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Title: COSMIC-RAY TRANSPORT THEORY IN PARTIALLY TURBULENT SPACE PLASMAS WITH COMPRESSIBLE MAGNETIC TURBULENCE

Abstract

Recently, a new transport theory of cosmic rays in magnetized space plasmas extending the quasilinear approximation to the particle orbit has been developed for the case of an axisymmetric incompressible magnetic turbulence. Here, we generalize the approach to the important physical case of a compressible plasma. As previously obtained in the case of an incompressible plasma, we allow arbitrary gyrophase deviations from the unperturbed spiral orbits in the uniform magnetic field. For the case of quasi-stationary and spatially homogeneous magnetic turbulence we derive, in the small Larmor radius approximation, gyrophase-averaged cosmic-ray Fokker-Planck coefficients. Upper limits for the perpendicular and pitch-angle Fokker-Planck coefficients and for the perpendicular and parallel spatial diffusion coefficients are presented.

Authors:
;  [1]
  1. Institut fuer Theoretische Physik, Lehrstuhl IV: Weltraum- und Astrophysik, Ruhr-Universitaet Bochum, D-44780 Bochum (Germany)
Publication Date:
OSTI Identifier:
22011884
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 745; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; APPROXIMATIONS; ASTROPHYSICS; AXIAL SYMMETRY; COSMIC RADIATION; COSMOLOGY; FOKKER-PLANCK EQUATION; INCLINATION; LARMOR RADIUS; MAGNETIC FIELDS; ORBITS; PLASMA; TRANSPORT THEORY; TURBULENCE

Citation Formats

Casanova, S., and Schlickeiser, R., E-mail: sabrina@tp4.rub.de. COSMIC-RAY TRANSPORT THEORY IN PARTIALLY TURBULENT SPACE PLASMAS WITH COMPRESSIBLE MAGNETIC TURBULENCE. United States: N. p., 2012. Web. doi:10.1088/0004-637X/745/2/153.
Casanova, S., & Schlickeiser, R., E-mail: sabrina@tp4.rub.de. COSMIC-RAY TRANSPORT THEORY IN PARTIALLY TURBULENT SPACE PLASMAS WITH COMPRESSIBLE MAGNETIC TURBULENCE. United States. doi:10.1088/0004-637X/745/2/153.
Casanova, S., and Schlickeiser, R., E-mail: sabrina@tp4.rub.de. 2012. "COSMIC-RAY TRANSPORT THEORY IN PARTIALLY TURBULENT SPACE PLASMAS WITH COMPRESSIBLE MAGNETIC TURBULENCE". United States. doi:10.1088/0004-637X/745/2/153.
@article{osti_22011884,
title = {COSMIC-RAY TRANSPORT THEORY IN PARTIALLY TURBULENT SPACE PLASMAS WITH COMPRESSIBLE MAGNETIC TURBULENCE},
author = {Casanova, S. and Schlickeiser, R., E-mail: sabrina@tp4.rub.de},
abstractNote = {Recently, a new transport theory of cosmic rays in magnetized space plasmas extending the quasilinear approximation to the particle orbit has been developed for the case of an axisymmetric incompressible magnetic turbulence. Here, we generalize the approach to the important physical case of a compressible plasma. As previously obtained in the case of an incompressible plasma, we allow arbitrary gyrophase deviations from the unperturbed spiral orbits in the uniform magnetic field. For the case of quasi-stationary and spatially homogeneous magnetic turbulence we derive, in the small Larmor radius approximation, gyrophase-averaged cosmic-ray Fokker-Planck coefficients. Upper limits for the perpendicular and pitch-angle Fokker-Planck coefficients and for the perpendicular and parallel spatial diffusion coefficients are presented.},
doi = {10.1088/0004-637X/745/2/153},
journal = {Astrophysical Journal},
number = 2,
volume = 745,
place = {United States},
year = 2012,
month = 2
}
  • A new transport theory of cosmic rays in magnetized space plasmas with axisymmetric incompressible magnetic turbulence is developed extending the quasilinear approximation to the particle orbit. Arbitrary gyrophase deviations from the unperturbed spiral orbits in the uniform magnetic field are allowed. For quasi-stationary and spatially homogeneous magnetic turbulence, we derive the small Larmor radius approximation gyrophase-averaged cosmic ray Fokker-Planck coefficients. The generalized Fokker-Planck coefficients correctly reduce to their known quasilinear values in the corresponding limit. New forms of the quasilinear Fokker-Planck coefficients in axisymmetric turbulence are derived which no longer involve infinite sums of products of Bessel functions, which facilitatemore » their numerical computation for specified turbulence field correlation tensors. The Fokker-Planck coefficients for arbitrary phase orbits of the cosmic ray particles provide strict upper limits for the perpendicular and pitch-angle Fokker-Planck coefficients, which in turn yield strict upper and lower limits for the perpendicular and parallel spatial diffusion coefficients, respectively, describing the spatial diffusion of the isotropic part of the cosmic ray phase space density. For the associated mean free paths, we find for this general case that the product of the minimum parallel mean free path with the sum of the maximum perpendicular mean free paths equals R{sup 2}{sub L}, where R{sub L} denotes the cosmic ray gyroradius.« less
  • We study the nonlinear growth of kinetic gyroresonance instability of cosmic rays (CRs) induced by large-scale compressible turbulence. This feedback of CRs on turbulence was shown to induce an important scattering mechanism in addition to direct interaction with the compressible turbulence. The linear growth is bound to saturate due to the wave-particle interactions. By balancing the increase of CR anisotropy via the large-scale compression and its decrease via the wave-particle scattering, we find the steady-state solutions. The nonlinear suppression due to the wave-particle scattering limits the energy range of CRs that can excite the instabilities and be scattered by themore » induced slab waves. The direct interaction with large-scale compressible modes still appears to be the dominant mechanism for isotropization of high-energy CRs (>100 GeV).« less
  • We develop a stochastic model for the turbulent transport of passive scalars based on the Fokker{endash}Planck equation for the probability density distribution of the displacements of infinitesimal fluid parcels ({open_quotes}particles{close_quotes}) in random turbulent motion. Such a theory is the microscopic basis behind semiempirical models of turbulent diffusion which apparently have been developed only for incompressible flow. Here, we specifically develop the theory so that it applies to compressible flow. We then apply it to the particular case of stratified mesoscale turbulent transport of tracers in the ocean, and we find that it generalizes the recent parametrization of Gent and McWilliamsmore » [J. Phys. Oceanogr. {bold 20}, 150 (1990)].« less
  • In honour of the 50th anniversary of the influential review/monograph on plasma turbulence by B. B. Kadomtsev as well as the seminal works of T. H. Dupree and J. Weinstock on resonance-broadening theory, an introductory tutorial is given about some highlights of the statistical–dynamical description of turbulent plasmas and fluids, including the ideas of nonlinear incoherent noise, coherent damping, and self-consistent dielectric response. The statistical closure problem is introduced. Incoherent noise and coherent damping are illustrated with a solvable model of passive advection. Self-consistency introduces turbulent polarization effects that are described by the dielectric functionmore » $${\mathcal{D}}$$. Dupree’s method of using$${\mathcal{D}}$$to estimate the saturation level of turbulence is described; then it is explained why a more complete theory that includes nonlinear noise is required. The general theory is best formulated in terms of Dyson equations for the covariance$C$$and an infinitesimal response function$$R$$, which subsumes$${\mathcal{D}}$$. An important example is the direct-interaction approximation (DIA). It is shown how to use Novikov’s theorem to develop an$$\boldsymbol{x}$$-space approach to the DIA that is complementary to the original$$\boldsymbol{k}$$-space approach of Kraichnan. A dielectric function is defined for arbitrary quadratically nonlinear systems, including the Navier–Stokes equation, and an algorithm for determining the form of$${\mathcal{D}}$$in the DIA is sketched. The independent insights of Kadomtsev and Kraichnan about the problem of the DIA with random Galilean invariance are described. The mixing-length formula for drift-wave saturation is discussed in the context of closures that include nonlinear noise (shielded by$${\mathcal{D}}$$). The role of$$R$in the calculation of the symmetry-breaking (zonostrophic) instability of homogeneous turbulence to the generation of inhomogeneous mean flows is addressed. The second-order cumulant expansion and the stochastic structural stability theory are also discussed in that context. In conclusion, various historical research threads are mentioned and representative entry points to the literature are given. In addition, some outstanding conceptual issues are enumerated.« less
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