Monte Carlo Particle Transport Methods: Neutron and Photon - gnssn

130 Monte Carlo Particle Transport Methods: Neutron and Photon Calculationsand set initial weight tow 0=IJdFdEf 41(F,E)2. Select next collision site r 1 + 1fromTXr^rJE 1)drT(r—r|E.)and multiply the initial weight bydr T(F 1-^r)E 1)3. Select the next energy E 1 +, and direction from1C(E-E 1Jr 1 + 1)JdEC(E-E 1Jr 1 + 1)and multiply the weight byC(E 1 + 1-E 1Ir 1 + 1) f .C(E 1 + 1-^EJr 1 + 1)4. Set i = i + 1 and return to Step 2.Note that here in the adjoint game the value (Jr 1is represented by the ' 'source" coordinatesthus 4* is the counterpart ofXand x is the counterpart of In other words, the value of aparticle leaving a collision is the density of pseudo-particles entering a pseudo-collision,and vice versa.Two steps of this cycle are further discussed in the following. First, we analyze the newsource term, the pay-off function. In Section 1). an explanation is given as to why a distortedkernel (C) in Step 3 replaced the adjoint collision kernel C.C. SAMPLING THE ADJOINT SOURCEAs has already been seen in Section A. of this Chapter, in the adjoint game the payofffunction plays the role of the source. On the other hand the pay-off describes the quantityto be determined, or simply the characteristics of the receptor, if we use this word in ageneral sense. Thus, with a slightly loose terminology one can say that the physical receptoris the adjoint source.Several examples of pay-off functions are given in Section 4.V.C. Let us first remindthe reader of the problems of estimation of the flux-at-a point. The pay-off function givenin Equation (4.71) could not be used as a score in the direct simulation, however, is anideal function for selecting the initial coordinate in the adjoint game. The relationf,„(r,E) = 5(r -rjmeans that all particles start from r = r„, that is the adjoint source is a point source.