Green's theorem and Green's functions for the steady-state cosmic-ray equation of transport

Details Green's theorem and Green's functions for the steady-state cosmic-ray equation of transport Green's theorem and Green's functions for the steady-state cosmic-ray equation of transport

Aug 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977ap%26ss..50..205w&link_type=abstract

Astrophysics and Space Science, vol. 50, no. 1, Aug. 1977, p. 205-223.

Astronomy and Astrophysics

Astrophysics

8

Cosmic Rays, Green'S Functions, Particle Diffusion, Transport Properties, Diffusion Coefficient, Galactic Radiation, Momentum Transfer, Solar Cosmic Rays, Steady State

Scientific paper

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 function can be determined in a region r(a) less than or equal to r less than or equal to r(b) when a source is specified throughout the region and the momentum spectrum is specified on the boundaries at r(a) and r(b). Evaluation requires a knowledge of the Green's function which corresponds to the solution for monoenergetic particles released at heliocentric radius R(0). Examples of Green's functions are given for the case r(a) = 0, r(b) = infinity and derived for the cases of finite r(a) and r(b). The diffusion coefficient k is assumed to be of a certain form. 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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