Development of a frequency-domain reactor noise simulator based on a neutron transport method

The neutron flux measured in a nuclear reactor is characterized by fluctuations around a main trend. These fluctuations are known as reactor neutron noise, and they may allow to identify anomalies in the reactor core. In this context, the CORTEX – COre monitoring Techniques and EXperimental validation and demonstration project, supported by the European Commission, aims at studying reactor neutron noise induced by different types of perturbations (e.g. vibrations of reactor components), and developing core monitoring techniques from the analysis of reactor neutron noise. When simulating reactor neutron noise, the reactor transfer function is needed. The reactor transfer function describes the system response to possible perturbations, and it can be modelled with the neutron transport equation. Most of the past work in this area relies on neutron diffusion theory. However, recent efforts focus on advanced computational capabilities that can provide more detailed insights into neutron noise problems and be used to assess the limitations of the diffusion approach.In the CORTEX project, Chalmers University of Technology is building a neutron noise simulator with a high-order approximation of the neutron transport equation. The equations are discretized according to a finite difference scheme for the spatial variable, a discrete ordinates approximation for the angle, and a multi-group formalism for the neutron energy. The simulation consists of two steps. The first step solves the criticality problem and calculates the static neutron flux. The second step determines the neutron noise in the frequency domain with respect to the prescribed neutron noise source and the static neutron flux previously estimated.The numerical solution of the equations is obtained from an iterative procedure. This is a computationally intensive task because a converged solution may require a very large number of iterations. A crucial factor in the reduction of the iterations is the implementation of a technique for the acceleration of the algorithm. For static calculations, methods such as the Diffusion Synthetic Acceleration (DSA) and the Coarse Mesh Finite Difference (CMFD) acceleration have been widely investigated. To some extent, these techniques have also been \ua0applied to time-dependent problems. On the other hand, no study on acceleration of neutron noise calculations in the frequency domain have been reported in the open literature. The current work also explores the extension of DSA and CMFD methods to the case of frequency-domain neutron noise simulations. Preliminary results will be presented for neutron noise calculations in a 2-dimensional heterogeneous system, with 2-energy groups