Cosmic-ray particle transport in weakly turbulent plasmas. Part 1. Theory

Schlickeiser, R.; Achatz, Ulrich

doi:10.1017/s0022377800016822

Cited by 71 publications

(71 citation statements)

References 13 publications

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“…Much attention has been devoted to the interaction with the low-frequency Alfvén and magnetosonic MHD waves j . For these waves the relevant Fokker-Planck coefficients are given by: 165,168 j Following 167 here we define low frequency waves as those having frequency ω << Ω i /β pl , where Ω i is the Larmor frequency of nonrelativistic ions…”

Section: Turbulent Accelerationmentioning

confidence: 99%

Cosmic Rays in Galaxy Clusters and Their Nonthermal Emission

Brunetti¹,

Jones

2014

Int. J. Mod. Phys. D

591

714

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Radio observations prove the existence of relativistic particles and magnetic field associated with the intra-cluster-medium (ICM) through the presence of extended synchrotron emission in the form of radio halos and peripheral relics. This observational evidence has fundamental implications on the physics of the ICM. Non-thermal components in galaxy clusters are indeed unique probes of very energetic processes operating within clusters that drain gravitational and electromagnetic energy into cosmic rays and magnetic fields. These components strongly affect the (micro-)physical properties of the ICM, including viscosity and electrical conductivities, and have also potential consequences on the evolution of clusters themselves. The nature and properties of cosmic rays in galaxy clusters, including the origin of the observed radio emission on cluster-scales, have triggered an active theoretical debate in the last decade. Only recently we can start addressing some of the most important questions in this field, thanks to recent observational advances, both in the radio and at high energies. The properties of cosmic rays and of cluster non-thermal emissions depend on the dynamical state of the ICM, the efficiency of particle acceleration mechanisms in the ICM and on the dynamics of these cosmic rays. In this review we discuss in some detail the acceleration and transport of cosmic rays in galaxy clusters and the most relevant observational milestones that have provided important steps on our understanding of this physics. Finally, looking forward to the possibilities from new generations of observational tools, we focus on what appear to be the most important prospects for the near future from radio and high-energy observations.

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Section: Turbulent Accelerationmentioning

confidence: 99%

Cosmic Rays in Galaxy Clusters and Their Nonthermal Emission

Brunetti¹,

Jones

2014

Int. J. Mod. Phys. D

591

714

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“…It can be verified a posteriori that the QLT scattering rates are independent of l ′ to lowest order in ρ/l. In contrast to most previous treatments, the turbulence is treated as strong, in the sense that fluctuations decorrelate in one linear wave period.In QLT, the turbulence causes the cosmic rays to diffuse in momentum space, with the diffusion coefficients determined by the statistical properties of the turbulence [15],where f is the cosmic-ray distribution function averaged over the small scales of the fluctuating fields, p is momentum, θ (the pitch angle) is the angle between p and B 0 , and ξ = cos θ. In equation (1) it has been assumed that the length scale characterizing variations in f is large compared to ρ, so that f can be taken to be independent of gyrophase.…”

mentioning

confidence: 99%

“…In QLT, the turbulence causes the cosmic rays to diffuse in momentum space, with the diffusion coefficients determined by the statistical properties of the turbulence [15],…”

mentioning

confidence: 99%

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Scattering of Energetic Particles by Anisotropic Magnetohydrodynamic Turbulence with a Goldreich-Sridhar Power Spectrum

2000

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accepted for publication in Physical Review Letters -Scattering rates for a Goldreich-Sridhar (GS) spectrum of anisotropic, incompressible, magnetohydrodynamic turbulence are calculated in the quasilinear approximation. Because the small-scale fluctuations are constrained to have wave vectors nearly perpendicular to the background magnetic field, scattering is too weak to provide either the mean free paths commonly used in Galactic cosmic-ray propagation models or the mean free paths required for acceleration of cosmic rays at quasi-parallel shocks. Where strong pitch-angle scattering occurs, it is due to fluctuations not described by the GS spectrum, such as fluctuations generated by streaming cosmic rays.The scattering of energetic particles by turbulent magnetic and electric fields plays an important role in the acceleration and propagation of cosmic rays [1][2][3][4][5][6][7]. The turbulent fields responsible for cosmic-ray scattering can be excited by the cosmic rays themselves or by some mechanism that is independent of the cosmic rays. This paper focuses upon the latter case. In previous treatments of scattering, different turbulence models have been used, including fluctuations with wave vectors k parallel to the ambient large-scale magnetic field B 0 (slab symmetry) or perpendicular to B 0 (2D), or power spectra that are isotropic in k-space [7][8][9][10]. On the other hand, a number of studies suggest that in magnetohydrodynamic (MHD) turbulence excited by large-scale stirring, small-scale fluctuations have non-zero values of k that are ≪ k ⊥ , where k ⊥ and k are the components of k ⊥ and to B 0 [12][13][14]. In this paper, the quasilinear approximation [11] is used to calculate general scattering rates for incompressible MHD turbulence and also shear-Alfvénic turbulence on the non-MHD scales shorter than the collisional mean free path of thermal particles [12]. These rates are then evaluated for the Goldreich-Sridhar power spectrum [12], which has significant power at small scales only for k ⊥ ≫ k . The condition k ⊥ ≫ k is found to significantly decrease the efficiency of pitch-angle scattering relative to the slab-symmetric and isotropic cases. Astrophysical applications and limitations of quasilinear theory (QLT) are discussed.It is assumed that there is an inertial-range spectrum of fluctuations extending from some large scale l to a much smaller scale d, with the fluctuations at scales ∼ l dominating the total magnetic energy. Only cosmic rays with gyroradii ρ ≪ l are considered. A scale l ′ is introduced, with ρ ≪ l ′ ≪ l. The energetically dominant fluctuations on scales > l ′ are treated as a uniform field B 0 . The magnetic fluctuations on scales < l ′ , denoted B 1 , are small compared to B 0 and are treated using QLT. It can be verified a posteriori that the QLT scattering rates are independent of l ′ to lowest order in ρ/l. In contrast to most previous treatments, the turbulence is treated as strong, in the sense that fluctuations decorrelate in one linear wave period.In QLT, the turbulen...

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“…which naturally results from wave damping processes in the case of wave turbulence (Schlickeiser & Achatz 1993) and dynamical turbulence (Bieber et al 1994), we then obtain in the diffusion limit t − t 0 t c…”

Section: Relation To Alternative Nonlinear Transport Theorymentioning

confidence: 99%

A New Cosmic Ray Transport Theory in Partially Turbulent Space Plasmas: Extending the Quasilinear Approach

Schlickeiser

2011

ApJ

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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 gyrophaseaveraged 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 facilitate 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 2 L , where R L denotes the cosmic ray gyroradius.

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Cosmic-ray particle transport in weakly turbulent plasmas. Part 1. Theory

Cited by 71 publications

References 13 publications

Cosmic Rays in Galaxy Clusters and Their Nonthermal Emission

Cosmic Rays in Galaxy Clusters and Their Nonthermal Emission

Scattering of Energetic Particles by Anisotropic Magnetohydrodynamic Turbulence with a Goldreich-Sridhar Power Spectrum

A New Cosmic Ray Transport Theory in Partially Turbulent Space Plasmas: Extending the Quasilinear Approach

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