# Development of a Novel Detector Response Formulation and Algorithm in RAPID and its Benchmarking

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## Abstract

Solving radiation shielding problems, i.e. deep penetration problems, is a challenging task from both computation time and resource aspects in field of nuclear engineering. This is mainly because of the complexity of the governing equation for neutral particle transport - Linear Boltzmann Equation (LBE). The LBE includes seven independent variables with presence of integral and differential operators. Moreover, the low successive rate of radiation shielding problem is also challenging for solving such problems.

In this dissertation, the Detector Response Function (DRF) methodology is proposed and developed for real-time and accurate radiation shielding calculation. The real-time capability of solving radiation shielding problem is very important for: (1) Safety and monitoring of nuclear systems; (2) Nuclear non-proliferation; and (3) Sensitivity study and Uncertainty quantification. Traditionally, the difficulties of solving radiation problem are: (1) Very long computation time using Monte Carlo method; (2) Extremely large memory requirement for deterministic method; and (3) Re-calculations using hybrid method. Among all of them, the hybrid method, typically Monte Carlo + deterministic, is capable of solving radiation shielding problem more efficiently than either Monte Carlo or deterministic methods. However, none of the aforementioned methods are capable of performing "real-time" radiation shielding calculation.

Literature survey reveals a number of investigation on improving or developing efficient methods for radiation shielding calculation. These methods can be categorized by: (1) Using variance reduction techniques to improve successive rate of Monte Carlo method; and (2) Developing numerical techniques to improve convergence rate and avoid unphysical behavior for deterministic method. These methods are considered clever and useful for the radiation transport community. However, real-time radiation shielding calculation capability is still missing although the aforementioned advanced methods are able to accelerate the calculation efficiency significantly. In addition, very few methods are "Physics-based"

For example, the mean free path of neutrons are typically orders of magnitude smaller than a nuclear system, i.e. nuclear reactor. Each individual neutron will not travel too far before its history is terminated. This is called the "loosely coupled" nature of nuclear systems. In principle, a radiation shielding problem can be potentially decomposed into pieces and solved more efficient. In the DRF methodology, the DRF coefficients are pre-calculated with dependency of several parameters. These coefficients can be directly coupled with radiation source calculated from other code system, i.e. RAPID (Real-time Analysis for Particle transport and In-situ Detection) code system. With this arrangement, detector/dosimeter response can be calculated on the fly.

Thus far, the DRF methodology has been incorporated into the RAPID code system, and applied on four different benchmark problems: (1) The GBC-32 Spent Nuclear Fuel (SNF) cask flooded with water with a

The results show that dosimeter/detector response or dose value calculations using the DRF methodology are all within

The radiation transport community can be greatly benefited by the development of DRF methodology. Users can easily utilize the DRF methodology to perform parametric studies, sensitivity studies, and uncertainty quantifications. The DRF methodology can be applied on various radiation shielding problems, such as nuclear system monitoring and medical radiation facilities. The appropriate procedure of DRF methodology and necessary parameters on DRF coefficient dependency will be discussed in detail in this dissertation.