Related papers: Fractional diffusion of cosmic rays
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 propagation of galactic cosmic rays in the fractal interstellar medium. Steady state solution of the fractional diffusion equation, describing cosmic ray propagation, is found. We show that the exponent of the steady state…
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…
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,…
Galactic transport models for cosmic rays involve the diffusive motion of these particles in the interstellar medium. Due to the large-scale structured galactic magnetic field this diffusion is anisotropic with respect to the local field…
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…
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 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…
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…
The growth of magneto-hydrodynamic fluctuations relevant to cosmic ray confinement in and near their sources, and the effects of local plasma conditions is revisited. We consider cases where cosmic rays penetrate a medium which may contain…
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…
Fractional kinetic equations employ non-integer calculus to model anomalous relaxation and diffusion in many systems. While this approach is well explored, it so far failed to describe an important class of transport in disordered systems.…
The problem of cosmic-ray scattering in the turbulent electromagnetic fields of the interstellar medium and the solar wind is of great importance due to the variety of applications of the resulting diffusion coefficients. Examples are…
"Diffuse" gamma rays consist of several components: truly diffuse emission from the interstellar medium, the extragalactic background, whose origin is not firmly established yet, and the contribution from unresolved and faint Galactic point…
We investigate the anisotropic diffusion of cosmic rays in the large-scale Galactic magnetic field, where diffusion occurs at different rates along and across the magnetic field lines. To model this process, we use stochastic differential…
We revisit propagation of galactic cosmic rays (CRs) in light of recent advances in CR diffusion theory in realistic interstellar turbulence. We use a tested model of turbulence in which it has been shown that fast modes dominate scattering…
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…
The problem of anomalous diffusion in the momentum space is considered on the basis of the appropriate probability transition function (PTF). New general equation for description of the diffusion of heavy particles in the gas of the light…
In classical diffusion, particle step-sizes have a Gaussian distribution. However, in superdiffusion, they have power-law tails, with transport dominated by rare, long L\'evy flights. Similarly, if the time interval between scattering…