Monte Carlo Particle Transport Methods: Neutron and Photon - gnssn

34 Monte Carlo Particle Transport Methods: Neutron and Photon CalculationsThus, in most Monte Carlo programs, special techniques are introduced to decrease thestatistical uncertainties. The introduction of such techniques leads to deviations from theone-to-one simulations, to so-called nonanalog games. Appropriate selection of the nonanalogprocedures is of major importance and will be discussed many times, in different levelsthroughout this book.Now, however — in spite of all its disadvantages — let us turn back and investigate indetail the analog simulation, from which the idea of Monte Carlo application for particletransport originated in the 1940s. Still now, a deep understanding of the simplest analogprocedures is the basis for understanding the more advanced techniques.In the same way as the life of a physical particle starts by its emission from some sortof source, in an analog Monte Carlo game first the initial coordinates have to be selected.The next step is the free flight of the neutron or photon up to its next collision, consequently,in the simulation, a path length has to be selected. From the starting point coordinates andthe direction of flight, the site of the subsequent interaction is to be determined.At the collision site, a large variety of interactions with the different atoms constitutingthe material at that point can take place. Accordingly, in the numerical simulation, first thetypes of both the collided atom and the interaction have to be selected. If the actual collisiondoes not lead to absorption the particle goes on its way with a new energy and direction —both of them are to be selected. In multiplicative events, or e.g. (n,y) reactions, new particlesare also created, the parameters of which are generally immediately selected but temporarilystored and handled as coordinates of particles from secondary sources. The histories of these"secondaries" are followed after the termination of the "primary" particle. (For correctnessit must be noted here that in, e.g. an (n,2n) reaction there is no physically correct distinctionbetween the two outcoming neutrons as to which one is the primary and which is thesecondary. The decision is arbitrary from the point of physics and is governed by practicalconsideration.)After the simulation of a scattering event, the process is followed by a next path selection.The repetition of this two step (transition + collision) cycle is terminated by one of thefollowing three events:• An absorption takes place• The particle leaves the system investigated in such a way that there is no possibilityto return• The energy of the particle falls out of the range of interestIf the event, whose frequency is just studied, occurs, the actual contribution is calculatedeither in the transition or in the collision phase. The sum of the contributions collectedduring the simulation of the history of a single primary source particle is called the score.And the average of an appropriately large number of scores is the Monte Carlo estimate ofthe physical quantity investigated.In the consecutive sections of this Chapter, the basic procedures used during these steps(source selection, transition and collision simulations, and scoring) are discussed, severalspecific procedures, frequently used in neutron and photon transport processes, are collectedin the Appendices of this Chapter.I. ANALOG SIMULATION OF THE RANDOM WALKA. SELECTION OF SOURCE PARAMETERSThere are six fundamental parameters of a particle emitted from a source, viz:• The three spatial coordinates: r = (x,y,z), in a Cartesian system• Two coordinates of the direction of flight: co = ((D„(o y,(o z), |to| = 1 and• The energy (E) of the particle