Abstract
Green's Theorem is developed for the spherically-symmetric steady-state cosmic-ray equation of transport in interplanetary space. By means of it the momentum distribution functionF o(r,p), (r=heliocentric distance,p=momentum) can be determined in a regionr a≤r≤rbwhen a source is specified throughout the region and the momentum spectrum is specified on the boundaries atr a andr b . Evaluation requires a knowledge of the Green's function which corresponds to the solution for monoenergetic particles released at heliocentric radiusr o , Examples of Green's functions are given for the caser a =0,r b =∞ and derived for the cases of finiter a andr b . The diffusion coefficient κ is assumed of the form κ = κo(p)r b. The treatment systematizes the development of all analytic solutions for steady-state solar and galactic cosmic-ray propagation and previous solutions form a subset of the present solutions.
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Webb, G.M., Gleeson, L.J. Green's theorem and Green's functions for the steady-state cosmic-ray equation of transport. Astrophys Space Sci 50, 205–223 (1977). https://doi.org/10.1007/BF00648532
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DOI: https://doi.org/10.1007/BF00648532