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Generalized view factor techniques for treating streaming and scattering in neutral-particle transport
View factor techniques, and their generalization to time dependent static geometries, for treating neutral particle transport involving free streaming in enclosures are described. An approximation of the standard view factor technique which uses retarded times to treat time-dependent, fixed-geometry, 3-D vacuum enclosures is described. Procedures for the numerical determination of the view factors and the transport calculations themselves are described. The advantages and disadvantages of this technique are discussed. The limitations give rise to a new generalized view factor approach which is discussed in detail. In this technique a functional expansion is made of the unknown emission densities on the surface of the enclosure. The coefficients in the expansion contain the time dependence, if any, of the emission, and the expansion functions describe the areal dependence of the emission. These coefficients enter into a series of coupled linear integral equations which contain quantities that are generalizations of the view factors and depend only on the geometry of the enclosure and the distribution of scattering material contained therein. Monte Carlo techniques are used to estimate the generalized view factors which are then adjusted slightly using the method of maximum likelihood and least squares minimization to satisfy appropriate thermodynamic consistency conditions. After the imposition of suitable initial and boundary conditions, the integral equations involving the expansion coefficients are solved