Non-linear damping of slab modes and cosmic ray transport

Journal of Geophysical Research, 1980

A simple heuristic argument is presented which suggests that the large rigidity independent mean free paths observed for low rigidity solar and galactic cosmic rays can be understood in terms of weak turbulence diffusion theory if one assumes that the interplanetary magnetic turbulence consists of a combination of Alfven waves propagating with constant field magnitude and a Qm.all (s5-10%) admixture of compressive fluctuations.

The Astrophysical Journal, 1981

New results from numerical simulations of cosmic-ray modulation by the solar wind are presented. It is argued that the scattering mean free path should be larger than the particle gyroradius in the average magnetic field. Since this constraint was violated in our previous paper, we discuss here simulations which incorporate the larger diffusion coefficients. We find that these simulations exhibit a greater influence of diffusion, as anticipated, and the difference between drift and no-drift solutions is not so great as before. Nonetheless, we still find profound effects of the drifts. The drifts still determine the origin of the bulk of the cosmic rays seen at any given time in the inner solar system. Thus, during the 1975 solar minimum, positively charged cosmic rays seen in the inner solar system came primarily from the outer boundary near the heliospheric poles, and negative particles came from the equatorial regions of the boundary. The situation reverses during alternate solar cycles and with the sign of the particle charge. The calculated energy spectra agree reasonably well with observations and are insensitive to the magnitude of the diffusion coefficient. Subject headings: cosmic rays: general-particle acceleration-Sun: solar wind

Journal of Geophysical Research, 1976

It is argued that the interplanetary magnetic field cannot be simply considered as consisting of small short-scale resonant fluctuations superposed on the long-term average spiral field if one wants to calculate the average transport properties of galactic cosmic rays. The interest is focused on pitch angle diffusion, where the relevant average field varies strongly on a medium scale exceeding the magnetic correlation length. This leads to an average Fokker-Planck equation for the average galactic intensity. Direct reflections and large-scale drift effects that may play a role on the same scale are not considered. When the interplanetary medium is assumed to be statistically axisymmetric, an average spatial diffusion coefficient is derived from the above Fokker-Planck equation and compared with the Pioneer 10 and 11 radial intensity gradients as obtained by the Chicago group: The medium-scale variations also introduce a solar cycle variation of the diffusion coefficient from which a corresponding variation of the galactic intensity is estimated. Quantitatively, the resulting solar cycle variation appears to be only of marginally sufficient strength. This may not be too surprising, since changes in magnetic field topology, drift effects, and direct particle reflections have not been considered. over the directional medium-scale fluctuations.

2011

We are studying the constraints obtained on transport and acceleration mechanisms of galactic cosmic rays by using statistical tools in combination with the propagation package GALPROP and recent PAMELA data. Using only PAMELA data allows us to avoid inconsistencies between data sets from different experiments, minimise uncertainties on solar modulation parameters, and have a complementary and precise data set on (anti-)matter as well as primary and secondary nuclei over 3 orders of magnitude in energy. This allows us to simultaneously place strong constraints on cosmic-ray propagation and acceleration models. We describe our methodology and present some preliminary results in this paper.

The Astrophysical Journal, 2008

We consider the propagation of cosmic rays in turbulent magnetic fields. We use the models of magnetohydrodynamic turbulence that were tested in numerical simulations, in which the turbulence is injected on large scale and cascades to small scales. Our attention is focused on the models of the strong turbulence, but we also briefly discuss the effects that the weak turbulence and the slab Alfvénic perturbations can have. The latter are likely to emerge as a result of instabilities with in the cosmic ray fluid itself, e.g., beaming and gyroresonance instabilities of cosmic rays. To describe the interaction of cosmic rays with magnetic perturbations we develop a non-linear formalism that extends the ordinary Quasi-Linear Theory (QLT) that is routinely used for the purpose. This allows us to avoid the usual problem of 90 degree scattering and enable our computation of the mean free path of cosmic rays. We apply the formalism to the cosmic ray propagation in the galactic halo and in the Warm Ionized medium (WIM). In addition, we address the issue of the transport of cosmic rays perpendicular to the mean magnetic field and show that the issue of cosmic ray subdiffusion (i.e., propagation with retracing the trajectories backwards, which slows down the diffusion) is only important for restricted cases when the ambient turbulence is far from what numerical simulations suggest to us. As a result, this work provides formalism that can be applied for calculating cosmic ray propagation in a wide variety of circumstances.

Research Journal of Applied Sciences, 2012

Using a framework of the radiation approximation followed by a two-term perturbation expansion for cosmic ray transport in the spherical polar coordinates (r, θ, φ) we identify the effect of cosmic ray radiation on shock dominated transport. The theory gives the possibility of an approximate description of some parameters (radiation and temperature) in cosmic ray propagation. This can be applied to solar wind acceleration. When the buoyancy parameter F r is negligible, we find that the cosmic ray density at shock boundary (E n) decreases with increasing temperature. It is also observed that the variation of radiation parameter N in cosmic ray transport has no significant effect in the temperature distribution. Thus, even when radiation is significant, it does not really modify the temperature within the cosmic ray region. However, for increases in the density at shock boundaries say (En), the temperature distribution decreases.

The Astrophysical Journal, 2005

The mean free path is widely used to measure the level of solar energetic particles' diffusive transport. We model a solar energetic particle event observed by Wind STEP at 0.31-0.62 MeV nucleon À1 , by solving the focused transport equation using the Markov stochastic process theory. With different functions of the pitch angle diffusion coefficient D , we obtain different parallel mean free paths for the same event. We show that the different values of the mean free path are due to the high anisotropy of the solar energetic particles. This makes it problematic to use just the mean free path to describe the strength of the solar energetic particle scattering, because the mean free path is only defined for a nearly isotropic distribution. Instead, a more complete function of pitch angle diffusion coefficient is needed.

Advances in Space Research, 2017

The physics of energetic particle propagation in magnetized environments plays a crucial role in both the processes of acceleration and transport of cosmic rays. Recent theoretical developments in the field of cosmic ray research have been mainly in the direction of exploring non-linear aspects of the processes in which these particles are involved, namely the action of cosmic rays on the environment in which the transport and/or acceleration take place. When cosmic rays propagate outside of the acceleration region, such action is mainly in two forms: 1) they generate hydromagnetic waves, through streaming instabilities, leading to a dependence of the scattering properties of the medium on the spectrum and spatial distribution of the energetic particles, and 2) they exert a dynamical action on the plasma, which may cause the launching of cosmic ray driven Galactic winds. In this article we discuss these and other recent developments and how they compare with the bulk of new observations on the spectra of primary nuclei (mainly H and He) and secondary to primary ratios, such as the B/C ratio and the p/p ratio, and the positrons ratio e + /(e -+ e + ). We also comment on some radically new models of the origin of CRs, in which the physical meaning of the secondary to primary ratios is not the same as in the standard model.

Astrophysics and Space Science, 1974

The spatial dependence of the pitch-angle and associated spatial diffusion coefficients for cosmic ray particles in interplanetary space is calculated in the WKB approximation. The model considers only Alfven waves of solar origin to be responsible for scattering of moderate energy particles. After developing the general theory results are presented for the asymptotic case corresponding to radial distances r greater than about 1 to 2 AU. The radial diffusion coefficient 34r increases with energy E like xr ~ E ~, where v -~. The radial mean free path turns out to increase proportional to r 8 at medium and low heliographic latitudes. This behaviour is consistent with a very small radial cosmic ray gradient and the existence of a 'free boundary' for particle diffusion. At equal radial distances the high latitude mean free path is not only much smaller than the one calculated at the lower latitudes but in addition increases only weakly with distance. Some conceivable dynamical implications for the outer solar system are indicated.

Advances in Astronomy, 2013

Three cases of large-amplitude, small spatial-scale interplanetary particle gradients observed by the anticoincidence shield (ACS) aboard the INTEGRAL spacecraft in 2006 are investigated. The high data rates provided by the INTEGRAL ACS allow an unprecedented ability to probe the fine structure of GCR propagation in the inner Heliosphere. For two of the three cases, calculating perpendicular and parallel cosmic ray diffusion coefficients based on both field and particle data results in parallel diffusion appearing to satisfy a convection gradient current balance, provided that the magnetic scattering of the particles can be described by quasi-linear theory. In the third case, perpendicular diffusion seems to dominate. The likelihood of magnetic flux rope topologies within solar ejecta affecting the local modulation is considered, and its importance in understanding the field-particle interaction for the astrophysics of nonthermal particle phenomena is discussed.