Monte Carlo Particle Transport Methods: Neutron and Photon - gnssn

240 Monte Carlo Particle Transport Methods: Neutron and Photon Calculationscalculation possible. The conclusions drawn from such approximate investigations are to bechecked in realistic Monte Carlo simulations. Two of the simplified transport models, theFermi scattering model and the straight-ahead scattering model, were introduced in Sections5.II.D and 5.VI.C, respectively. In this Chapter, a less idealized situation is considered andapproximate solutions of the moment equations are established for monoenergetic, isotropic,homogeneous cases.Let us mention that besides the method discussed here, almost all the standard methodsof approximating solutions to the transport equation can be adopted for the approximatecalculation of moments. Thus, diffusion and S ncalculations have been successfully appliedfor Monte Carlo moment calculations.'- 16 - 4 'A. THE SIMPLIFIED MODELLet V be a simply connected convex region containing a homogeneous medium. Considera monoenergetic transport process in V with isotropic postcollisional direction distributionin the laboratory system. In this model, every reaction rate is proportional to the expectednumber of collisions in the region; therefore, we shall assume that the latter is the quantityto be estimated by Monte Carlo. This means that the weighting function, f(P), in the reactionrate is unity inside V and vanishes outside, i.e., the reaction rate readsK J dPi)j(P) (5.242)The kernels describing the transport model above have the formsT(P,P')dP' = e M T J M W - co'Kko' (5.243)andC(P',P")dP" = — do' (5.244)4TTwhere P = (r.co.i P' = (r + Dw,w), and T = crD is the optical distance between P andP' along to. D is the corresponding geometrical distance, 0 (5.246)where n is the inward normal to S. Finally, we suppose that the score moments due to aparticle started from outside V is zero, i.e.,M r(P) = 0, if r j V U SThis assumption can be interpreted in two ways. Either it is assumed that the region is