Yu. I. Fedorov

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.

Non-diffusive particle pulse transport – Application to an anisotropic solar GLE

A theory of the transport of an anisotropic pulse of charged particles injected into the interplanetary magnetic field is applied to an anisotropic ground level event on 24 May 1990. For this event the kinetic regime is considered when the mean free path is comparable with the distance from particle source. Both the source angular particle distribution and the angular dependence of a detector response are included. The theoretically predicted temporal profiles are compared with the particle intensity records measured by several neutron monitors with different asymptotic directions.

Modulation of galactic cosmic ray intensity in the turbulent heliosphere

The modulation of galactic cosmic ray intensity by heliospheric magnetic fields is considered. The spatial and energy distribution of cosmic ray density and anisotropy is investigated based on the obtained analytical solution of the transport equation. The magnitude and direction of galactic cosmic ray energy flux are estimated.

Charged particle acceleration in the front of the shock wave bounding supersonic solar wind

The process of cosmic ray acceleration in the front of the spherical shock wave bounding the supersonic solar wind is studied. On the basis of our analytical solution of the transport equation, the energy and spatial distributions of cosmic ray intensity and anisotropy are investigated. It is shown that the shape of accelerated particle spectrum is determined by the medium compressibility at the shock front and by cosmic ray modulation parameters.

Statistical acceleration of cosmic rays in anisotropic turbulent medium

Acceleration of cosmic rays interacting with the anisotropic magnetohydrodynamic turbulent medium is studied. Particle acceleration is caused by a large-scale electric field arising in a turbulent medium due to the α-effect. A comparison is made of equilibrium spectra of cosmic rays, characteristic of the specific acceleration mechanism, with the energy distribution of particles corresponding to the statistical Fermi acceleration.

Intensity of Cosmic Rays at the Initial Stage of a Solar Flare

The propagation of solar cosmic rays in the interplanetary space is analyzed by solving the Fokker–Planck equation in the small-angle approximation. The particle source is assumed to be instantaneous and point-like. The spatiotemporal distribution of density of energetic particles in the anisotropic phase of a solar cosmic-ray enhancement is examined. Prolonged particle injection into the interplanetary medium is also discussed.

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.

Propagation of galactic cosmic rays in the outer heliosphere

The propagation of galactic cosmic rays in heliospheric magnetic fields is studied. An approximate solution to the cosmic ray transport equation has been derived on the basis of a method that takes into account the small value of anisotropy of particle angular distribution. The spatial and energy distributions of the cosmic ray intensity and anisotropy have been investigated, and estimates of cosmic ray energy flux have been carried out.

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.