Monte Carlo Particle Transport Methods: Neutron and Photon - gnssn

36 Monte Carlo Particle Transport Methods: Neutron and Photon CalculationszthyFIGURE 3.1.Selection of a random point from a line source.then let us put this line into the coordinate system as given in Figure 3.1, and define theaxis t along the source line. ThenQ(t) dt =p(t)dtif t = 0 at R 1and R 2= R 1+ T(R 2- R)Now the i-th source point is selected as:r, = R 1+ P 1T(R 2 R 1)More complicated, one-dimensional sources (or more precisely sources that can beapproximated by one-dimensional curves) seldom occur in practice. But if they do occur,the best approach is to describe the curve in a parametric form, then select the parameter tfrom p(t) and determine the Cartesian coordinates by transformation.After, the zero- and one-dimensional forms let us continue with sources that can bedescribed by surfaces.If the surface is a region of a plane, let us fix a (£„r\) coordinate system to the plane.Points from sources that have simple boundaries can be easily selected. Recipes to pick-uppoints from a square (or from a rectangle, after linear transformations) and a circle are givenin Sections 2.1.1 and 2.I.J, respectively. For other surfaces with complicated boundaries,the application of the rejection technique is recommended — if the user cannot find a special,efficient tricky method for his problem. In the application of the rejection method the sourceregion is to be covered by a rectangle (Figure 3.2.a) from which tentative coordinates areselected. The points lying out of the region of interest are to be rejected.If the area of the covering rectangle is much larger than that of the source, it is expedientto cover the source region by several smaller rectangles (Figure 3.2.b). In this case, firstone of the rectangles is to be selected. The i-th one is chosen with a probability of