Application of the First Collision Source Method to CSNS Target Station Shielding Calculation

Ray effects are the inherent problem of discrete ordinates method. RAY3D, a functional module of ARES which is a discrete ordinates code system, employs a semi-analytic first collision source method to mitigate ray effects. This method decomposes the flux into uncollided and collided components, and then calculates them with analytical method and discrete ordinates method respectively. In this article, RAY3D is validated by the Kobayashi benchmarks and applied to the neutron beamline shielding problem of China Spallation Neutron Source (CSNS) target station. Numerical results of the Kobayashi benchmarks indicate that DONTRAN3D with RAY3D solutions agree well with the Monte Carlo solutions. The dose rate at the end of the neutron beamline is less than 10.83 {\mu}Sv/h in CSNS target station neutron beamline shutter model. RAY3D can effectively mitigate ray effects and obtain relatively reasonable results.

💡 Research Summary

The paper addresses the well‑known “ray effect” problem inherent to the discrete ordinates (SN) method, which manifests as artificial streaks or oscillations in the angular flux when the angular discretization is insufficient, especially in geometries containing voids adjacent to highly absorbing media. To mitigate this deficiency, the authors present RAY3D, a three‑dimensional module of the ARES deterministic transport code system that implements a semi‑analytic first‑collision‑source (FCS) technique. The FCS approach decomposes the total neutron flux into an uncollided component, which can be evaluated analytically using point‑source geometry and optical distances, and a collided component, which is solved with the conventional SN solver (DONTRAN3D). By reconstructing the total flux from these two parts, the method effectively suppresses the spurious angular artifacts that plague pure SN calculations.

The validation of RAY3D is carried out using the Kobayashi 3‑D benchmark problems (Problem 2 and Problem 3), which consist of a source region, a void, and a shielding region. These benchmarks are particularly sensitive to ray effects because of the large void. The authors compare three sets of results: Monte‑Carlo reference solutions (MCNP), TORT with the FNSUNCL3 library, and DONTRAN3D with and without RAY3D. For purely absorbing configurations the maximum deviation of the RAY3D‑enhanced solution from MCNP is under 4 %; for mixed scattering cases the deviation remains below 13 %. In contrast, DONTRAN3D without the FCS correction exhibits errors an order of magnitude larger, confirming the efficacy of the first‑collision source treatment.

Having established credibility, the method is applied to a realistic engineering problem: the neutron beamline shutter of the China Spallation Neutron Source (CSNS) target station. The model spans 10 m in height and 1.15 m in width, incorporating stainless steel 316, low‑carbon steel, and several void channels. Because the CSNS source produces high‑energy neutrons (up to 150 MeV), the authors employ the HEST1.0 multi‑group library (originally 253 neutron groups, condensed to 31 groups) and a 48‑group photon set, both derived from ENDF/B‑VII.0 via NJOY. Angular discretization uses an S₈ quadrature with P₃ Legendre expansion of the scattering matrix.

Simulation results reveal that a plain DONTRAN3D calculation matches TORT in the heavily shielded region (z < 450 cm) but fails dramatically in the downstream void region, either under‑predicting or over‑predicting the neutron flux by orders of magnitude. When RAY3D is coupled with DONTRAN3D, the dose‑rate profile along the beamline becomes smooth and physically plausible. In the critical region from 450 cm to 1000 cm, the dose rate declines steadily, reaching a value of 10.83 µSv h⁻¹ at the beamline exit. This level satisfies safety criteria for occupational exposure and demonstrates that the first‑collision source correction restores the reliability of deterministic calculations for deep‑penetration, void‑dominated problems.

Additional visualizations—contour plots of scalar flux for a representative energy group and of the total dose rate in the y‑z plane—show that RAY3D eliminates the artificial “ray” patterns seen in the uncorrected SN solution, yielding a continuous flux distribution across material interfaces and voids.

In conclusion, the first‑collision‑source implementation in RAY3D successfully mitigates ray effects, enabling accurate deterministic transport analysis of complex, high‑energy neutron shielding problems such as the CSNS beamline shutter. The authors note future work to further improve the method, including the incorporation of an angle‑integrated mesh‑cell balance equation to refine the source term and the development of libraries extending to higher energies. The study demonstrates that ARES + RAY3D provides a practical, cost‑effective alternative to Monte‑Carlo simulations for engineering design and safety assessment in large‑scale neutron facilities.