Green's theorem and Green's functions for the steady-state cosmic-ray equation of transport |
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| Authors: | G M Webb L J Gleeson |
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| Institution: | (1) Monash University, Clayton, Australia |
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| 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 rrbwhen 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  is assumed of the form = o(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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| Keywords: | |
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