Monte Carlo Methods for Radiation Transport by Oleg N. Vassiliev

Author:Oleg N. Vassiliev
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(4.74)

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This example shows how simple this technique can be. In the above proof, for example, we did not have to write the rotation matrix, or its inverse. Solving with Monte Carlo this problem in its original formulation, with an infinite planar source and a point detector, would be very challenging. In an algorithm copying the real process, particle trajectories would start at random positions on an infinite plane, and only a very small fraction of them reaching a small volume around the detector location would contribute to the tally. Using symmetry of the problem results in a much more efficient algorithm. In the modified algorithm, all particles start at the origin and contribute to the tally each time they undergo a collision at a point outside a sphere of radius | z ∗ | centered at the origin. Finally, it would be difficult, if possible, to derive the modified detector response function , Eq. (4.74), solely from intuitive arguments, without using our formalism.

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