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. R. Jokipii

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


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
Issue number1 I
StatePublished - Sep 20 2003


  • Acceleration of particles
  • Cosmic rays
  • Turbulence

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


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