B. A. Shakhov

Description of non-diffusive solar cosmic ray propagation in a homogeneous regular magnetic field

In the present paper the propagation of energetic charged particles in a magnetic field with a homogeneous regular component is studied. On the basis of the Boltzmann equation the analytical expressions for particle density and anisotropy are derived under instantaneous isotropic injection of particles into the scattering medium. Starting from the set of equations for spherical harmonics of the distribution function the new transport equation taking into account the second harmonic is carried out. The solution of this transport equation is reached and comparison with analytical solutions of the kinetic equation is performed. The telegraph equations for particle density and flux are derived and their solutions are analyzed. The transport of energetic particles under multiple small angle scattering is considered.

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.

Effect of the Heliopause and the Termination shock on the Galactic Cosmic rays distribution in stationary model of heliosphere

Standard model of galactic cosmic rays (GCR) propagation in heliosphere and adjacent interstellar space is considered. Here heliosphere is considered as a two-layered medium consisting of two spherical regions symmetrical about the Sun and adjacent to each other. In the internal region of the heliosphere, which is bounded by termination shock, solar wind has supersonic speed, and in the external region, which is bounded by heliopause, solar wind has subsonic speed. GCR scattering in these regions is happening in different ways and is characterized by corresponding diffusion rates. In the interstellar medium speed of the solar wind is supposed to be equal to zero and scattering became more weak. Here we suppose that there are no any sources of particles on the boundaries between layers. Exact analytical solution of corresponding mathematical problem is not difficult in principle, but is exceedingly bulky, therefore in this work analytic expressions are obtained both for high energy particles (>2500 MeV) and for low energy particles (<1400 MeV) for each region of their propagation. Distribution of the low energy particles confirm to results obtained on the «Voyager» spacecrafts. It is shown that irrespective of the scattering conditions in internal and external parts of the heliosphere density of the low energy particles is continuously growing from the Sun to the heliosphere boundaries.

Description of Solar Cosmic Ray Propagation in the Interplanetary Medium on the Basis of the Kinetic Equation

The propagation of solar cosmic rays in interplanetary space is considered based on the kinetic equation. The expression for cosmic ray density under instantaneous particle injection by a point-like source is obtained. The set of a differential equation system for harmonics of cosmic ray distribution function is obtained starting from the kinetic equation. The cosmic ray transport equation, taking into account the presence of the second harmonic of particle angular distribution, is derived and the solution of this equation is obtained.

Intensity of galactic cosmic rays in the early sun epoch

The process of heliospheric modulation of intensity of galactic cosmic rays is investigated by solving the transport equation. The spatial-energetic distribution of cosmic rays in the present epoch and in the past is analyzed. It is demonstrated that the particle density and the energy density of cosmic rays in the Solar System in the distant past were much lower than the corresponding current values. The cosmic ray intensity modulation in the early heliosphere was especially strong in the case of low-energy particles.

Ballistic and diffusive components in the dynamic spectra of ultrahigh energy cosmic rays from nearby transient sources

Ultrahigh energy cosmic rays (UHECRs, E > 1018 eV) from extragalactic sources deviate in the galactic and intergalactic magnetic fields, which explains the diffusive character of their propagation, the isotropization of their total flux, and the absence of UHECR clusters associated with individual sources. Extremely high energy cosmic rays (E > 1019.7 eV) are scattered mainly in localized magnetized structures, such as galaxy clusters, filaments, etc., with a mean free path of tens of megaparsecs; therefore, in the case of nearby transient sources, a substantial contribution to the observed flux is expected from unscattered and weakly scattered particles, which may be a decisive factor in the identification of these sources. We propose a method for calculating the time evolution of the UHECR energy spectra based on analytical solutions of the transport equation with the explicit determination of the contributions from scattered and unscattered particles. As examples, we consider the cases of transient activity of the nearest active galactic nucleus, Centaurus A, and the acceleration of UHECRs by a young millisecond pulsar.

The effect of solar wind high-speed streams on the galactic cosmic rays intensity

The effect of high-speed recurrent solar wind streams from coronal holes on the galactic cosmic rays intensity is investigated. The distribution of galactic cosmic rays for different solar cycles is considered based on the data of the world network of neutron monitors. Within the inhomogeneous model, which includes a homogeneous background and regions of high-speed streams (HSS’s), the transport equation has been solved and the effect of HSS’s on the spatial distribution of galactic cosmic rays is estimated. It is shown that theoretical calculations are agreed with the experimental results obtained for 2000–2014 under different assumptions about the mean free path of cosmic rays in the corresponding period of HSS’s.

On the coronal effect on the distribution of galactic cosmic rays in the absence of their interaction with the interstellar medium

Two problems of the stationary galactic cosmic ray (GCR) modulation in the closed heliospheric model are considered. It is assumed that the heliosphere is a spherically symmetric medium, which is limited by the heliopause, and GCRs propagate from it to the region spherically symmetric with respect to the Sun (corona). The GCR scattering beyond the coronal region is characterized by the constant diffusion coefficient. The solar wind velocity is also constant in this region. In the first problem GCRs are absorbed at the coronal boundary due to the interaction with the coronal material. In the second problem, GCRs are elastically scattered by coronal magnetic fields. As a result of solving these problems in the paper, it is shown that the coronal effect on the GCR modulation occurs only in a restricted region near the Sun.

Dynamics of solar cosmic ray energetic spectra during the solar flare on January 20, 2005

Propagation of cosmic rays in the interplanetary space that accelerated during the solar flare on January 20, 2005 is investigated based on the kinetic equation. The cases of instantaneous and continuous particle injection into the interplanetary medium are considered. Based on the analytic solution of the kinetic equation, it is shown that there is a sharp increase in the cosmic ray intensity in the Earth’s orbit in the case of the instantaneous particle injection, while their concentration increases gradually in the case of the continuous particle injection. The dynamics of the energy distribution of solar cosmic rays is analyzed.

Statistical acceleration and spatial diffusion of cosmic rays in turbulent medium

Statistical acceleration of cosmic rays in a turbulent medium is considered. Charged particles are assumed to acquire energy in a bounded region of space and leave the acceleration region due to spatial diffusion caused by the scattering of cosmic rays in turbulent magnetic fields. Analytical solutions of the cosmic ray transport equation are obtained and equilibrium space-energy distributions of high-energy particles are studied in the acceleration region and beyond.