Monte Carlo Particle Transport Methods: Neutron and Photon - gnssn

SSspace region. According to the two different definitions given in Section 2.11.C the programmercan calculate the flux integral in two ways:1. To store score contribution of 1/cr before the simulation of every collision taking placein the region of interest, or2. To sum up the chord lengths of the paths in the region.(Needless to say the first method cannot be used if the flux integral is to be calculatedin a region containing vacuum.)Reaction rates, net currents, etc. can be compiled in similar straightforward manner, bysimply registering the occurrence of the events investigated.From the quantities used in dosimetry kerma (or kerma rate) is calculated most easilythe difference between the energies of a particle before and after collision is just the ' 'kineticenergy released to matter" at the collision site. Absorbed dose can exactly be computedonly by codes in which the histories of the charged particles are also followed.Let us briefly mention here another quantity which will be repeatedly discussed severaltimes throughout this book. That is the fiux-at-a-point. The importance of it needs noexplanation. In measurements one can produce very small, "point-like" detectors, however,if the sensitive volume of the instrument is too small, large times are needed to achieveacceptable statistics. In the case of Monte Carlo simulations the same method is triviallyusable: to surround the point of interest by a small but finite space element and to computethe flux integral in it. However, the difficulty with the statistics is aggravated in the numericalsimulations since the required computer time may exceed even hours or days. Thus, othermethods are preferred — and given later.II. PLAUSIBLE MODIFICATIONS OF THE ANALOG GAMEIn the previous Chapter, the whole Monte Carlo game was based on an as precise aspossible simulation of the physical processes. The application of such a method will necessarilylead to correct results — to the extent that the physical laws governing the randomwalk of the particles are well known and correctly built into the actual computer program,Reliable final results, however, can be reached only after averaging many individual scoresobtained during the individual simulations.There might be many paths that end before they have made arty contribution to thescore. It is worth recalling here that the situation is the same again as in experiments:generally only a fraction of the emitted particles reaches the region of interest. In the physicalmeasurements if the count rate in a detector is very low, long detection times, or manyrepetitions of the experiment are required to obtain good statistics. Similarly in the numericalexperiments many particle histories have to be simulated in order to reach a reliable estimateof the quantity of interest. However, even in the fastest modern computers, the numericalsimulation of a long series of collisions and transitions requires an incomparably longer timethan the total flight time of a physical particle. A necessary — necessary from the point ofgood statistics — increase in the number of simulations might frequently lead to prohibitedlylarge computer times and thus the possibility of solving complex problems by analog MonteCarlo method would be out of the question.This problem motivated — from the very beginning of the Monte Carlo applications —efforts to find methods which modify the analog simulation process in such a way that:• More particle simulations have non-zero contributions to the score, than in the analogsimulation,• But these individual scores differ just so from the analog ones that the expected resultsof the analog and the modified simulations be identical.