the upper cut-off rigidity (R_c) of the cosmic-ray diurnal anisotropy during the period 1968–1995. This period covers almost three solar cycles and includes three epochs of the solar polar field reversals. The diurnal variation observed by two detectors characterized by linearly independent kernels has been inverted in order to estimate the greatest lower bound (GLB) of R_c. We obtain a step function solution for the cosmic-ray anisotropy in free space which vanishes at the GLB of R_c. The greatest lower bound shows a magnetic cycle variation. The highest value of the amplitude of the anisotropy in free space at the GLB have been estimated as well.     

Variations of cosmic-ray energy in interplanetary space

A consistent theory of energy exchange between high-energy charged cosmic-ray particles and the random inhomogeneities of a magnetic field frozen in the moving solar wind plasma is developed. It is shown that the mode of the particle energy variations at a given law of plasma velocity variation in space is determined by the specific form of the particle distribution function. The equation for the density of cosmic-ray energy is obtained. Consideration is given to the generation of a charged particle energy spectrum in the course of multiple scatterings by the random inhomogeneities of the magnetic field.     

Significance of the turbulent sheath following the interplanetary shocks in producing forbush decreases

The physical processes responsible for transient cosmic-ray decreases have been investigated for two types of interplanetary shock events associated with helium enhancement (He-shocks) and those not associated with helium enhancement (non-He-shocks). The Calgary cosmic-ray neutron monitor data and the interplanetary field data have been subjected to a superposed-epoch Chree analysis. The difference in the profiles of the cosmic-ray intensity have been compared with the interplanetary field data and its variance. It is suggested that the turbulence sheath following the shock front is very effective and of major importance for producing cosmic-ray decreases. A simple model has been proposed to explain the observations which show that a Forbush decrease modulating region consists of a shock front associated with a plasma sheath in which the magnetic field is turbulent and the sheath, in turn, is followed by an ejected plasma cloud having ordered structure and high magnetic field strength.     

High-Speed Solar wind Streams and Cosmic-Ray Intensity Variations During 1991–1996

High-speed plasma streams identified in the solar wind measurements can be separated into two categories: coronal-hole-associated streams and flare-generated streams. Effects of these plasma streams on cosmic-ray intensity are studied for the period of 1991–1996. It is investigated that both of these high-speed solar wind plasma streams (CS and FGS) are found equally effective in producing the cosmic-ray intensity decrease on short-term basis.