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 a long‑standing limitation of the discrete ordinates method (DOM) – the so‑called ray effect – by introducing and validating a first‑collision source technique implemented in the RAY3D module of the ARES code system. Ray effects arise because DOM discretizes angular space into a finite set of directions; in regions with strong anisotropy, high‑energy neutrons, or near sharp material interfaces, the angular discretization produces artificial “spikes” or shadows in the calculated flux, leading to significant numerical errors. Traditional remedies, such as increasing angular quadrature order, dramatically raise computational cost, while Monte Carlo methods, although free of ray effects, are often too time‑consuming for iterative engineering design.
The first‑collision source method mitigates this problem by decomposing the neutron flux into an uncollided component (particles that have not yet interacted) and a collided component (particles that have undergone at least one interaction). The uncollided flux can be obtained analytically or semi‑analytically because it follows straight‑line attenuation governed solely by material macroscopic cross sections. This analytical solution provides an exact source term for the collided transport equation, which is then solved with the conventional DOM solver (DONTRAN3D). By feeding the accurate uncollided source into the DOM, the method eliminates the artificial angular bias that gives rise to ray effects, while retaining the fast convergence and deterministic nature of DOM.
RAY3D automates the entire workflow: after a simple activation flag in the ARES input file, the module computes the uncollided source for each spatial cell, runs DONTRAN3D for the collided flux, and finally superposes the two contributions to obtain the total flux. The implementation supports fully three‑dimensional geometries and complex material distributions, making it suitable for realistic engineering problems.
Validation is performed against the internationally recognized Kobayashi benchmark suite, which includes a variety of materials (water, concrete, lead) and geometries (planar, cylindrical, spherical). Results show that RAY3D‑enhanced DONTRAN3D predictions agree with high‑fidelity Monte Carlo reference solutions within an average absolute error of less than 5 %. The improvement is most pronounced in high‑energy regions and near material boundaries where conventional DOM exhibits severe ray artifacts.
The method is then applied to a practical shielding problem at the China Spallation Neutron Source (CSNS) target station. A detailed model of the neutron beamline shutter is constructed, and the dose rate at the downstream end of the beamline is evaluated. Using standard DOM without the first‑collision source, the calculated dose rate is inflated to about 20 µSv/h due to ray effects. With RAY3D, the dose rate drops to 10.83 µSv/h, comfortably below the design limit of 15 µSv/h, thereby confirming the method’s practical utility. Moreover, the RAY3D‑based calculation converges 3–4 times faster than an equivalent Monte Carlo simulation and does not require substantially more memory, demonstrating its efficiency for large‑scale facility design.
In summary, the first‑collision source approach embodied in RAY3D provides a robust, computationally efficient solution to the ray‑effect problem in deterministic neutron transport calculations. It preserves the deterministic advantages of DOM—speed, ease of mesh‑based modeling, and straightforward sensitivity analysis—while delivering accuracy comparable to Monte Carlo methods. The successful application to the CSNS shielding case illustrates its relevance for high‑energy neutron sources, complex shielding configurations, and safety‑critical dose assessments. Future work suggested by the authors includes extending the technique to multi‑group energy treatments, incorporating anisotropic scattering kernels, and integrating the method into automated design‑optimization loops, which could further broaden its impact across nuclear engineering, medical radiation therapy, and space radiation protection.