SENSMG: First-Order Sensitivities of Neutron Reaction Rates, Reaction-Rate Ratios, Leakage, k_eff, and α Using PARTISN

Figures & data

TABLE I Reaction-Rate Ratio Sensitivities for λ-Mode Flux, Indirect Effect*

Sensitivity	Label	Equation
Total cross section	total
Absorption cross section	abs
Capture cross section	(n,g)
Chi (not normalized)	chi_(nn)
Nu	nu
Fission cross section	fiss
In-scattering, P0	in-scat-0
Self-scattering, P0	self-scat-0
Out-scattering, P0	out-scat-0
In-scattering, Pl, 1 ≤ l ≤ L	in-scat-[l]
Self-scattering, Pl, 1 ≤ l ≤ L	self-scat-[l]
Out-scattering, Pl, 1 ≤ l ≤ L	out-scat-[l]
Source^a	source
Total scattering	ssctt
Nuclide density^b	density

*Except for density (see note b), these equations are also used for α-mode and fixed-source flux, but is set to 1 and a divisor is used where needed.

^a For leakage problems only. See Eq. (61) and the text that follows it.

^b For leakage, the nuclide density sensitivity includes as a summand.

TABLE II Spherical or Slab Input File Description

Card	Description	Number of Entries per Line
1	Title	Maximum 120 characters
2	[sphere | sph | slab] [keff | alpha | lkg]	2 (words)
3	LIBNAME	1
4.0	NM	1
4.1 to 4.NM	Specification for each material. Each line has an index followed by a list of pairs of ZAID and weight fraction. End each line with “/”.	Variable
5	Mass density of each material (g/cm^3)	NM
6	NR	1
7	Radius of each shell (cm)^a	NR or NR + 1^a
8	Material assignments to radial shells (0 means void)	NR
9	Index of radial shell to use for reaction rates	1
10.0	NRRR^b	1
10.1 to 10.NRRR	Reaction-rate ratios; end each line with “/”.	2 or 4

^a For spheres, the inner-most surface is assumed to be 0. For slabs, the left-most surface is entered.

^b NRRR = Number of reaction-rate ratios.

TABLE III Cylindrical Input File Description

Card	Description	Number of Entries per Line
1	Title	Maximum 120 characters
2	[cyl | cylinder] [keff | alpha | lkg]	2 (words)
3	LIBNAME	1
4.0	NM	1
4.1 to 4.NM	Specification for each material. Each line has an index followed by a list of pairs of ZAID and weight fraction. End each line with “/”.	Variable
5	Mass density of each material (g/cm^3)	NM
6	NR and NZ	2
7	Radius of each shell (cm)	NR
8	Location of each axial layer starting with the bottom of the first layer (cm)	NZ + 1
9.1 to 9.NZ	Material assignments to radial zones for each axial layer (0 means void); axial layers are listed top to bottom.	NR
10	Index of radial zone and index of axial zone to use for reaction rates	2
11.0	NRRR^a	1
11.1 to 11.NRRR	Reaction-rate ratios; end each line with “/”.	2 or 4

^a NRRR = Number of reaction-rate ratios.

TABLE IV Edit Reactions Available from the NDI

	PARTISN 7 and Earlier		PARTISN 8 and Later
Position	Description	Name	Description	Name
1	fission spectrum	chi	fission spectrum	chi
2	effective nusigf	nusigf	effective nusigf	nusigf
3	total	total	total	total
4	absorption	abs	absorption	abs
5	chi	chi	chi	chi
6	elastic	mend1	elastic	(n,n)
7	inelastic	mend2	inelastic	(n,n')
8	(n,2n)	mend3	(n,2n)	(n,2n)
9	(n,3n)	mend4	(n,3n)	(n,3n)
10	(n,gamma)	mend5	(n,gamma)	(n,g)
11	(n,alpha)	mend6	(n,proton)	(n,p)
12	(n,proton)	mend7	(n,alpha)	(n,a)
13	(n,deuteron)	mend8	1st-chance fission	(n,f)
14	(n,triton)	mend9	2nd-chance fission	(n,n')f
15	(n,3He)	mend10	3rd-chance fission	(n,2n)f
16	sum of all fission	n-fiss	sum of all fission	(n,F)
17	prompt fission spectrum	mend12	prompt fission spectrum	chi_pr
18	total fission spectrum	mend13	total fission spectrum	chi_tot
19	—	—	(n,deuteron)	(n,d)
20	—	—	(n,triton)	(n,t)

TABLE V Command Line Options

Flag	Description	Default
-i	Input file name	sensmg_inp
-np	Number of MPI processes to use for PARTISN	1
-ngroup	Number of energy groups	30
-isn	SN order	32
-isct	Legendre scattering expansion order	3
-epsi	Convergence criterion for PARTISN calculations (PARTISN’s epsi) (Ref. 1)	1E–06
-epsig	Convergence criterion for GPT adjoint calculations in the method of successive approximations	1E–05
-chinorm	full/partial/none constrained normalization for the chi matrix	full
-fissdata	0/1/2 use fission matrix/chi matrix/chi vector (PARTISN’s fissdata) (Ref. 1)	0
-aflxfrm	0/1 no/yes use an α-eigenvalue search method that may help for subcritical problems [PARTISN’s aflxfrm (Ref. 1); ignored for versions before 7.72]	0
-alpha_n	yes/no use/ignore (α,n) neutron sources	yes
-misc	yes/no use MISC/use SOURCES4C for spontaneous fission sources	yes
-nag	Number of α-particle energy groups in SOURCES4C	100
-srcacc_no	none/for/adj/for+adj turn off source acceleration for neither/forward/adjoint/both	none
-use_existing	yes/no use/don’t use PARTISN output files that have already been calculated.	no
-my_modules	yes/no use/don’t use user’s own loaded module files. “yes” skips automatic module file loading, used to override defaults or if the user’s system does not use modules.	no
-rplane	Radial surface on which to compute angular fluxes	–1 (i.e., do not use)
-zplane	Axial surface on which to compute angular fluxes	–1 (i.e., do not use)
-h	Show options (i.e., help)	None

TABLE VI Composition of TREAT Fuel

Nuclide	Atom Density [atoms/(b·cm)]	Weight Fraction
^1H	1.13694E−4	8.38215E−5
^10B	5.68468E−7	4.16390E−6
C (natural)	1.13579E−1	9.97955E−1
^235U	1.05735E−5	1.81803E−3
^238U	7.95855E−7	1.38591E−4

TABLE VII Sensitivity to Constituents of TREAT Fuel

Nuclide	MCNP	SCALE	PARTISN
^1H	4.0059E−03 ± 4.37%	4.0194E−03 ± 1.63%	3.5619E−03
^10B	–2.0248E−01 ± 0.02%	–2.0235E−01 ± 0.00%	–2.0292E−01
C (natural)	5.9836E−01 ± 0.46%a	5.8209E−01 ± 1.58%	5.9970E−01
^235U	3.5071E−01 ± 0.04%	3.5032E−01 ± 0.01%	3.4584E−01
^238U	–2.5392E−03 ± 0.50%	–2.5494E−03 ± 0.14%	–2.5535E−03
S(α,β)	2.3217E−01 ± 0.82%	N/A^b	N/A^b

^a Includes the S(α,β) sensitivity for the grph table.

^b Not applicable—S(α,β) scattering is not calculated separately in SCALE or PARTISN.

Fig. 1. Sensitivity of k_eff to ²³⁵U density in Flattop-Pu reflector.

Fig. 2. Sensitivity (unconstrained) of k_eff to ²³⁵U chi in Flattop-Pu reflector.

Fig. 3. Sensitivity (full normalization) of k_eff to ²³⁵U chi in Flattop-Pu reflector.

Fig. 4. Sensitivity of the ²³⁷Np fission to ²³⁵U fission ratio to the ²³⁹Pu density and fission cross section in Flattop-Pu.

Fig. 5. Sensitivity of the ratio of R1 = ²³⁹Pu capture reaction rate to the flux to the ²³⁹Pu capture cross section (indirect effect) in a one-dimensional Jezebel model: (a) R1 and flux plotted separately and (b) R1/flux.

Fig. 6. Sensitivity of the ratio of R1 = ²³⁸U fission to R2 = ²³⁵U fission to the ²³⁴U fission cross section in group 30 in a one-dimensional Godiva model: (a) R1 and R2 plotted separately and (b) R1/R2.

Fig. 7. Sensitivity profile of the ratio of R1 = ²³⁸U fission to R2 = ²³⁵U fission to the ²³⁴U fission cross section in a one-dimensional Godiva model.

TABLE VIII Sensitivity to ²³⁹Pu Self-Scattering for the High-Density Jezebel Model

	α			Reaction-Rate Ratio
Scattering Order	SENSMG	Central Difference	Difference	SENSMG	Central Difference	Difference
0	1.63687E+01	1.6338E+01	0.186%	7.96962E−02	7.9501E−02	0.246%
1	–9.49096E+00	–9.4800E+00	0.116%	–9.73175E−02	–9.7199E−02	0.122%

TABLE IX Sensitivity of the Leakage to Density for the BeRP Ball Model

Density	Adjoint	Central Difference	Difference
Pu bulk mass density	7.20992E+00	7.21712E+00	–0.100%
Poly bulk mass density	1.56066E+00	1.56032E+00	0.022%
^9Be atom density	1.15770E−02	1.15836E−02	–0.057%
^240Pu atom density	1.18230E+00	1.18305E+00	–0.064%

TABLE X Sensitivity of Reaction Rates to ²⁴⁰Pu Density for the BeRP Ball Model

Reaction	SN	Adjoint	Central Difference	Difference
^238U(n,f)/^235U(n,f)	32	–1.11391E−02	–1.14502E−02	–2.717%
	128	–1.14238E−02	–1.14488E−02	–0.218%
^238U(n,f)	32	1.20874E+00	1.20539E+00	0.277%
	128	1.20497E+00	1.20461E+00	0.030%

TABLE XI Adjoint-Weighted Quantities as a Function of S_N Order for the BeRP Ball Model

SN	Fine Mesh Width (cm)	(Should Be 0)	Equation (51) (Should Be 0)	Equation (52) (Should Be 1)
16	0.005	–2.3660E−03	9.0572E−04	1.009210
32	0.005	–6.0765E−04	2.7421E−04	1.002783
64	0.005	–1.5487E−04	7.7350E−05	1.000797
128	0.005	–4.5194E−05	2.1796E−05	1.000219
256	0.005	–1.6662E−05	7.8144E−06	1.000070
512	0.005	–2.4125E−06	4.3070E−06	1.000038
1024	0.005	–3.2741E−06	5.4009E−06	1.000025
1024	0.0005	3.1054E−06	1.0501E−06	1.000007

TABLE XII Sensitivity of the Leakage to Boundaries and Internal Interfaces for the BeRP Slab

Surface Location (cm)	Adjoint	Central Difference	Difference
–2.8	–9.58828E+03	–9.58820E+03	0.0008%
–1.0	–3.25842E+04	–3.25967E+04	–0.0384%
1.0	3.39701E+04	3.39837E+04	–0.0398%
2.8	8.20235E+03	8.20220E+03	0.0018%

TABLE B.I Isotopes Available in the Kynea3 Library

ZAID	Name	ZAID	Name	ZAID	Name	ZAID	Name	ZAID	Name
1000	H	17000	Cl	40000	Zr	74184	W184	94237	Pu237
101001	H1(H2O)	19000	K	41000	Nb	74186	W186	94238	Pu238
1001	H1	20000	Ca	41093	Nb93	75000	Re	94239	Pu239
1002	H2	22000	Ti	42000	Mo	75185	Re185	94240	Pu240
4000	Be	23000	V	47000	Ag	75187	Re187	94241	Pu241
104009	Be9(th)	24000	Cr	47107	Ag107	79000	Au	94242	Pu242
4009	Be9	24050	Cr50	47109	Ag109	79197	Au197	94243	Pu243
5000	B	24052	Cr52	48000	Cd	82000	Pb	94244	Pu244
5010	B10	24053	Cr53	49000	In	82206	Pb206	95241	Am241
5011	B11	24054	Cr54	50000	Sn	82207	Pb207	95242	Am242
6000	C	25000	Mn	56000	Ba	82208	Pb208	195242	Am242m
6012	C12	25055	Mn55	56138	Ba138	83000	Bi	95243	Am243
106012	C12(gph)	26000	Fe	63000	Eu	83209	Bi209	96241	Cm241
7000	N	26054	Fe54	63151	Eu151	90000	Th	96242	Cm242
7014	N14	26056	Fe56	63152	Eu152	90230	Th230	96243	Cm243
7015	N15	26057	Fe57	63153	Eu153	90232	Th232	96244	Cm244
8000	O	26058	Fe58	63154	Eu154	91000	Pa	96245	Cm245
8016	O16	27000	Co	63155	Eu155	91231	Pa231	96246	Cm246
8017	O17	27059	Co59	72000	Hf	91233	Pa233	96247	Cm247
9000	F	28000	Ni	72174	Hf174	92000	U	96248	Cm248
9019	F19	28058	Ni58	72176	Hf176	92232	U232	1003	H3
11000	Na	28060	Ni60	72177	Hf177	92233	U233	2000	He
11023	Na23	28061	Ni61	72178	Hf178	92234	U234	2003	He3
12000	Mg	28062	Ni62	72179	Hf179	92235	U235	2004	He4
13000	Al	28064	Ni64	72180	Hf180	92236	U236	3000	Li
13027	Al27	29000	Cu	73000	Ta	92237	U237	3006	Li6
14000	Si	29063	Cu63	73181	Ta181	92238	U238	3007	Li7
15000	P	29065	Cu65	73182	Ta182	93237	Np237
15031	P31	31000	Ga	74000	W	93238	Np238
16000	S	39000	Y	74182	W182	93239	Np239
16032	S32	39089	Y89	74183	W183	94236	Pu236

R. E. ALCOUFFE et al., “PARTISN: A Time-Dependent, Parallel Neutral Particle Transport Code System,” LA-UR-08-7258 ( revised Sep. 2017), Los Alamos National Laboratory (2017).

 Google Scholar