Diffusive-Compression Acceleration and Turbulent Diffusion of Cosmic Rays in Quasi-Periodic and Turbulent Flows

G. M. Webb, C. M. Ko, G. P. Zank, J. Randy Jokipii

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

Multiple scale perturbation methods are used to study the transport and acceleration of energetic charged particles in quasi-periodic, fluid velocity structures in one, two, or three space dimensions, with spatial period l u, where lu is much less than the diffusion scale length ld = κ0/u0 and κ0 and u0 are characteristic values of the energetic particle diffusion coefficients and fluid speed, respectively. The particle diffusion tensor K is also allowed to vary periodically on the scale lu. In the case in which the perturbation parameter ε = lu/ld = u 0lu is small (0 < ≪ 1), the long space and time behavior of the energetic particle distribution function 〈 f 〉 at lowest order is shown to satisfy a modified Fokker-Planck equation. This equation arises from compatibility conditions imposed on the perturbation equations in order to obtain a consistent perturbation expansion that is free of secular terms. The analysis shows that the particles are accelerated stochastically on the large scale as a result of the divergence ∇ δu of the background fluid velocity perturbation δu. The net acceleration of the particles due to the velocity variations can be described in part by a second-order Fermi-like momentum space diffusion term in the long-scale transport equation obtained by averaging over the short-scale variations. The momentum space diffusion coefficient DT describing the effect depends on the two-point correlation of the fluid velocity divergence ∇ δu at different points in the flow. There is also a further energization term in the long-scale transport equation, corresponding to the work done by the scattering center fluid against the differential cosmic-ray pressure gradient that is modified as a result of the short-scale variations. The convective particle streaming is also modified as a result of the short-scale variations. The analysis shows that the effective spatial diffusion tensor for low-energy particles can be significantly modified as a result of turbulent diffusion, whereas higher energy particles with much larger diffusion tensor elements are not significantly affected by turbulent diffusion. Averaging over a random ensemble of short-scale, quasi-periodic velocity structures generalizes the turbulent transport coefficients obtained by previous authors.

Original languageEnglish (US)
Pages (from-to)195-226
Number of pages32
JournalAstrophysical Journal
Volume595
Issue number1 I
DOIs
StatePublished - Sep 20 2003

Fingerprint

turbulent diffusion
turbulent flow
cosmic ray
cosmic rays
compression
perturbation
fluid
energetic particles
fluids
energetics
particle diffusion
velocity structure
tensors
particle energy
momentum
divergence
diffusion coefficient
particle
pressure gradient
Fokker-Planck equation

Keywords

  • Acceleration of particles
  • Cosmic rays
  • Turbulence

ASJC Scopus subject areas

  • Space and Planetary Science

Cite this

Diffusive-Compression Acceleration and Turbulent Diffusion of Cosmic Rays in Quasi-Periodic and Turbulent Flows. / Webb, G. M.; Ko, C. M.; Zank, G. P.; Jokipii, J. Randy.

In: Astrophysical Journal, Vol. 595, No. 1 I, 20.09.2003, p. 195-226.

Research output: Contribution to journalArticle

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