ANISOTROPIC SCATTERING IN THE TRANSPORT EQUATION. AN EVALUATION OF COMMON APPROXIMATIONS
Technical Report
·
OSTI ID:4715605
In the monoenergetic transport equation, the infinite medium diffusion length is calculated for ratios of the mean number of secondaries per collision less than unity. The diffusion length is calculated using several common approximations to scattering laws which attempt to account for anisotropic scattering. Results of these calculations are compared to direct solutions of the transport equation obtained using the exact scattering law for elastic scattering by hydrogen and a three term expansion in inverse powers of the atom mass for deuterium elastic scattering. In addition to common anisotropic scattering approximations, a step function approximation is developed and examined. A variational expression is derived for the diffusion length which appears as an eigenvalue in the transport equation. A quadratic trial function is found to provide an upper bound for the values of the eigenvalue and to give approximate expressions that are improvements over the usual small absorption expansions. Accuracy of the various approximations for calculating the infinite medium diffusion length and for describing hydrogen elastic scattering is compared. (auth)
- Research Organization:
- Los Alamos Scientific Lab., N. Mex.
- DOE Contract Number:
- W-7405-ENG-36
- NSA Number:
- NSA-17-020958
- OSTI ID:
- 4715605
- Report Number(s):
- LAMS-2873
- Country of Publication:
- United States
- Language:
- English
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