Impact of PHITS spallation models on the neutronics design of an accelerator-driven system

Figures & data

Table 1. Model parameters used.

	Nuclear reaction model
			Systematics of nucleon–nucleus
Case	INC	De-excitation	interactions
INCL (PN)	INCL4.6	GEM	Pearlstein–Niita
Bertini (PN)	Bertini INC	GEM	Pearlstein–Niita
INCL (Sato)	INCL4.6	GEM	Sato

Table 2. Main characteristics of ADS.

Plant
Thermal power	800 MWth
Maximum keff	0.97
Coolant	LBE
Structural material	T91*^1
Operation period	600 EFPDs*^2
Proton beam
Energy	1.5 GeV
Beam shape	Gaussian
Beam width	111.6 mm (1σ) at PBW
Inner radius of beam duct	225.0 mm
Target material	LBE
Window material	T91*^1
Thickness of proton beam window	2 mm
Fuel assembly
Type	Duct-less
Number of fuel assemblies	84
Pitch	233.9 mm
Fuel
Fuel	(Pu+MA)N
Inert matrix	ZrN
Active length	1000 mm
Gas plenum length	1000 mm

*¹Modified 9Cr-1Mo steel

*²Effective full power days

Table 3. Fuel composition at BOC.

Number density of transuranic isotopes (atoms/cm/barn)
^237Np	1.05510E−03
^238Pu	2.17558E−05
^239Pu	4.87890E−04
^240Pu	2.15845E−04
^241Pu	1.06114E−04
^242Pu	6.16020E−05
^241Am	6.74178E−04
^242mAm	1.29568E−06
^243Am	2.77740E−04
^242Cm	1.75204E−08
^243Cm	7.60905E−07
^244Cm	9.01829E−05
^245Cm	7.94921E−06
^246Cm	8.20618E−07
Volume ratio (%)
ZrN/(ZrN+PuN+MAN)	56.2
PuN/(MAN+PuN)	25.9

Figure 1. Cross-sectional views of the PHITS calculation model.

Table 4. Nuclear data libraries and calculation modules used.

	Code/library name
Nuclear data library	JENDL-4.0
High-energy transport calculation	PHITS version 2.76
Reactor physics calculation	ADS3D
Cell calculation	SLAROM-UF
Criticality calculation	PARTISN
Fixed-source calculation	PARTISN
Burnup calculation	BURNUP
Group constant set	UFLIB.J40U1 (73 groups)
SP inventory calculation	DCHAIN-SP2001

Table 5. Peak values of parameters related to radiation damage and nuclear heat density per 1 mA at PBW at BOC. The symbols n and p denote contributions from neutrons and protons, respectively.

		INCL (PN)		INCL (Sato)
Case	Bertini (PN) value	value	rel. diff.	value	rel. diff.
Helium gas production^1
n (< 20 MeV)	0.006	0.005	–	0.005	–
n (> 20 MeV)	0.020	0.024	–	0.028	–
p	0.378	0.372	–	0.432	–
Total	0.404	0.401	−1%	0.465	15%
Hydrogen gas production^1
n (< 20 MeV)	0.05	0.05	–	0.05	–
n (> 20 MeV)	0.17	0.21	–	0.24	–
p	2.99	2.88	–	3.29	–
Total	3.21	3.13	−2%	3.57	11%
DPA^2
n (< 20 MeV)	13.63	11.56	–	12.55	–
n (> 20 MeV)	0.72	0.77	–	0.88	–
p	1.56	1.64	–	1.96	–
Total	15.91	13.97	−12%	15.39	−3%
Nuclear heat density^3
n (< 20 MeV)†	0.39	0.33		0.36	–
Ionisation and recoil	24.69	24.12		25.44	–
Total	25.08	24.45	−3%	25.80	3%

¹Unit is (appm/day/mA).

²Unit is (× 10⁻³ dpa/day/mA).

³Unit is (W/cm³/mA).

†Deduced from KERMA approximation.

Figure 2. Neutron and proton energy spectra per 1 mA at PBW.

Figure 3. Total cross sections of ⁵⁶Fe for an incident proton and neutron, and the relative difference from the Pearlstein–Niita systematics.

Figure 4. Helium and hydrogen gas production cross sections of T91 as a function of incident proton energy and the relative difference from INCL (P.N.).

Figure 5. Charge distribution of spallation products in LBE target and relative difference from INCL (PN).

Figure 6. Average excitation energy for the p + ²⁰⁸Pb reaction transferred from the INC to the de-excitation model.

Table 6. Parameters in consideration of the initial burnup cycle, together with the number of cut-off neutrons.

		INCL (PN)		INCL (Sato)
Case	Bertini (PN) value	value	rel. diff.	value	rel. diff.
Number of cut-off neutrons (n/p)	45.25	38.94	−13.9%	39.97	−11.7%
Proton beam
Beam current at BOC (mA)	10.59	12.10	14.3%	11.82	11.6%
Beam current at EOC (mA)	19.92	22.82	14.6%	22.30	11.9%
Core
Burnup reactivity (pcm)^1	−2800	−2808	0.3%	−2807	0.3%
Peaking factor	1.723	1.714	−0.5%	1.712	−0.1%
Transmutation of ^237Np (kg)	−367.4	−367.4	0.0%	−367.4	0.0%
Spallation target
Inventory of ^210Po (Bq)	1.873 × 10^17	1.874 × 10^17	0.0%	1.874 × 10^17	0.0%
Inventory of ^127Xe (Bq)	4.636 × 10^13	3.555 × 10^13	−23.3%	3.693 × 10^13	−20.3%

¹pcm = 10⁻⁵ Δk/k.

Table 7. Cumulative peak parameter values related to the PBW radiation damage for the initial burnup cycle (600 EFPDs). The symbols n and p denote contributions from neutrons and protons, respectively.

		INCL (PN)		INCL (Sato)
Case	Bertini (PN) value	value	rel. diff.	value	rel. diff.
Helium gas production^1
n (< 20 MeV)	52	48	–	54	–
n (> 20 MeV)	180	253	–	280	–
p	3429	3857	–	4377	–
Total	3661	4159	14%	4711	30%
Hydrogen gas production^1
n (< 20 MeV)	485	448	–	506	–
n (> 20 MeV)	1569	2180	–	2419	–
p	27091	29839	–	33313	–
Total	29144	32467	11%	36237	24%
DPA^2
n (< 20 MeV)	115	111	–	119	–
n (> 20 MeV)	7	8	–	9	–
p	14	17	–	20	–
Total	136	136	0%	147	8%
Nuclear heat density at EOC^3
n (< 20 MeV)	5.3	5.0	–	5.5	–
Ionisation and recoil	355.0	417.7	–	445.0	–
Total	360.3	422.8	17%	450.5	25%

¹Unit is (appm).

²Unit is (dpa).

³Unit is (W/cm³).

Figure 7. Comparison of proton-induced non-elastic and neutron-induced total cross sections. Experimental data of the proton-induced non-elastic cross sections and the neutron-induced total cross sections are taken from [26] and [27–29], respectively.

Figure 8. Energy distribution of cut-off neutrons.

Figure 9. Comparison of spectral thick target neutron yields for 1.5-GeV protons on 20-cm-thick lead.

Figure 10. Comparison of spectral thick target neutron yields for 0.5-GeV protons on 20-cm-thick lead.

Figure 11. Comparison of the angular distribution of thick target neutron yields in the 2–20 MeV energy range for 20-cm-thick lead on 1.5- and 0.5-GeV protons.

Figure 12. Activation cross sections of ¹¹⁵In(n, n′)^115mIn and ²⁷Al(n, 2n2p)²⁴Na.

Figure 13. Comparison of ¹¹⁵In(n, n′)^115mIn and ²⁷Al(n, 2n2p)²⁴Na reaction-rate distributions parallel to the axis of a mercury target.

Figure 14. Schematic of the mercury target and detector positions (circles).

Figure 15. Comparison of ¹¹⁵In(n, n′)^115mIn reaction-rate distributions on four surfaces of the target vessel.

Figure 16. Comparison of ²⁷Al(n, 2n2p)²⁴Na reaction-rate distributions on four surfaces of the target vessel.

Dietrich FS, Hartouni EP, Johnson SC, et al. Proton reaction cross sections measured in the BNL/AGS E943 experiment. J Nucl Sci Technol Suppl. 2002;2:269–271.

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