Related papers: Anomalous diffusion of the cosmic rays: steady-sta…
We consider the propagation of galactic cosmic rays under assumption that the interstellar medium is a fractal one. An anomalous diffusion equation in terms of fractional derivatives is used to describe of cosmic ray propagation. The…
The problem of the origin of cosmic rays in the shocks produced by supernova explosions at energies below the so called 'knee' (at ~3*10$^6$ GeV) in the energy spectrum is addressed, with special attention to the propagation of the…
We have made a new calculation of the cosmic ray electron spectrum using an anomalous diffusion model to describe the propagation of electrons in the Galaxy. The parameters defining the anomalous diffusion have been recently determined from…
Cosmic ray propagation is diffusive because of pitch angle scattering by waves. We demonstrate that if the high-amplitude magnetohydrodynamic turbulence with $\tilde B/\langle B\rangle \sim 1$ is present on top of the mean field gradient,…
Fractional differential approach to cosmic ray physics problems is discussed. A short review in this field is given, some results are represented, analyzed and criticized. A new model called the bounded anomalous diffusion model is offered.…
Possible formulations of the problem of cosmic rays acceleration in the interstellar galactic medium are considered with the use of fractional differential equations. The applied technique has been physically justified. A Fermi result has…
We consider the problem of the cosmic ray spectrum formation assuming that cosmic rays are produced by Galactic sources. The anomalous diffusion equation proposed in our recent papers is used to describe cosmic ray propagation in the…
We derive explicit, algebraic expressions for the steady-state number density of cosmic ray electrons as a function of position and energy using Green's function of the diffusion equation with energy losses for an axisymmetric distributions…
The origin of the ultrahigh energy cosmic ray remains being a mystery. However, a considerable progress has been made in the past few years due to the good quality data recorded by current cosmic ray observatories. One of the recent…
We calculate the energy spectra and mass composition of cosmic rays in energy region 1 - 10^8 GeV/particle under the assumption that cosmic rays propagation in the Galaxy is described by anomalous diffusion equation. Our results and…
The propagation of cosmic rays in turbulent magnetic fields is a diffusive process driven by the scattering of the charged particles by random magnetic fluctuations. Such fields are usually highly intermittent, consisting of intense…
Recent direct measurements of Galactic cosmic ray spectra by balloon/space-borne detectors reveal spectral hardenings of all major nucleus species at rigidities of a few hundred GV. The all-sky diffuse gamma-ray emissions measured by the…
We study the solution of the diffusion equation for Ultra-High Energy Cosmic Rays in the general case of an expanding universe, comparing it with the well known Syrovatsky solution obtained in the more restrictive case of a static universe.…
The propagation of Galactic Cosmic Ray nuclei having energies between 100 MeV/nuc and several PeV/nuc is strongly believed to be of diffusive nature. The particles emitted by a source located in the disk do not pervade the whole Galaxy, but…
We reconsider the scenario in which the knee in the cosmic ray spectrum is explained as due to a change in the escape mechanism of cosmic rays from the Galaxy from one dominated by transverse diffusion to one dominated by drifts. We solve…
Diffusion coefficients are usually used to describe the propagation of Cosmic Rays through the Universe. Whereas such transport parameters can be obtained from experiments in the Solar System, it is difficult to determine diffusion…
Cosmic rays propagating in the Galaxy may excite a streaming instability when their motion is super-alfvenic, thereby producing the conditions for their own diffusion. In this paper we present the results of a self-consistent solution of…
The macroscopic behaviour of cosmic rays in turbulent magnetic fields is discussed. An implementation of anisotropic diffusion of cosmic rays with respect to the magnetic field in a non-conservative, high-order, finite-difference…
The energy spectrum of high energy cosmic rays emitted by sources change during propagation in the Galaxy. Using the spectrum observed at the Earth and two different transport models, based on anomalous and normal diffusion equations, we…
Determining the spatial distribution of Galactic cosmic rays (CRs) is fundamental to understand how these particles propagate in interstellar space and to infer their source spectra. The most sensitive method of studying this problem is…