Mathematics
Scientific paper
Feb 1981
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981apj...243.1103s&link_type=abstract
Astrophysical Journal, Part 1, vol. 243, Feb. 1, 1981, p. 1103-1114.
Mathematics
16
Cosmic Rays, Electron Transfer, Extragalactic Radio Sources, High Energy Electrons, Astronomical Models, Distribution Functions, Energy Spectra, Fokker-Planck Equation, Matrices (Mathematics), Transport Properties
Scientific paper
An investigation has been made of Fokker-Planck equation for cosmic ray transport, with applications for extragalactic radio sources. The equation contains terms describing particle streaming, pitch angle scattering by magnetic irregularities, particle 'focusing' by a nonuniform magnetic field, and energy loss due to synchrotron radiation. A method of solution similar to that used by Earl has been employed, consisting of expansion of the electron distribution function in terms of the eigenfunctions of the scattering and focusing operators. An analytical solution for the expansion coefficients has been found. The coefficients are determined by the characteristic values of a matrix. The results of a calculation in which the number density function was expanded to fourth order in the eigenfunctions are presented. The calculations indicate that a self-preserving phase, in which the number density function is separable in position, pitch angle, and energy, will generally occur. It is also found that spectral index gradients will be observed only if measurements are made over a very wide frequency interval. Finally, the model predicts that in an idealized case, the observed radio brightness should decrease exponentially with distance from the electron injection site.
Basart John P.
Spangler Steven R.
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