A CONTRIBUTION TO THE THEORY OF ELEMENTARY SOLUTIONS OF THE NEUTRON TRANSPORT EQUATION
It is shown that the monoenergetic neutron transport equation with anisotropic scattering can be solved in closed form by use of elementary solutions. Consideration is restricted to stationary states in plane geometry with optical dimension x and direction variable mu . The elementary solutions are complete in the space of functions with prescribed boundary variation in mu at a given x. Thus, probleris involving such boundary conditions are solved in a manner analogous to the eigenfunction method of solution of differential equations. For cases with boundary values given in the closed mu -interval (-- 1, +1), the eigenfunction expansion coefficients are readily obtained through the use of orthogonality conditions. For partial range conditions of physical interest, i.e., the mu -intervals (-- 1,0) or (0, +1), orthogonality relations are not found. Rather, methods of solution of singalar integral equations are employed in the evaluation of the expansion coefficients. These methods lead ultimately to inhomogeneous Fredholm integral equations of the second kind with degenerate kernels. The method of application of the elementary solution procedure to a variety of physical problems is illustrated. Equations are formulated from which analytical approximation or numerical calculation can proceed for several important theoretical problems of neutron transport. (Dissertation Abstr.)
- Research Organization:
- Originating Research Org. not identified
- NSA Number:
- NSA-18-000996
- OSTI ID:
- 4162464
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
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