A General Method of Importance Sampling the Angle of Scattering in Monte Carlo Calculations

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Abstract
The application of the Monte Carlo method to the solution of deep-penetration radiation transport problems requires the use of “importance sampling.” A systematic approach to obtaining an importance function is to calculate the solution of the inhomogeneous adjoint transport equation (using the Monte Carlo estimator of the answer of interest as the source term) and to use this adjoint flux (or value function) as the importance function. The adjoint flux is calculated for simplified geometries using one-dimensional discrete ordinates methods.In three-dimensional deep-penetration Monte Carlo calculations the alteration of both the transport and the collision kernel is desirable. The exponential transform is quite useful for altering the transport kernel. However, selection from the altered collision kernel is much more difficult. The approach taken here is to introduce an angular grid with 30 discrete directions fixed in the laboratory coordinate system, along which particles are required to travel....

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