SCR Distribution Function in the Radial IMF Approximation

The transport of cosmic rays in the interplanetary medium is considered in terms of the kinetic equation describing the energetic particle scattering by magnetic irregularities and their focusing by the regular interplanetary magnetic field. The analytical expression for solar cosmic ray distribution function in the approximation of radial regular magnetic field is obtained and the evolution of energetic particle angular distribution is analyzed. The obtained results can be used for the analysis of ground-level enhancements of cosmic ray intensity.     

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.     

SCR Steady State Distribution Function and Scattering Properties of the Interplanetary Medium

The propagation of energetic particles in the interplanetary space is considered on the basis of kinetic equation describing the scattering of charged particles by magnetic irregularities and the particle focusing by regular magnetic field. Our analysis confirms that angular distribution of solar cosmic rays contains a valuable information about properties of the particle scattering in the interplanetary magnetic field. Steady state solutions of the kinetic equation are applied to the analysis of solar proton events.     

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.     

Spiral arms as cosmic ray source distributions

The Milky Way is a spiral galaxy with (or without) a bar-like central structure. There is evidence that the distribution of suspected cosmic ray sources, such as supernova remnants, are associated with the spiral arm structure of galaxies. It is yet not clearly understood what effect such a cosmic ray source distribution has on the particle transport in our Galaxy. We investigate and measure how the propagation of Galactic cosmic rays is affected by a cosmic ray source distribution associated with spiral arm structures.We use the PICARD code to perform high-resolution 3D simulations of electrons and protons in galactic propagation scenarios that include four-arm and two-arm logarithmic spiral cosmic ray source distributions with and without a central bar structure as well as the spiral arm configuration of the NE2001 model for the distribution of free electrons in the Milky Way. Results of these simulation are compared to an axisymmetric radial source distribution. Also, effects on the cosmic ray flux and spectra due to different positions of the Earth relative to the spiral structure are studied.We find that high energy electrons are strongly confined to their sources and the obtained spectra largely depend on the Earth’s position relative to the spiral arms. Similar finding have been obtained for low energy protons and electrons albeit at smaller magnitude. We find that even fractional contributions of a spiral arm component to the total cosmic ray source distribution influences the spectra on the Earth. This is apparent when compared to an axisymmetric radial source distribution as well as with respect to the Earth’s position relative to the spiral arm structure. We demonstrate that the presence of a Galactic bar manifests itself as an overall excess of low energy electrons at the Earth.Using a spiral arm geometry as a cosmic ray source distributions offers a genuine new quality of modeling and is used to explain features in cosmic ray spectra at the Earth that are else-wise attributed to other propagation effects. We show that realistic cosmic ray propagation scenarios have to acknowledge non-axisymmetric source distributions.     

Cosmic-ray anisotropy in interplanetary space

The kinetic equation describing cosmic-ray propagation in interplanetary space has been used to construct a consistent theory of cosmic-ray anisotropy including the second spherical harmonic of particle angular distribution. The amplitude and phase of semi-diurnal cosmic-ray variation have been calculated. Expressions describing the relationships of the semi-diurnal variation parameters to helio-latitude distribution of cosmic rays have been derived. The results obtained are compared with observational data.     

Saturated magnetic field amplification at supernova shocks

Cosmic ray streaming instabilities at supernova shocks are discussed in the quasi-linear diffusion formalism which takes into account the feedback effect of wave growth on the cosmic ray streaming motion. In particular, the non-resonant instability that leads to magnetic field amplification in the short wavelength regime is considered. The linear growth rate is calculated using kinetic theory for a streaming distribution. We show that the non-resonant instability is actually driven by a compensating current in the background plasma. The non-resonant instability can develop into a non-linear regime generating turbulence. The saturation of the amplified magnetic fields due to particle diffusion in the turbulence is derived analytically. It is shown that the evolution of parallel and perpendicular cosmic ray pressures is predominantly determined by non-resonant diffusion. However, the saturation is determined by resonant diffusion which tends to reduce the streaming motion through pitch angle scattering. The saturated level can exceed the mean background magnetic field.     

Time-dependent transport of energetic particles in magnetic turbulence: computer simulations versus analytical theory

We explore numerically the transport of energetic particles in a turbulent magnetic field configuration. A test-particle code is employed to compute running diffusion coefficients as well as particle distribution functions in the different directions of space. Our numerical findings are compared with models commonly used in diffusion theory such as Gaussian distribution functions and solutions of the cosmic ray Fokker–Planck equation. Furthermore, we compare the running diffusion coefficients across the mean magnetic field with solutions obtained from the time-dependent version of the unified non-linear transport theory. In most cases we find that particle distribution functions are indeed of Gaussian form as long as a two-component turbulence model is employed. For turbulence setups with reduced dimensionality, however, the Gaussian distribution can no longer be obtained. It is also shown that the unified non-linear transport theory agrees with simulated perpendicular diffusion coefficients as long as the pure two-dimensional model is excluded.     

Cosmic energy equation and clustering of non-point mass system of galaxies

Cosmic energy equation is an important equation for studying the gravitational galaxy clustering in the expanding universe. We derive the distribution function for fluctuations in particle number by using the cosmic energy equation for extended structures (galaxies with halos). From spatial distribution function, containing particle fluctuations, we derive the velocity distribution function to understand the influence of particle fluctuations on the velocities of galaxies.With the help of cosmic energy equation we try to find out the physical constraints for the application of quasi-equilibrium approximation.     

The differential cosmic ray energy flux in the light of an ultrarelativistic generalized Lorentzian thermodynamics

The ultrarelativistic generalized Lorentzian quasi-equilibrium thermodynamic energy distribution is tentatively applied to the energy spectrum of galactic cosmic ray fluxes. It is found that the inferred power law slopes contain a component which evolves with cosmic ray energy in steps of thirds, resembling the sequence of structure functions in fully developed Kolmogorov turbulence. Within the generalized thermodynamics the chemical potential is estimated from the deviation of the fluxes at decreasing energy, presumably throwing light on the cosmic ray acceleration mechanism. A relation between involved turbulent volumina and structure functions is obtained. The conclusions drawn hold only within the realm of applicability of thermodynamics to cosmic ray spectra.     

On the escape of particles from cosmic ray modified shocks

Stationary solutions to the problem of particle acceleration at shock waves in the non-linear regime, when the dynamical reaction of the accelerated particles on the shock cannot be neglected, are known to show a prominent energy flux escaping from the shock towards upstream infinity. On physical grounds, the escape of particles from the upstream region of a shock has to be expected in all those situations in which the maximum momentum of accelerated particles,   p _max  , decreases with time, as is the case for the Sedov–Taylor phase of expansion of a shell supernova remnant, when both the shock velocity and the cosmic ray induced magnetization decrease. In this situation, at each time t , particles with momenta larger than   p _max( t )  leave the system from upstream, carrying away a large fraction of the energy if the shock is strongly modified by the presence of cosmic rays. This phenomenon is of crucial importance for explaining the cosmic ray spectrum detected at the Earth. In this paper, we discuss how this escape flux appears in the different approaches to non-linear diffusive shock acceleration, and especially in the quasi-stationary semi-analytical kinetic ones. We apply our calculations to the Sedov–Taylor phase of a typical supernova remnant, including in a self-consistent way particle acceleration, magnetic field amplification and the dynamical reaction on the shock structure of both particles and fields. Within this framework, we calculate the temporal evolution of the maximum energy reached by the accelerated particles and of the escape flux towards upstream infinity. The latter quantity is directly related to the cosmic ray spectrum detected at the Earth.     

On possible 'cosmic ray cocoons' of relativistic jets

We consider effects on an (ultra)relativistic jet and its ambient medium caused by high-energy cosmic rays accelerated at the jet side boundary. As illustrated by simple models, during the acceleration process a flat cosmic ray distribution can be created, with gyro-radii for the highest particle energies reaching scales comparable to the jet radius or energy density comparable to the pressure of the ambient medium . In the case of efficient radiative losses, a high-energy bump in the spectrum can dominate the cosmic ray pressure. In extreme cases, the cosmic rays are able to push the ambient medium off, providing a 'cosmic ray cocoon' separating the jet from the surrounding medium. The considered cosmic rays provide an additional jet braking force and lead to a number of consequences for the jet structure and its radiative output. In particular, the dynamic and acceleration time-scales involved are in the range observed in variable active galactic nuclei.     

Cosmic ray scintillations in random magnetic fields with non-zero helicity

The cosmic ray scintillation theory is modified for the case of non diagonal IMF correlation tensor. We introduce the term helicity of cosmic ray scintillation. It describes rotation of the cosmic ray distribution function.It is shown that the helicity of the cosmic ray scintillations and the IMF helicity are alike in nonresonant frequency band. The behaviour of the cosmic ray distribution function in resonant frequency band is considered.The algorithm for two-canal spectral analysis based on an autoregressional method is developed. Empirical functions of helicity of the cosmic ray scintillation and of IMF helicity are obtained for the same time intervals.Observational results are found to be in a good agreement with the theory.     

Cosmic Ray Nonlinear Processes in Space Plasma: Applications to the Dynamic Heliosphere

Influence of cosmic ray pressure and kinetic stream instability on space plasma dynamics and magnetic structure are considered. It is shown that in the outer Heliosphere are important dynamics effects of galactic cosmic ray pressure on solar wind and interplanetary shock wave propagation as well as on the formation of terminal shock wave of the Heliosphere and subsonic region between Heliosphere and interstellar medium. Kinetic stream instability effects are important on distances more than 40–60 AU from the Sun: formation of great anisotropy of galactic cosmic rays in about spiral interplanetary magnetic field leads to the Alfven turbulence generation by non isotropic cosmic ray fluxes. Generated Alfven turbulence influences on cosmic ray propagation, increases the cosmic ray modulation, decreases the cosmic ray anisotropy and increases the cosmic ray pressure gradient in the outer Heliosphere (the later is also important for terminal shock wave formation). This revised version was published online in July 2006 with corrections to the Cover Date.     

Cosmic ray fluctuations in compressible turbulent medium

The influence of compressibility of the medium on cosmic ray (CR) fluctuations has been investigated. The CR transport equation has been used to obtain an equation for the second moment of CR particle density (correlation function of the particle density). It is shown that the effects due to the compressibility of the medium has an essential influence on CR fluctuations. The relations between CR power spectra and random velocity field have been determined. For the turbulence which is created by an ensemble of weak sound waves we have obtained the connection between the spectral indices of CR power spectra and the velocity field. It is shown that the spectral indices of CR power spectra and the velocity field of random sound waves coincide.     

Investigation of the relative abundance of one-fold neutrons in an incident flux of the cosmic rays from neutron monitors data

The behaviour of relative content of one-fold neutrons in the incident flux of cosmic rays during Forbush-decreases and solar cosmic ray flares is considered based on the network of cosmic ray stations. The barometric dependence of this value on the network of cosmic ray stations. The barometric dependence of this value on the latitude and see level altitude of a cosmic ray station is obtained.     

A new approximate coupling function: The case of Forbush decreases

We attempt the derivation of a new coupling function between ground level and primary cosmic rays for the case of Forbush decreases. The calculations for the new function are based on basic Quantum Field Theory theoretical tools, something that has not been attempted till now in other widely used cosmic ray coupling functions. The use of Quantum Field Theory calculations in cosmic rays events in general, is expected to be a suitable frame of work since it describes well the high energy particle interactions which result in variations to the total number of the particles involved through annihilation or creation of particles. The newly computed function is tested to the case of two events of Forbush decreases, February 2011 and March 2012, using data from the high resolution neutron monitor database. Results for the primary particle intensity values obtained from this function are compared directly to the corresponding ones from the use of the Dorman's widely accepted coupling function. The two sets are discussed in detail in order to deduce the possible suitability of Quantum Field Theory tools to cosmic ray events.     

Description of anisotropic particle pulse transport based on the kinetic equation

The non-diffusive transport of an anisotropic pulse of cosmic ray charged particles in an inhomogeneous medium with a regular magnetic field is considered. Both the angle particle distribution in a source and the angle dependence of a detector response as well as the time dependent particle injection from the source into the medium are comprised. The temporal dependences of the particle number and of the detected particle intensity are demonstrated at various distances from the source. It is shown that the temporal profiles are strongly dependent on the anisotropy value and they have dissimilar behaviour for different asymptotic direction of detector.