Science and Technology of Nuclear Installations

Volume 2017 (2017), Article ID 9152580, 5 pages

https://doi.org/10.1155/2017/9152580

## Analyses of the TIARA 43 MeV Proton Benchmark Shielding Experiments Using the ARES Transport Code

North China Electric Power University, No. 2 Beinong Road, Changping District, Beijing 102206, China

Correspondence should be addressed to Bin Zhang

Received 29 April 2017; Revised 16 June 2017; Accepted 27 June 2017; Published 24 July 2017

Academic Editor: Rafael Miró

Copyright © 2017 Bin Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

ARES is a multidimensional parallel discrete ordinates particle transport code with arbitrary order anisotropic scattering. It can be applied to a wide variety of radiation shielding calculations and reactor physics analysis. To validate the applicability of the code to accelerator shielding problems, ARES is adopted to simulate a series of accelerator shielding experiments for 43 MeV proton-^{7}Li quasi-monoenergetic neutrons, which is performed at Takasaki Ion Accelerator for Advanced Radiation Application. These experiments on iron and concrete were analyzed using the ARES code with FENDL/MG-3.0 multigroup libraries and compared to direct measurements from the BC501A detector. The simulations show good agreement with the experimental data. The ratios of calculated values to experimental data for integrated neutron flux at peak and continuum energy regions are within 64% and 25% discrepancy for the concrete and iron experiments, respectively. The results demonstrate the accuracy and efficiency of ARES code for accelerator shielding calculation.

#### 1. Introduction

Validation is an essential part of software quality assurance to ensure that the solutions obtained from the code match reality sufficiently well. Therefore, validation requires comparison of computed results with experimentally measured data. For reliable accelerator shielding calculations, it is necessary to validate the transport code through analyses of shielding experiments. This paper reports on the validation exercise based on the Takasaki Ion Accelerator for Advanced Radiation Application (TIARA) [1] at Japan Atomic Energy Research Institute (JAERI), one of a set of international benchmark experiments for accelerator shielding.

Shielding analyses for the TIARA pose significant computational challenges, including highly anisotropic high energy sources and a combination of deep penetration shielding and unshielded beamline. The experiments on iron and concrete were analyzed using the ARES code with FENDL/MG-3.0 [2] multigroup libraries to validate ARES performance.

The ARES methodologies are described and summarized in Section 2, and the shielding experiment details are presented in Section 3. Results and analysis are summarized in Section 4, and our concluding remarks are presented in Section 5.

#### 2. ARES Methodology

ARES [3, 4] is a multidimensional parallel discrete ordinates neutral particle transport code that uses state-of-the-art methods to obtain accurate solutions to the Boltzmann transport equation. The ARES transport code system consists of seven main modules: DONTRAN1D, DONTRAN2D, DONTRAN3D, RAY2D, RAY3D, ARES_PRE, and ARES_POST. DONTRAN1D, DONTRAN2D, and DONTRAN3D are the DONTRAN series to solve one-, two-, and three-dimensional transport problems, respectively. RAY adopts the first collision source method to mitigate ray effects in two or three dimensions (RAY2D and RAY3D, resp.). ARES_PRE incorporates the geometry and material information of the calculated model and deals with the quadrature sets and cross section message. Preliminary verification and validation for the ARES transport code system had been performed by experiment benchmarking and reference code.

ARES employs discrete ordinates method in discretizing angular variables and adopts spherical harmonic to expand scattering source. The angular variable is usually discretized by replacing angular integrals with quadrature sums. Ray effects are nonphysical anomalies that often appear in optically thin multidimensional discrete ordinates calculations because the solution propagates along a finite set of directions defined by the angular quadrature set. The first collision source method was used to eliminate or mitigate ray effects.

A variety of spatial differencing scheme options are available, including diamond difference (DD), with or without linear-zero flux fixup; theta weighted (TW); directional theta weighted (DTW); exponential directional weighted (EDW); and linear discontinuous finite element. The most general solution technique is source iteration, which is a simple and effective method for many classes of transport problems. However, for optically thick problems dominated by scattering, the source iteration method converges very slowly. Diffusion synthetic acceleration (DSA) has been shown to significantly decrease the iterations. ARES uses the Koch-Baker-Alcouffe parallel sweep algorithm to obtain high parallel efficiency.

The neutron transport calculation in the energy region between 20 and 100 MeV is the most crucial problem for accelerator shielding designs, because high energy neutrons have strong penetrability. The spatial differencing schemes are very important to accurately simulate neutron transport. The diamond difference method assumes a linear relationship between the directional flux at the cell center and cell boundaries and is simple and accurate for small mesh intervals. However, when the mesh interval is too large, measured along the discrete direction through the cell, the difference equations may yield negative fluxes, which cause oscillations in the iterative process and frequently cause negative scalar flux. The TW, DTW, and EDW variations on the DD method were developed to eliminate negative fluxes without significantly sacrificing computational cost or accuracy.

The balance equation can be obtained by integrating the angular discretized form of the transport equation over the mesh cell :where is the discretized direction-of-flight variables, is the cell average flux, and the entering and exiting angular fluxes are referred to using “in” and “out” subscripts. is the total cross section. is known from previous source iteration and the entering angular fluxes are known from the boundary values. When using diamond difference scheme, the cell averaged angular flux can be calculated bywhere ; ; .

Ray effects are nonphysical oscillations in the scalar flux. They are caused by the inability of a quadrature set in discrete ordinates approximation to accurately integrate the angular flux. Ray effects may represent the most significant deficiency of the method. The first collision source method [5] was employed to mitigate ray effects. The method analytically calculates the uncollided flux to obtain the first collision source term, which is then applied to calculate the collided flux using the standard method. The total flux is composed of the uncollided and collided flux.

Thus, the first collision source method decomposes the flux into uncollided components and collided components :and the transport equation is decomposed intowhere is fixed source and is the first collision source, which is calculated from uncollided flux moments. is the Legendre moment of scattering cross section from group to group , and is spherical harmonics.

RAY employs ray tracing method to accelerate optical distance calculations, and the point source correction factor is introduced to improve the accuracy of calculation results. The RAY module within ARES has been verified elsewhere by a series of international benchmarks, such as Kobayashi benchmarks [6], and can effectively eliminate ray effects and obtain reasonable results.

#### 3. Overview of Shielding Experiments

Figure 1 shows a cross sectional view of the TIARA facility with the experimental arrangement [7]. Quasi-monoenergetic source neutrons were generated by 43 MeV protons bombarding ^{7}Li targets. Neutrons produced in the forward angle reached the experiment room through a 10.9 cm diameter, 225 cm long iron collimator embedded in the concrete wall. A test shield of iron or concrete 10–150 cm thick was located at the end of the collimator with an additional iron shield. To measure the neutron energy spectra, a 12.7 cm diameter, 12.7 cm long BC501A liquid scintillation detector was placed behind the test shields. The density and the atomic composition of the concrete and iron shields are described in [8].