M. Stehlik

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.

Stochastic acceleration by the induced electric field versus the Fermi acceleration

The acceleration of energetic particles is investigated using the kinetic equation in a statistically anisotropic helical turbulent magnetic field in the diffusion approximation. It is known that large-scale magnetic and electric fields are generated in a medium with statistically anisotropic magnetohydrodynamic turbulence. The particle acceleration by the large-scale electric field can be very efficient if the magnetic helicity of a turbulent medium is sufficiently high. The effectiveness of this acceleration mechanism is compared with the Fermi acceleration of the second order. The steady-state cosmic ray energetic spectra as well as their evolution during their approach to an equilibrium state of both acceleration processes are studied.

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.

Statistical acceleration of energetic particles and their diffusion in turbulent magnetic fields

Two processes of statistical cosmic ray (CR) acceleration and CR diffusion in turbulent magnetic fields are studied. It is assumed that the charged particles gain energy in a bounded space region and then they leave the acceleration region as a result of the spatial diffusion caused by particle scattering in the turbulent inhomogeneous medium. Both the second-order Fermi acceleration and the acceleration by the induced electric field (α-mechanism) are considered. Analytical solutions of the CR transport equation by the Fourier–Laplace method are obtained for various spatial diffusion coefficients. The equilibrium energetic spectra and the spatial distributions of CRs inside and outside the acceleration region are investigated.

Cosmic-ray propagation in inhomogeneous large-scale magnetic fields: A pitch-angle diffusion and convection

A drift kinetic theory of cosmic-ray (CR) propagation in inhomogeneous random large-scale magnetic fields (MF) is considered. An averaging of the drift kinetic equation for CR particles distribution was performed in the statistical ensemble of MF realization, whereby the curvature radius of randomly wandering MF is much larger than gyro-radiusRH of CR particles. Collisions of CR particles on the small-scale MF inhomogeneities with the characteristics scalelO ≪RH is not taken into account. It is proved that this random MF raises non-zero pitch-angle diffusion of the CR particles, which is very strong for particles with zero pitch angle. The transport equation is derived for a case of weak inhomogeneity of the random MF in the direction of MF mean value. In this case additional convection of particles in the direction of energy density gradient of random MF variables.

Cosmic-ray fluctuations in interplanetary space

Cosmic-ray (CR) fluctuations in both the drift and diffusion approximations are investigated and the results compared with experimental data. Kinetic equation is used to obtain equations for the second moment of the CR distribution function (the correlation function of the distribution function fluctuations) in both approximations. An application of these approximations to the correlation function equation gives the relations between the CR power spectra and random magnetic fields in interplanetary space. Different magneto-turbulence models are taken in consideration and the relations between the spectral indices are obtained in various frequency intervals.The theoretical results are compared with experimental data obtained by the network of neutron monitors. The CR power spectra observed at the ground level during the years 1978–1981 has been calculated. The investigated frequency range of 3×10−8 to 10−4 Hz consists of two parts, with a ‘transient’ region of 10−6 to 10−5 Hz. Together with the ‘background’ CR fluctuations the contribution of both the periodic and aperiodic phenomena is observed.

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.