Impact of Modeling Assumptions on Muon Scattering Images of Loaded Dry Storage Casks

Figures & data

TABLE I Tabulated Materials Used for the Individual Components of the Models

Geometrical Component	Material	Geometrical Component	Material
Monolithic body	Ductile iron	Moderator rods	Polyethylene
Primary lid	Stainless steel	Fuel rods	Uranium oxide
Secondary lid	Stainless steel	Guide tubes	Zirconium alloy

TABLE II Overview of the Dimensions of the Reference Model*

Height	5944 mm
Diameter	2436 mm
Cavity height	5023 mm
Cavity diameter	1480 mm

*Compare with Fig. 1a.

Fig. 1. Exploded view of the components of each model.

Fig. 2. Depiction of the orientation of the cask models in the x-, y-, and z-directions relative to the detector plates.

Fig. 3. Scattering images for all models with and without fuel assemblies, as well as difference scattering images. The color code represents the mean of the effective scattering angle ${\theta }_{\mathit{eff}}$ distribution (in degrees) for each pixel, with the x- and y-positions indicating the muon position after traversing the incoming detector.

Fig. 4. Cross-sectional view of the fuel basket, highlighting the fuel assemblies selected for further analysis. These fuel assemblies are labeled with ID numbers 1 through 7 and are color-coded gray for clarity. The fuel assembly had a one-quarter symmetry. Fuel assemblies 5 and 7 were chosen for analysis due to their proximity to the trunnions, while fuel assemblies 4 and 6 were selected for comparison. Fuel assemblies 2 and 3 were chosen for a comprehensive assessment.

TABLE III Calculated Test Statistics for the Anderson-Darling Test and the Calculated p-Value for the Kolmogorov-Smirnov and Kuiper’s Tests After Comparison Between the Reference Model and All Simplified Models*

	ID	Anderson-Darling		Kolmogorov-Smirnov		Kuiper’s Test
Number of muons		4.5 × 10^6	15 × 10^6	4.5 × 10^6	15 × 10^6	4.5 × 10^6	15 × 10^6
Reference versus	1	−0.44005	−0.47863	0.77235	0.42468	0.57763	0.92316
simplified model 1	2	−0.64648	−0.02685	0.88048	0.44341	0.91303	0.08630
	3	−0.64944	0.03012	0.94116	0.58468	0.97497	0.65694
	4	0.44497	5.02497	0.31281	0.00964	0.82401	0.02131
	5	1.96998	7.47372	0.15056	0.00027	0.19996	0.00896
	6	0.75842	3.34086	0.18695	0.01066	0.18328	0.20213
	7	0.61845	6.35889	0.20115	0.00200	0.68386	0.01048
Reference versus	1	−0.41614	−0.78526	0.26775	0.73489	0.77667	0.38569
simplified model 2	2	−0.78383	−0.82529	0.95828	0.80412	0.82780	0.98605
	3	−0.76802	−0.81225	0.71804	0.91882	0.78876	0.61051
	4	−0.84654	0.8453	0.73727	0.31954	0.44890	0.21850
	5	−0.38159	1.76414	0.72196	0.14144	0.14010	0.54692
	6	0.22059	0.15172	0.58521	0.44156	0.29952	0.41748
	7	0.12956	1.47785	0.05910	0.12367	0.87213	0.36858
Reference versus	1	−0.92746	−0.89796	0.67472	0.88712	0.43205	0.57559
simplified model 3	2	−0.51529	−0.02316	0.87405	0.49242	0.74126	0.43538
	3	−0.54906	0.06878	0.84193	0.71632	0.87818	0.71944
	4	1.42972	10.70780	0.06391	0.00073	0.57374	0.01572
	5	4.47591	16.87124	7.86835E-25	0.00001	0.01285	0.00062
	6	4.04571	7.46859	0.09898	0.00659	0.0516	0.00034
	7	2.84604	14.82826	0.03102	0.00003	0.23082	0.00004

*Results for both particle numbers are listed.

Fig. 5. Illustration of the rejection of the null hypothesis after comparing the difference data of the simplified models to the simplified models. The fuel assembly regions are colored turquoise if the data sets with the scattering angles contained therein led to a rejection of the null hypothesis. The results for all three tests for simulations performed with 4.5 million and 15 million muons are shown in (a) and (b), respectively.

Fig. 6. (left) Comparison of the probability distribution function and (right) the cumulative probability function of the reference model (black) with the simplified models (red) of scatter data stored in the pixels representing fuel assembly 5 generated using 15 million muons.