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

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

Sep 2003

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003apj...595..195w&link_type=abstract

The Astrophysical Journal, Volume 595, Issue 1, pp. 195-226.

Astronomy and Astrophysics

Astronomy

15

Acceleration Of Particles, Ism: Cosmic Rays, Turbulence

Scientific paper

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 lu, 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 ɛ=lu/ld≡u0lu/κ0 is small (0<ɛ<<1), the long space and time behavior of the energetic particle distribution function 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.

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