Optimization of stochastic global variance reduction techniques for Monte Carlo neutron transport with applications to the ITER geometry

Resumen

In the field of nuclear fusion reactor design, the study of neutronics is of particular relevance. The neutrons released by the fusion reactions that take place in this type of reactors carry a large amount of energy, which will eventually be transformed to generate electricity in future fusion power plants. However, the adverse outcomes caused by these neutrons, such as the capability of activating materials or their harmful effects as ionizing radiation, requires a proper characterization of the neutron distribution within the reactor. In order to achieve a proper assessment of the neutron fluxes within the reactor, the neutrons must be transported throughout its geometry; considering all the interactions they encounter with the materials along their trajectories. For this purpose, the transport codes based on the Monte Carlo sampling method are widely used in the nuclear industry. However, its applicability is limited by the current computing capabilities. To optimize the neutron transport, there are several techniques (implemented in the Monte Carlo codes) that reduce the variance of the sampling, hence reducing the computational effort. Nevertheless, when characterizing a system within all the points in its phase-space, these techniques are not enough, due to them being locally oriented. Therefore, in large geometries where characterization of certain response functions (such as dose or decay heat, amongst others) is needed throughout the entire phase-space, the transport codes based on Monte Carlo sampling require a great amount of computational effort. This problem is enhanced when, in addition to the large region in need of sampling, highly absorbent materials are present, and most of the particles are absorbed. In most of these cases, transport calculations performed within an acceptable computational time becomes an impossible task. To solve this problem, global variance reduction techniques consider all points throughout the geometry as equally important, allowing a uniform transport in terms of the relative error. Hybrid methods generate the necessary parameters for the implementation of the global variance reduction techniques by calculating the neutron flux using deterministic transport codes; these parameters are subsequently used as part of the Monte Carlo input for a final simulation (since the Monte Carlo simulations are more precise when dealing with complex geometries). Currently, there are several techniques that globally reduce the variance, being the hybrid FW-CADIS technique the reference method. The main goal of this thesis is to implement a global variance reduction method for neutron transport calculations performed with the MCNP transport code (based on the Monte Carlo sampling method), without the need of a deterministic code. To achieve this, in the first part of this dissertation an overview of the existing global variance reduction techniques for neutron transport is presented. The strengths and limitations of each method are described and special emphasis is made on van Wijk’s methodology. This purely stochastic technique presents several issues for complex geometries featuring highly absorbent materials. These problems are examined and based on the results two solutions are proposed to overcome them. The second part of this thesis consists of the application of the proposed techniques, as well as van Wijk’s original algorithm, using two different geometries. In the first place, ITER’s computational benchmark is used; this model consists of a simplified geometry used for verification purposes. Over this model, an analog run (without variance reduction), van Wijk’s algorithm, and the proposed modifications are compared in terms of computing time optimization and sampling throughout the geometry. Additionally, a verification of the reliability of the methods is performed by comparing the calculated neutron flux in a defined region with the MCNP analog run. The second geometry used, the ITER neutronics model, is significantly larger and more complex; and the same comparisons as the ones performed over the benchmark are made. In addition, the maps for the two most optimized methods are used to calculate the shutdown dose rate over the equatorial port of the reactor. In this thesis two optimizations of global variance reduction techniques are proposed for the MCNP transport code, without the need of using a deterministic code for the previous calculations. The applications presented show consistency in the results when compared to an analog simulation, as well as a significant improvement of the computational time.