The theory of particle diffusion in a strong random magnetic field with an allowance for higher multipole moments of the distribution function

The kinetic equation including a small-scale collisional integral for the particles propagating in a strong random and regular magnetic field [29] is solved by expanding the distribution function into series in spherical harmonics of the particle momentum angles. Using methods of the quantum theory of the angular moment [41], the equations for higher multipole moments of the distribution function in the space of momentum angles are derived and solved in the stationary case for the galactic cosmic rays in interplanetary space. The observed amplitudes and phases of the diurnal variation harmonics can be explained using the results of measurements of the interplanetary magnetic field performed on board the Ulysses spacecraft [12–14] and other satellites [45, 46] with an allowance for redistribution of the interplanetary and interstellar magnetic field lines. The spatial structure of the convection and diffusion fluxes of the galactic cosmic rays is refined. Formulas taking into account a change in the Earth’s axis tilt relative to the direction toward the Sun are derived, which allow the annual changes in contributions to the diurnal variation harmonics to be determined. The equation of diffusion taking into account the 2nd harmonic is obtained, and the contribution of this effect to the relative particle density in the cosmic rays in a spherically symmetric case is analyzed.     

Propagation of solar cosmic rays in loop-like interplanetary magnetic field structures

Features of propagation of relativistic solar cosmic rays in magnetic clouds have been considered on the basis of model calculations. Magnetic clouds have a structure of magnetic flux ropes and are extended from the Sun to the Earth via coronal mass ejections. Features of propagation of particles of different energies in a magnetic cloud are discussed. The propagation of high-energy solar protons in the loop-like structure of the interplanetary magnetic field in the event of October 28, 2003 is analyzed.     

Scattering of galactic cosmic rays by a magnetic cloud injected into interplanetary space during active solar processes

The scattering of charged particles as they pass through areas of the interplanetary magnetic field with large-scale inhomogeneities (magnetic clouds) is studied using the Monte Carlo method and the numerical simulation of trajectories. Charged particles (protons) with energies ranging from 1 to 100 GeV in magnetic clouds with sizes of 0.01–0.1 a.u. and magnetic flux densities of 5 to 50 nT are modeled. It is established that an important factor in determining the nature of galactic cosmic ray scattering is the relationship between the Larmor radii of particles, the size of a magnetic cloud, and the degree of magnetic field inhomogeneity.     

Transparency of a magnetic cloud boundary for cosmic rays

A magnetic cloud model is proposed in the form of a torus with a characteristic type of magnetic field (a flux rope) located inside an interplanetary coronal mass ejection propagating away from the Sun into interplanetary space. The magnetic field in the torus is determined. The transparency of the magnetic cloudsolar wind boundary is calculated for cosmic rays with different energies.     

Ground level enhancement of cosmic rays on November 6, 1997: Spectra and anisotropy

Variations of the rigidity spectrum and anisotropy of cosmic rays in the period of the ground-level enhancement (GLE) of cosmic rays on November 6, 1997, according to the data from the worldwide network of ground-based stations and satellites have been studied by the unique spectrographic global survey method developed at the Institute of Solar–Terrestrial Physics, Siberian Branch, Russian Academy of Sciences. Rigidity spectra of cosmic rays in various periods of the event under study have been determined. It has been shown that the acceleration of protons in the period of this GLE event was observed to a rigidity of ~10–12 GV, and neither a power-law nor an exponential function of the rigidity of particles describes the differential rigidity spectra of cosmic rays in the event under consideration. The analysis has indicated that the Earth at the time of the GLE event was in a looplike structure of the interplanetary magnetic field.     

Heliospheric modulation of high-energy cosmic rays: I. Basic model of cosmic-ray modulation with solar cycle

We have constructed a greatly simplified theory for the heliospheric modulation of high-energy cosmic rays in which no adjustable parameters are used. The only parameter k, which characterizes the degree of regularity of the interplanetary magnetic field, varies in the model in a definite way with solar cycle phase. The approximations used lead to solutions expressed in terms of elementary functions. The role of the magnetic drift of particles has been revealed. Quantitative agreement with the observed cosmic-ray variations has been achieved.     

Crossing resonance of stochastically interacting wave fields

The dynamic susceptibilities (Green’s functions) of the system of two interacting wave fields of different physical natures with a stochastically inhomogeneous coupling parameter between them with zero mean value have been examined. The well-known self-consistent approximation taking into account all diagrams with noncrossing correlation/interaction lines has been generalized to the case of stochastically interacting wave fields. The analysis has been performed for spin and elastic waves. The results obtained taking into account the processes of multiple scattering of waves from inhomogeneities are significantly different from those obtained for this situation earlier in the Bourret approximation [R.C. Bourret, Nuovo Cimento 26, 1 (1962)]. Instead of frequencies degeneracy removal in the wave spectrum and the splitting of resonance peaks of dynamic susceptibilities, a wide single-mode resonance peak should be observed at the crossing point of the unperturbed dispersion curves. The fine structure appears at vertices of these wide peaks in the form of a narrow resonance on the Green’s-function curve of one field and a narrow antiresonance on the vertex of the Green’s-function curve of the other field.     

Analysis of the anisotropy of the muon flux, according to data obtained by the URAGAN muon hodoscope during heliospheric disturbances

Features of studying heliospheric disturbances caused by changes in the parameters of the interplanetary magnetic field by the anisotropy of the muon flux of cosmic rays detected on the surface of the Earth by the URAGAN muon hodoscope are considered. The anisotropy of the muon flux in the period 2007–2011 is analyzed. The forecasting potential of our approaches to studying heliospheric disturbances using the penetrating component of cosmic rays is evaluated.     

Localized pits and peaks in forbush decrease, associated with stratified structure of disturbed and undisturbed magnetic fields

Summary Forbush decrease (FD) is generally interpreted as a result of diffusion-convection of cosmic rays in a disturbed interplanetary magnetic field associated with the magnetohydrodynamic shock wave caused by solar flare. In this paper, we point out that a large number of FDs contain an isolated region or regions with pit-type time profile, in which cosmic rays are not in a diffusion-convection state but in a trapped state in undisturbed, uniform and strong magnetic field perpendicular to the solar wind. The trapped state is also characterized with a large ratio of the magnetic to ion thermal energy. The median duration time of the state is about 8 hours. About half of these states are associated with the northward (or southward) magnetic field, while the other half with the eastward (or westward) magnetic field. Flares responsible for the former state seem to be concentrated in an eastward region from about 30°W on the solar disk, while those for the latter state seem rather symmetric with respect to the centre of the solar disk. It is suggested that the trapped state is produced inside a magnetic tube of force which is not of a small scale such as that of the magnetic bubble pointed out by Klein and Burlaga, but of a large scale, having a horseshoe structure with its ends supposed to be connected to somewhere in an inner region near the Sun and with its cross-section supposed to be of a thin filament with radial and transverse dimensions of ≈0.1 a.u. and ≈1.1 a.u. at the Earth’s orbit. This belt-like tube of force is supposed to be produced on the solar surface or near the Sun and to be carried out by solar wind in a frozen state, trapping in itself low-density cosmic rays near the Sun. In addition to the pits, we point out also the existence of some peaks which are observed not only in the trapped region but also in a region of extremely disturbed magnetic field neighbouring in between two trapped regions. It is suggested that cosmic rays in the region of the latter type are supposed to be guided freely (or easily) from outer space through a path with similarly disturbed magnetic state, and therefore, they could maintain their density in the region always higher than in the neighbouring regions. Two kinds of cosmic-ray-guiding mechanism in the above can be regarded as being at opposite poles.     

Characteristics of Forbush Decreases Measured by the PAMELA Instrument During 2006–2014

During the several decades of Forbush decrease (FD) studies the main properties of this phenomenon were established. Today is clear that Forbush decreases originate as the responses of cosmic ray particle fluxes to solar-induced processes inside interplanetary space. Moreover the profiles of FD’s are the manifestation of the complex structure of coronal mass ejections (CMEs) which are driving from the Sun and often accompanied by flares. So the investigation of FD’s is a useful tool for understanding the dynamics of CME processes and the effects they have on in the interplanetary space. Classification and theoretical interpretation of different FD’s are important for understanding the complex effect of CME’s as well as the search for new features of their behavior. Spectra of cosmic ray protons and helium nuclei obtained by the PAMELA experiment in the rigidity range between 1–15 GV were used to investigate the characteristics of Forbush decreases. Additional data on the interplanetary magnetic field and solar wind speed were taken from the ACE data center for correlation analysis. Rigidity dependences for selected Forbush decreases are also presented.

     

Forbush decrease in the intensity of cosmic rays in a toroidal model of a magnetic cloud

The time dynamics of the particle distribution function in a magnetic cloud with the shape of a toroidal segment with the characteristic (forceless) structure of a magnetic field has been calculated. The shape of the cloud at the subsequent propagation in the interplanetary space has been determined by the kinematic model. The magnetic field of the cloud is calculated using the freezing-in condition. A significant effect of regions connecting the magnetic cloud with the Sun on the propagation of particles in the region of perturbation has been revealed. The calculation of the particle density and anisotropy of the intensity demonstrates reasonable agreement with the measurements. The results indicate the decisive role of the characteristic structure of the magnetic field in the time dynamics of the Forbush decrease in the intensity of cosmic rays.     

Combined mechanisms of solar cosmic ray acceleration

Spectra of solar cosmic rays on the Sun’s surface at a flare site and near Earth are modeled using the Monte Carlo method. Two of the most important mechanisms of energy accumulation by the particles are considered simultaneously: the regular acceleration of ions by the impulsive electric field of the current sheet and stochastic acceleration by the Alfvenic turbulence. This leads to substantial variations in the particle spectra in the low-energy region.     

Fluctuations of cosmic rays and interplanetary magnetic field in the vicinity of interplanetary shock fronts

The spectral characteristic of fluctuations of cosmic rays (CRs) and the interplanetary magnetic field in the prefront region of interplanetary shock waves, where coherent CR fluctuations with energies from ～10 keV to ～1 GeV are often observed, have been studied. It is concluded that the spectrum of CR fluctuations is subjected to modulation by fast magnetosonic waves generated by low-energy CRs reflected and/or accelerated at the shock fronts.     

Transport of charged particle pulses in interplanetary magnetic fields

The charged particle scattering in the presence of a regular magnetic field is considered starting from the Boltzmann kinetic equation in the case of an arbitrary relation between the mean free path and the distance from a particle source. It is shown that the Green function for the kinetic equation can be represented as the sum of the distribution functions of non-scattered particles which propagate with the injection pitch angle and of the scattered ones. The obtained Green function of the Boltzmann equation and also the particle density describe the space-time-pitch angle cosmic ray distribution that corresponds to an instantaneous particle injection at a particular pitch angle.This work was supported by International Science Foundation (grant N UC 8000) and by Slovak Grant Agency for Science (grant No. 1353/95).     

DIMENSIONAL METHOD TO SOLVE THE DIFFUSION CONVECTION EQUATION OF SOLAR COSMIC RAYS

Physical processes of the propagation of the solar cosmic rays in the interplanetary space include the diffusion in interplanetary disordered magnetic fields and the convection in solar winds. Dimensional method can be applied to solve those equations convertible into Bessel equation, the results obtained are identical with those solved by the commonly used separate variable method. In order to derive an analytic solution to the diffusion convection equation in an unbounded, uniform medium, two dimensionless parameters reflecting the diffusion and convection characteristics of the particles are introduced. In the diffusion dominated case, the solution is similar in form to the diffusion of a source moving with the convection velocity and is modified by another convection term, which can be expanded into a power series of the convection parameter with coefficients composed of the generalized hypergeometric function series of the diffusion parameter. This solution has a clear physical meaning, and can suitably be used in the discussion of the rise phase characteristics of the solar cosmic rays from medium to high energies （E_p≥10¹ MeV）.     

Particle acceleration at astrophysical shocks: A theory of cosmic ray origin

The theory of first order Fermi acceleration at collisionless astrophysical shock fronts is reviewed. Observations suggest that shock waves in different astrophysical environments accelerate cosmic rays efficiently. In the first order process, high energy particles diffuse through Alfvén waves that scatter them and couple them to the background plasma. These particles gain energy, on the average, every time they cross the schock front and bounce off approaching scattering centers. Calculations demonstrate that the distribution function transmitted by a plane shock is roughly a power law in momentum with slope similar to that inferred in galactic cosmic ray sources. The generation of the scattering Alfvén waves by the streaming cosmic rays is described and it is argued that the wave amplitude is probably non-linear within sufficiently strong astrophysical shocks. Hydromagnetic scattering can operate on the thermal particles as well, possibly establishing the shock structure. This suggests a model of strong collisionless shocks in which high energy particles are inevitably produced very efficiently. Observable consequences of this model, together with its limitations and some alternatives, are described. Cosmic ray origin and astrophysical shocks can no longer be considered separately.     

PROPAGATION EFFECTS OF SOLAR COSMIC RAYS

Computer calculations have been made on the dimensional solution to the anisotropic diffusion convection equation for solar cosmic rays propagating in an uniform and unbounded interplanetary medium. This paper presents the results calculated by means of Jokipii's diffusion coefficients. Discussion is restricted to the influences of solar wind convection on the rise to maximum times and on the peak intensities of solar cosmic ray events with solar corotation effect taken into consideration. The model well explains the asymmetrical variations of the propagation charateristics of the events with solar longitudes of their parents flares relative to the interplanetary magnetic field lines passing through the earth, and the theoretical curves of the rise times fit satisfactorily the observations of solar events ranging from relativistic to about 30 MeV medium energies.     

Temporal changes in the energy spectrum of Forbush decreases in 20–23 solar activity cycles

Variations in the energy spectrum of galactic cosmic rays during Forbush decreases registered in the 20–23 solar activity cycles are studied, using the data from neutron monitors and the Yakutsk cosmic ray spectrograph. It is shown that the Forbush decreases in the 23rd cycle of solar activity had a harder energy spectrum than in the three previous cycles, due to the relatively low level of turbulence of the interplanetary magnetic field during the 23rd solar activity cycle.     

Heliospheric modulation of high-energy cosmic rays: II. Deformation of the neutral surface

Analysis of neutron monitor data in the periods of negative and positive polarities of the general solar magnetic field has revealed a dependence of the long-term cosmic-ray modulation on both deformation of the neutral surface of the interplanetary magnetic field and solar activity level. The effects of solar activity and neutral surface deformation dominate at positive and negative polarities, respectively. The magnetic drift of cosmic rays with different trajectories in the epochs of positive and negative polarities is responsible for this behavior of the 11-year and annual density modulations.