Visualization of Space-Dependency of Reponses of Monte Carlo Calculations Using Legendre Polynomials

Visualization of space dependency of quantities of interest is not typically a task to set for Monte Carlo calculations. Often it is, though, useful and desired. Most commonly, it is done by segmenting the phase space into meshes on a surface, and obtaining estimates in each subregion. In this paper we investigate the possibility of using an orthogonal function basis for visual description of the quantities of interest and the determination of the coefficients by Monte Carlo. The basic formulas for determining the expansion coefficients and their variance from a Monte Carlo calculation are given. To test the flux expansion method, first a simple geometry problem is considered to represent the radial flux in a plane. Next, a more complicated geometry is chosen and a reconstruction of the neutron flux in a plane using Legendre polynomials is compared with the classical method of subdivision in segments and scoring the average flux over each segment. The Legendre expansion method shows more detail in the flux reconstruction. Using Laguerre polynomials for the flux expansion did not work out satisfactory.