Monte Carlo Particle Transport Methods: Neutron and Photon - gnssn

150 Monte Carlo Particle Transport Methods: Neutron and Photon Calculations1. A starting point P is selected from the source density Q(P) and the starting statisticalweight W of the particle is determined. (The weight will depend on how the nonanalogsource density differs from the analog one.)2. The next collision point P' is selected from the transition kernel T(P,P'). The statisticalweight is changed so as to compensate for the bias in the nonanalog kernel. The newweight wall be denoted by W'. If there is some contribution of the free flight from Pto P' to the final score, this contribution is added.3. The number and coordinates of the particles (a number of points P"), which emergefrom the collision at P', are selected from the collision kernel C(P',P'). The numberof secondaries must be selected so that its expected value isGenerally, the collision kernel is the sum of kernels that correspond to different eventsand a different number of secondaries, as will be detailed in the next section. Again,the weights of the progeny are chosen so as to account for the weight of the particlethat entered the collision, and also for the alteration of the nonanalog kernel, comparedto the analog. The possible scores, associated with the event that the actual numberof particles leave the collision, are added to the final estimate.4. One of the emerging particles (if there are any) is selected, the coordinates of theothers are stored, and the selected particle is followed by returning to step 2.5. Tracking of a particle is terminated if no particle emerges from the collision (i.e., anabsorption) and also if the particle leaves (either in space or in energy) the systemwith no chance of returning to it. Note that escape may also be considered an absorptionif the spatial region from where there is no return to the simulated system is thoughtto be filled with a black absorber.If the trace of a particle is terminated, another particle from among those that havebeen generated in previous collisions and have not yet been followed is started fromits birthplace, and the procedure is repeated from step 2.6. The history terminates if there is no particle left in the system.In step 5 above, the idea of a vacuum-equivalent black absorber is raised. This substitutionmerits further discussion. Let us call the spatial region, V, where the simulation isperformed the domain of simulation. Unless it is the entire geometrical space, it will beassumed to be surrounded by vacuum. The domain of simulation can safely be regarded asconvex, since even if the physically interesting spatial region is concave, a line connectingany two points of this region may be a part of the random walk. Now, if the domain ofsimulation is not the entire geometrical space, the integral of the transition kernel over thedomain in certain directions is not necessarily unity, i.e., the probability of an endless freeflight is different from zero. This would cause some inconveniences in the subsequentderivations. On the other hand, since a particle that leaves the domain of simulation has nochance to return to it, it is immaterial from the point of view of the simulation whether therest of the space is vacuum or is filled with any purely absorbing material. Assuming thelatter case and denoting by P, the phase-space point at the boundary of the domain ofsimulation which is crossed by a free flight from P = i.r,to.h). the transition kernel usedin the simulation can be redefined asT(P,P') :if r' -v V (5.24)