Progress and prospects of calculation methods for radiation shielding

Figures & data

Pie charts of summarized results for questionnaire survey.

Table 1. Technological roadmap of radiation shielding field.

Figure 2. Schematic diagram of the improved statistical geometry model.

Figure 3. k-infinity as a function of burn-up in a MOX-fueled BWR assembly of OECD/NEA/NSC benchmark on MOX-BWR.

Figure 4. Comparison among the calculation with and without the binding effect and the measurement on scattering photon spectrum from copper at the energy of 40 keV.

Figure 5. Current status of PHITS development and distribution.

Figure 6. List of models used in PHITS to simulate nuclear and atomic collisions.

Figure 7. Example of Sn angular quadrature set: ω ≡ ω(μ,η). ω; direction vector of particle travel. μ η, ζ = (1-μ²-η²)^1/2; direction cosine of vector ω.

Figure 8. Calculation geometries for one-, two-, and three-dimensional discrete ordinate transport codes.

Figure 9. Particle (neutron/photon) balance.

Note: ${\Phi }_L\mu dy+{\Phi }_B\eta dx-{\Phi }_R\mu dy-{\Phi }_T\eta dx-{\sum }_t{\Phi }_{C}dv=Q_{s}dv+Sdv$. Φ_L; left boundary flux; Φ_B; bottom boundary flux; Φ_R; right boundary flux; Φ_T; top boundary flux; μ,η; direction cosine; Φ_C; flux at the center; Σ_t; total cross section; Q_s; scattering source; S; fixed source.

Figure 10. Various models for within-cell flux extrapolation along X-axis. (1)  α = 0.5, linear model; (2)  α  = 1.0, step model; (3) 0.5 ≦ α ≦ 1, weighted difference model; (4) 0.5 ≦ γ(θ) ≦ α,  θ weighted difference model.

Figure 11. Schematic illustration of weighted/θ-weighted difference model to determine Φ_C, Φ_R-, and Φ_T.

Figure 12. Convergence of flux solution observed in 20 × 20 mesh problem with a source region at the corner mesh interval.

Table 2. Effect of Bremsstrahlung to gamma-ray buildup factors. (Maximum ratio of buildup with and without Bremsstrahlung between 0.5 and 40 mfp for each energy and material)

Material/Energy	Be	B	C	N	O	Na	Mg	Al	Si
15.0 MeV	1.072	1.082	1.094	1.098	1.113	1.186	1.213	1.242	1.268
10.0 MeV	1.043	1.046	1.051	1.052	1.057	1.087	1.097	1.108	1.118
8.0 MeV	1.034	1.035	1.037	1.037	1.04	1.059	1.065	1.071	1.077
6.0 MeV	1.024	1.024	1.024	1.024	1.025	1.035	1.039	1.042	1.045
5.0 MeV	1.02	1.019	1.019	1.019	1.019	1.026	1.028	1.03	1.032
4.0 MeV	1.016	1.014	1.014	1.013	1.013	1.017	1.019	1.02	1.021
3.0 MeV	1.012	1.01	1.009	1.009	1.008	1.01	1.011	1.012	1.012
2.0 MeV	1.008	1.006	1.005	1.005	1.004	1.005	1.005	1.005	1.006
1.5 MeV	1.005	1.004	1.003	1.003	1.003	1.003	1.003	1.003	1.003
Material/Energy	P	S	Ar	K	Fe	Cu	Water	Concrete	Air
15.0 MeV	1.297	1.327	1.378	1.433	1.808	2.044	1.093	1.203	1.098
10.0 MeV	1.127	1.138	1.152	1.169	1.276	1.328	1.047	1.094	1.049
8.0 MeV	1.082	1.088	1.095	1.106	1.163	1.188	1.032	1.063	1.034
6.0 MeV	1.048	1.05	1.053	1.058	1.086	1.095	1.02	1.038	1.021
5.0 MeV	1.033	1.035	1.037	1.04	1.057	1.063	1.015	1.027	1.016
4.0 MeV	1.022	1.023	1.024	1.026	1.036	1.038	1.01	1.018	1.011
3.0 MeV	1.013	1.013	1.014	1.014	1.019	1.02	1.006	1.011	1.007
2.0 MeV	1.006	1.006	1.006	1.006	1.008	1.008	1.003	1.005	1.003
1.5 MeV	1.003	1.003	1.003	1.003	1.004	1.004	1.002	1.003	1.002