Astronomy and Astrophysics – Astrophysics
Scientific paper
Jun 1977
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977ap%26ss..49...83f&link_type=abstract
Astrophysics and Space Science, vol. 49, no. 1, June 1977, p. 83-97.
Astronomy and Astrophysics
Astrophysics
27
Correlation, Cosmic Rays, Diffusion Coefficient, Scattering Coefficients, Solar Wind Velocity, Fokker-Planck Equation, Liouville Equations, Pitch (Inclination)
Scientific paper
It is shown that Earl's (1973) eigenvalue sum for the cosmic-ray spatial diffusion coefficient parallel to the mean magnetic field is precisely equivalent to the time integral of the particle-velocity correlation function parallel to the mean field. A derivation due to Kubo (1957) is applied to cosmic-ray pitch-angle scattering, and it is proven that all nine components of the cosmic-ray diffusion tensor can be expressed as integrals over the velocity correlation function. A pitch-angle correlation function is derived, and the effect of long-wavelength turbulence on the velocity correlation function and spatial diffusion coefficients is examined. Application of the velocity-correlation method to a realistic case involving both pitch-angle scattering and appreciable fluctuation in the direction of the local field indicates that long-wavelength turbulence in the local field reduces the parallel diffusion coefficient and places an upper limit on the ratio of the perpendicular to parallel diffusion coefficients.
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