Monte Carlo Particle Transport Methods: Neutron and Photon - gnssn

350 Monte Carlo Particle Transport Methods: Neutron and Photon Calculations2. Second MethodThe procedure above can be reformulated in an alternative way.Let us assume thatthe physical system under investigation is either critical or subcritical. Then a steady-state(physical) collision density can only be reached if an external source is present in the system.Let Cp(P) denote the (physical) collision density produced in the system by an external sourceS(P). Then (J)(P) satisfies the equation(J)(P) = J dP"cf)(P")fK s(P",P) + K f(P",P)] + (J) 11(P) (6.95)with the first collision densitycJ) c(P) - JdP'S(P')T(P',P) (6.96)Let us now consider the iterative solution of the following equation system:(J)M(P)=JdP"(J) :, n> (P) = jdP"4> ln -"(P")K. f.(P",P) (6.98)withC(P)= (J) 0(P)given in Equation (6.96). In this procedure, (J)"'(P) is the collision density due to the externalsource S(P) if collisions leading to fission do not contribute to the collision density (firstgeneration). cf) (n) (P) is the collision density of neutrons created in fission that are provokedby the (n - l)st-generation neutrons. Let the n-th iterate of the multiplication factor bedefined ask n= JdPcJ) 0" M) (P)/JdP(J)f (P) = S 1TS 01...,,or, sinceS (n_„ - dP(J)W(P) = dF'(pW-'>(P") Cf(P")k„ readsdP(J)