Astronomy and Astrophysics – Astronomy
Scientific paper
Dec 1995
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995apj...454..749e&link_type=abstract
Astrophysical Journal v.454, p.749
Astronomy and Astrophysics
Astronomy
5
Acceleration Of Particles, Methods: Numerical, Ism: Cosmic Rays
Scientific paper
The treatments invoked direct finite-difference solutions of the fundamental equation for rectilinear transport, solutions of the matrix form of the transport equation in terms of Fourier integrals, and Monte Carlo simulations, which kept track of ≍6.4 × 107 particles. Variables selected for comparison were the first four coefficients in the expansion of the distribution function in terms of scattering eigenfunctions. These coefficients embody detailed information not only about isotropic density but also about the lowest order anisotropy, which controls diffusion, and about two higher order anisotropies, which control dispersion. Finite-difference and Fourier methods gave results in better agreement with each other (deviations for each coefficient of ≍0.1 % for Vt/λ > 1) than with results of Monte Carlo simulations (deviations of ≍0.1% for Vt/λ > 1). However, the latter deviations are essentially those expected from statistical fluctuations. To obtain deviations as small as the former ones, great care must be taken to compute parameters accurately and to derive from finite approximations results that accurately represent those of the continuous formulation. To document precautions that lead to accurate results, computations and extrapolations invoked during the comparison are described in detail.
Bieber John W.
Earl James A.
Pauls Louis H.
Ruffolo David
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