On-line subcriticality measurement using a pulsed spallation neutron source

Figures & data

Figure 1. Horizontal cross-section of Core A.

Figure 2. Horizontal cross-section of Core B.

Figure 3. Schematic of fuel and polyethylene assemblies and C/S rods.

Table 1. Conditions of Core A configuration and the reactivity values estimated from rod-drop and positive-period methods compared to the calculated values of k_eff.

State	Full in	Full out	ρ ($)	keff	k^ceff^a	C/E
Critical	−	C1,C3,S4,S5,S6	0.000	1.00000	0.99927	0.9993
	−	C1,C2,C3,S4,S5,S6	0.181	1.00142	1.00078	0.9994
AU	C2	C2,C3,S4,S5,S6	−0.552	0.99592	0.99515	0.9992
AV	C1,C2	C3,S4,S5,S6	−0.766	0.99402	0.99312	0.9991
AW	C1,C2,C3	S4,S5,S6	−1.384	0.98924	0.98756	0.9983
AX	C1,C2,C3,S6	S4,S5	−1.628	0.98736	0.98575	0.9984
AY	C1,C2,C3,S5,S6	S4	−2.247	0.98265	0.98046	0.9977
AZ	C1,C2,C3,S4,S5,S6	−	−2.949	0.97735	0.97458	0.9972

^aStatistical error: 0.008% (1σ).

Table 2. Calculated values of β_eff, ρ, Λ, and ℓ_p.

	β^ceff^a	ρ^c^b	Λ^c^c	ℓ^cp^d
State	(pcm)	($)	(μs)	(μs)
AU	779	−0.626	50.54	50.29
AV	790	−0.877	50.42	50.07
AW	791	−1.593	49.14	48.53
AX	782	−1.849	49.04	48.34
AY	781	−2.552	47.59	46.66
AZ	791	−3.297	46.64	45.45

^aStatistical error: 1.3% (1σ).

^bStatistical error: 1.3% (1σ).

^cStatistical error: 0.2% (1σ).

^dℓ^c_p = k_eff^cΛ^c, statistical error: 0.2% (1σ).

Table 3. Conditions of Core B configuration and k_eff, β_eff, ρ, Λ, and ℓ_p values deduced from the calculation.

			k^ceff^a	β^ceff^b	ρ^c^c	Λ^c^d	ℓ^cp^e
State	Full in	Full out		(pcm)	($)	(μs)	(μs)
BU	−	C1,C2,C3,S4,S5,S6	0.95323	795	−6.014	52.10	53.05
BV	C1	C2,C3,S4,S5,S6	0.94609	794	−7.008	50.66	51.61
BW	C1,C2	C3,S4,S5,S6	0.94221	811	−7.424	49.94	50.88
BX	C1,C2,C3,S5	S4,S6	0.93878	798	−8.016	48.78	49.72
BY	C1,C2,C3,S4,S5,S6	−	0.92788	800	−9.591	46.34	47.27

^aStatistical error: 0.008% (1σ).

^bStatistical error: 1.3% (1σ).

^cStatistical error: 1.3% (1σ).

^dStatistical error: 0.2% (1σ).

^eℓ^c_p = k_eff^cΛ^c, statistical error: 0.2% (1σ).

Table 4. Proton beam and spallation target.

Proton beam
Energy	100 MeV
Beam current	20–250 pA
Pulse width	50 ns
Repetition	20 Hz
Spot size	50 mm in diameter
Spallation target
Material	Solid lead-bismuth
Dimension	50 mm in diameter × 18 mm in depth

Figure 4. Schematic of the temporal relationship of the measurement parameters.

Figure 5. Typical detector response to pulsed proton-beam injection obtained from Fiber #1 with the Core AX for a duration of 3 s.

Figure 6. Time evolution of ρ obtained from area-ratio method in Core A.

Figure 7. Time evolution of ρ obtained from area-ratio method in Core B.

Table 5. Statistical values of ρ obtained from the area-ratio method in Core A and Core B steady states for short-time durations.

				Fiber #1		Fiber #2		FC#3
	ρ^e^a	ρ^cMCNP^b	NS^c	Mean	RSD^d	Mean	RSD^d	Mean	RSD^d
State	($)	($)		($)	(%)	($)	(%)	($)	(%)
AU	−0.552	−0.626	60	−0.510	12.4	−0.551	9.1	−0.492	6.9
AV	−0.766	−0.877	60	−0.754	14.7	−0.829	11.0	−0.751	8.9
AW	−1.384	−1.593	60	−1.457	8.6	−1.479	8.4	−1.440	6.7
AX	−1.628	−1.849	60	−1.705	12.0	−1.723	10.9	−1.704	9.9
AY	−2.247	−2.552	60	−2.368	8.0	−2.073	6.1	−2.385	4.7
AZ	−2.949	−3.297	60	−3.057	8.4	−2.572	8.3	−3.144	5.0
BU	–	−6.014	60	−5.095	8.3	−4.675	9.3	−5.740	5.7
BV	–	−7.008	60	−5.837	11.9	−5.234	9.7	−6.689	7.6
BW	–	−7.424	60	−6.699	13.9	−5.506	10.6	−7.302	8.6
BX	–	−8.016	60	−6.891	13.2	−5.764	11.1	−7.760	8.2
BY	–	−9.591	50	−8.055	17.2	−6.723	12.8	−9.724	9.1

^aReactivity deduced from the rod-drop and positive-period methods.

^bReactivity deduced from the MCNP calculations.

^cNumber of detector responses in sample.

^dRelative standard deviation (1σ).

Figure 8. Time evolution of α obtained from the conventional α-fitting method in Core A.

Figure 9. Time evolution of α obtained from the conventional α-fitting method in Core B.

Figure 10. Example of fitting failure by the nonlinear least-squares method.

Figure 11. Histograms representing the frequency distribution of delayed neutrons (t = 30–50 ms) for the three different neutron detectors. Circles with dashed lines indicate the Poisson distributions.

Figure 12. Time evolution of α obtained from the modified α-fitting method in Core B.

Table 6. Comparison of α values obtained from the conventional and modified α-fitting methods for long time durations.

			Conventional method	Modified method	Difference
Detector	State	Duration (s)	Value, a (${\mathrm{ms}}^{-1}$)	Value, b (${\mathrm{ms}}^{-1}$)	(a − b)/b (%)
Fiber #1
	AU	180	0.232	0.234	−0.4
	AV	120	0.275	0.274	0.7
	AW	180	0.387	0.390	−0.7
	AX	180	0.440	0.439	0.2
	AY	180	0.526	0.544	−3.2
	AZ	180	0.655	0.675	−2.9
	BU	180	0.957	0.997	−3.9
	BV	180	1.117	1.160	−3.6
	BW	180	1.270	1.295	−1.9
	BX	180	1.373	1.398	−1.7
	BY	150	1.703	1.723	−1.1
Fiber #2
	AU	180	0.197	0.204	−3.5
	AV	120	0.242	0.252	−4.0
	AW	180	0.348	0.351	−0.9
	AX	180	0.387	0.393	−1.7
	AY	180	0.494	0.492	0.3
	AZ	180	0.623	0.622	0.1
	BU	180	0.961	0.959	0.4
	BV	180	1.131	1.122	0.9
	BW	180	1.229	1.220	0.8
	BX	180	1.347	1.332	1.3
	BY	150	1.655	1.637	1.1
FC#3
	AU	180	0.232	0.231	0.3
	AV	120	0.273	0.273	0.0
	AW	180	0.390	0.389	0.2
	AX	180	0.430	0.428	0.5
	AY	180	0.542	0.541	0.2
	AZ	180	0.672	0.673	−0.2
	BU	180	0.988	1.001	−1.3
	BV	180	1.146	1.161	−1.2
	BW	180	1.252	1.258	−0.4
	BX	180	1.343	1.354	−0.7
	BY	150	1.623	1.643	−1.2

Figure 13. Relationship between α and ρ.

Figure 14. Time evolution of ρ obtained from the modified α-fitting method in Core A.

Figure 15. Time evolution of ρ obtained from the modified α-fitting method in Core B.

Table 7. Statistical values of ρ obtained from the modified α-fitting method with the conversion formula in Core A and Core B steady states for short-time durations.

				Fiber #1		Fiber #2		FC#3
	ρ^e^a	ρ^cMCNP^b		Mean	RSD^d	Mean	RSD^d	Mean	RSD^d
State	($)	($)	NS^c	($)	(%)	($)	(%)	($)	(%)
AU	−0.552	−0.626	60	−0.453	17.7	−0.265	20.5	−0.436	11.3
AV	−0.766	−0.877	60	−0.704	19.2	−0.568	14.2	−0.699	8.9
AW	−1.384	−1.593	60	−1.423	6.9	−1.178	5.1	−1.413	3.7
AX	−1.628	−1.849	60	−1.728	7.3	−1.442	5.2	−1.657	2.9
AY	−2.247	−2.552	60	−2.374	3.9	−2.055	4.0	−2.357	1.8
AZ	−2.949	−3.297	60	−3.191	3.4	−2.862	3.6	−3.179	1.7
BU	−	−6.014	60	−5.186	3.5	−4.947	3.3	−5.212	1.7
BV	−	−7.008	60	−6.203	3.8	−5.962	3.8	−6.206	1.8
BW	−	−7.424	60	−7.039	4.7	−6.576	4.5	−6.806	2.0
BX	−	−8.016	60	−7.674	5.4	−7.266	5.2	−7.400	2.5
BY	−	−9.591	50	−9.684	6.5	−9.158	7.7	−9.192	3.0

^aReactivity deduced from the rod-drop and positive-period methods.

^bReactivity deduced from the MCNP calculations.

^cNumber of detector responses in sample.

^dRelative standard deviation (1σ).