Output parameters

This page lists the output parameters in the main [input]_res.m output file.

Homogenized group constants

Notes:

• Group constants are calculated by first homogenizing the geometry using a multi-group structure with H energy groups. The data is then collapsed into the final few-group structure with G groups using the infinite and B₁ leakage-corrected flux spectra.
• The methodology used in Serpent for spatial homogenization is described in a paper published in Annals of Nuclear Energy in 2016.
• The B₁ calculation is off by default, and invoked by the set fum option.
• The intermediate multi-group structure is defined using option set micro.
• The few-group structure is defined using option set nfg.
• The universes in which the group constants are calculated are listed in option set gcu. The calculation is performed for root universe 0 by default, and can be switched off with "set gcu -1".
• If data is produced in multiple universes within a single run, the data is assigned with different run indexes (idx)
• The parameter names can be listed in the set coefpara option, and they will be included in the group constant output file when the automated burnup sequence is invoked.
• The order in which two-dimensional data (scattering matrices, ADF and pin-power parameters) is printed in the [input].coe output file is different from what is listed below in update 2.1.24 and earlier versions.

Common parameters

Parameter	Size	Description
GC_UNIVERSE_NAME	(string)	Name of the universe where spatial homogenization was performed
MICRO_NG	1	Number of energy groups in the intermediate multi-group structure (referred to as H below)
MICRO_E	H + 1	Group boundaries in the intermediate multi-group structure (in ascending order)
MACRO_NG	1	Number of energy groups in the final few-group structure (referred to as G below)
MACRO_E	G + 1	Group boundaries in the final few-group structure (in descending order)

Group constants homogenized in infinite spectrum

Parameter	Size	Description
INF_MICRO_FLX	2H	Multi-group flux spectrum (integral, un-normalized)
INF_FLX	2G	Few-group flux (integral, normalized)
INF_KINF	2	Infinite multiplication factor

Reaction cross sections

Parameter	Size	Description
INF_TOT	2G	Total cross section
INF_CAPT	2G	Capture cross section
INF_FISS	2G	Fission cross section
INF_NSF	2G	Fission neutron production cross section
INF_KAPPA	2G	Average deposited fission energy (MeV)
INF_INVV	2G	Inverse neutron speed (s/cm)
INF_NUBAR	2G	Average neutron yield
INF_ABS	2G	Absorption cross section (capture + fission)
INF_REMXS	2G	Removal cross section (group-removal + absorption)
INF_RABSXS	2G	Reduced absorption cross section (total - scattering production)

Fission spectra

Parameter	Size	Description
INF_CHIT	2G	Fission spectrum (total)
INF_CHIP	2G	Fission spectrum (prompt neutrons)
INF_CHID	2G	Fission spectrum (delayed neutrons)

Scattering cross sections

Notes:

• Scattering production includes multiplying (n,2n), (n,3n), etc. reactions.

Parameter	Size	Description
INF_SCATT0	2G	Total P0 scattering cross section
INF_SCATT1	2G	Total P1 scattering cross section
INF_SCATT2	2G	Total P2 scattering cross section
INF_SCATT3	2G	Total P3 scattering cross section
INF_SCATT4	2G	Total P4 scattering cross section
INF_SCATT5	2G	Total P5 scattering cross section
INF_SCATT6	2G	Total P6 scattering cross section
INF_SCATT7	2G	Total P7 scattering cross section
INF_SCATTP0	2G	Total P0 scattering production cross section
INF_SCATTP1	2G	Total P1 scattering production cross section
INF_SCATTP2	2G	Total P2 scattering production cross section
INF_SCATTP3	2G	Total P3 scattering production cross section
INF_SCATTP4	2G	Total P4 scattering production cross section
INF_SCATTP5	2G	Total P5 scattering production cross section
INF_SCATTP6	2G	Total P6 scattering production cross section
INF_SCATTP7	2G	Total P7 scattering production cross section

Scattering matrices

Notes:

• Scattering production includes multiplying (n,2n), (n,3n), etc. reactions.
• The order of values ([input].coe) or value pairs ([input]_res.m) is: $\Sigma_{1,1} \, \Sigma_{1,2} \, ... \, \Sigma_{2,1} \, \Sigma_{2,2} \, ...$ where $\Sigma_{g,g'}$ refers to scattering from group g to g'.
• The data in the [input]_res.m file can be read into a G by G matrix with Matlab reshape-command, for example:

reshape(INF_S0(idx,1:2:end), G, G);

Parameter	Size	Description
INF_S0	4G2	P0 scattering matrix
INF_S1	4G2	P1 scattering matrix
INF_S2	4G2	P2 scattering matrix
INF_S3	4G2	P3 scattering matrix
INF_S4	4G2	P4 scattering matrix
INF_S5	4G2	P5 scattering matrix
INF_S6	4G2	P6 scattering matrix
INF_S7	4G2	P7 scattering matrix
INF_SP0	4G2	P0 scattering production matrix
INF_SP1	4G2	P1 scattering production matrix
INF_SP2	4G2	P2 scattering production matrix
INF_SP3	4G2	P3 scattering production matrix
INF_SP4	4G2	P4 scattering production matrix
INF_SP5	4G2	P5 scattering production matrix
INF_SP6	4G2	P6 scattering production matrix
INF_SP7	4G2	P7 scattering production matrix

Diffusion parameters

Notes:

• Calculation of sensible values for INF_TRANSPXS and INF_DIFFCOEF requires fine enough intermediate multi-group structure.
• The cumulative migration method was first developed for the OpenMC code. Currently the method works only when the homogenized region covers the entire geometry, and is surrounded by periodic or reflective boundary conditions.
• Calculation of TRC_TRANSPXS and TRC_DIFFCOEF requires defining energy-dependent correction factors using the set trc option.
• Calculation of CMM_TRANSPXS and CMM_DIFFCOEF requires that their calculation is not switched off using the set cmm option.

Parameter	Size	Description
INF_TRANSPXS	2G	Transport cross section (calculated using the out-scattering approximation)
INF_DIFFCOEF	2G	Diffusion coefficient (calculated using the out-scattering approximation)
CMM_TRANSPXS	2G	Transport cross section calculated using the cumulative migration method (equivalent with the in-scattering approximation)
CMM_TRANSPXS_X	2G	X-component of the directional transport cross section calculated using the cumulative migration method (equivalent with the in-scattering approximation)
CMM_TRANSPXS_Y	2G	Y-component of the directional transport cross section calculated using the cumulative migration method (equivalent with the in-scattering approximation)
CMM_TRANSPXS_Z	2G	Z-component of the directional transport cross section calculated using the cumulative migration method (equivalent with the in-scattering approximation)
CMM_DIFFCOEF	2G	Diffusion coefficient calculated using the cumulative migration method (equivalent with the in-scattering approximation)
CMM_DIFFCOEF_X	2G	X-component of the directional diffusion coefficient calculated using the cumulative migration method (equivalent with the in-scattering approximation)
CMM_DIFFCOEF_Y	2G	Y-component of the directional diffusion coefficient calculated using the cumulative migration method (equivalent with the in-scattering approximation)
CMM_DIFFCOEF_Z	2G	Z-component of the directional diffusion coefficient calculated using the cumulative migration method (equivalent with the in-scattering approximation)
TRC_TRANSPXS	2G	Transport cross section calculated by applying user-defined transport correction factors to total cross section
TRC_DIFFCOEF	2G	Diffusion coefficient calculated by applying user-defined transport correction factors to total cross section

Poison cross sections

Notes:

• Printed only if poison cross section option is on (see set poi).

Parameter	Size	Description
INF_I135_YIELD	2G	Fission yield of I-135 (cumulative, includes all precursors)
INF_XE135_YIELD	2G	Fission yield of Xe-135
INF_PM149_YIELD	2G	Fission yield of Pm-149 (cumulative, includes all precursors)
INF_SM149_YIELD	2G	Fission yield of Sm-149
INF_I135_MICRO_ABS	2G	Microscopic absorption cross section of I-135
INF_XE135_MICRO_ABS	2G	Microscopic absorption cross section of Xe-135
INF_PM149_MICRO_ABS	2G	Microscopic absorption cross section of Pm-149
INF_SM149_MICRO_ABS	2G	Microscopic absorption cross section of Sm-149
INF_XE135_MACRO_ABS	2G	Macroscopic absorption cross section of Xe-135
INF_SM149_MACRO_ABS	2G	Macroscopic absorption cross section of Sm-149

Group constants homogenized in B₁ leakage-corrected spectrum

Parameter	Size	Description
B1_MICRO_FLX	2H	Multi-group flux spectrum (integral, un-normalized)
B1_FLX	2G	Few-group flux (integral, normalized)
B1_KINF	2	Infinite multiplication factor
B1_KEFF	2	Effective multiplication factor
B1_B2	2	Critical buckling
B1_ERR	2	Absolute deviation of keff from unity

Reaction cross sections

Parameter	Size	Description
B1_TOT	2G	Total cross section
B1_CAPT	2G	Capture cross section
B1_FISS	2G	Fission cross section
B1_NSF	2G	Fission neutron production cross section
B1_KAPPA	2G	Average deposited fission energy (MeV)
B1_INVV	2G	Inverse neutron speed (s/cm)
B1_NUBAR	2G	Average neutron yield
B1_ABS	2G	Absorption cross section (capture + fission)
B1_REMXS	2G	Removal cross section (group-removal + absorption)
B1_RABSXS	2G	Reduced absorption cross section (total - scattering production)

Fission spectra

Parameter	Size	Description
B1_CHIT	2G	Fission spectrum (total)
B1_CHIP	2G	Fission spectrum (prompt neutrons)
B1_CHID	2G	Fission spectrum (delayed neutrons)

Scattering cross sections

Notes:

• Scattering production includes multiplying (n,2n), (n,3n), etc. reactions.

Parameter	Size	Description
B1_SCATT0	2G	Total P0 scattering cross section
B1_SCATT1	2G	Total P1 scattering cross section
B1_SCATT2	2G	Total P2 scattering cross section
B1_SCATT3	2G	Total P3 scattering cross section
B1_SCATT4	2G	Total P4 scattering cross section
B1_SCATT5	2G	Total P5 scattering cross section
B1_SCATT6	2G	Total P6 scattering cross section
B1_SCATT7	2G	Total P7 scattering cross section
B1_SCATTP0	2G	Total P0 scattering production cross section
B1_SCATTP1	2G	Total P1 scattering production cross section
B1_SCATTP2	2G	Total P2 scattering production cross section
B1_SCATTP3	2G	Total P3 scattering production cross section
B1_SCATTP4	2G	Total P4 scattering production cross section
B1_SCATTP5	2G	Total P5 scattering production cross section
B1_SCATTP6	2G	Total P6 scattering production cross section
B1_SCATTP7	2G	Total P7 scattering production cross section

Scattering matrices

Notes:

• Scattering production includes multiplying (n,2n), (n,3n), etc. reactions.
• The order of values ([input].coe) or value pairs ([input]_res.m) is: $\Sigma_{1,1} \, \Sigma_{1,2} \, ... \, \Sigma_{2,1} \, \Sigma_{2,2} \, ...$ where $\Sigma_{g,g'}$ refers to scattering from group g to g'.
• The data in the _res.m file can be read into a G by G matrix with Matlab reshape-command, for example:

reshape(B1_S0(idx,1:2:end), G, G).

Parameter	Size	Description
B1_S0	4G2	P0 scattering matrix
B1_S1	4G2	P1 scattering matrix
B1_S2	4G2	P2 scattering matrix
B1_S3	4G2	P3 scattering matrix
B1_S4	4G2	P4 scattering matrix
B1_S5	4G2	P5 scattering matrix
B1_S6	4G2	P6 scattering matrix
B1_S7	4G2	P7 scattering matrix
B1_SP0	4G2	P0 scattering production matrix
B1_SP1	4G2	P1 scattering production matrix
B1_SP2	4G2	P2 scattering production matrix
B1_SP3	4G2	P3 scattering production matrix
B1_SP4	4G2	P4 scattering production matrix
B1_SP5	4G2	P5 scattering production matrix
B1_SP6	4G2	P6 scattering production matrix
B1_SP7	4G2	P7 scattering production matrix

Diffusion parameters

Parameter	Size	Description
B1_TRANSPXS	2G	Transport cross section (calculated from diffusion coefficient)
B1_DIFFCOEF	2G	Diffusion coefficient

Poison cross sections

Notes:

• Printed only if poison cross section option is on (see set poi).

Parameter	Size	Description
B1_I135_YIELD	2G	Fission yield of I-135 (cumulative, includes all precursors)
B1_XE135_YIELD	2G	Fission yield of Xe-135
B1_PM149_YIELD	2G	Fission yield of Pm-149 (cumulative, includes all precursors)
B1_SM149_YIELD	2G	Fission yield of Sm-149
B1_I135_MICRO_ABS	2G	Microscopic absorption cross section of I-135
B1_XE135_MICRO_ABS	2G	Microscopic absorption cross section of Xe-135
B1_PM149_MICRO_ABS	2G	Microscopic absorption cross section of Pm-149
B1_SM149_MICRO_ABS	2G	Microscopic absorption cross section of Sm-149
B1_XE135_MACRO_ABS	2G	Macroscopic absorption cross section of Xe-135
B1_SM149_MACRO_ABS	2G	Macroscopic absorption cross section of Sm-149

Delayed neutron data

Notes:

• The output always consists of 9 values: total, followed by precursor group-wise values. If the number of groups is 6, the last two values are zero.
• The actual number of groups depends on the cross section library used in the calculations. JEFF-3.1, JEFF.3.2 and later evaluations use 8 precursor groups, while earlier evaluations, as well as all ENDF/B and JENDL data is based on 6 groups.

Parameter	Size	Description
BETA_EFF	9	Effective delayed neutron fraction (currently calculated using the Meulekamp method)
LAMBDA	9	Decay constants

Assembly discontinuity factors

Notes:

• Calculation of assembly discontinuity factors requires the set adf option.
• Surface flux and current tallies are used to calculate the boundary currents and fluxes. Mid-point and corner values are approximated by integrating over a small surface segment.
• Fluxes and currents are normalized average values.
• When the homogenized region is surrounded by reflective boundary conditions (zero net-current) the homogeneous flux becomes flat and equal to the volume-averaged heterogeneous flux. When the net currents are non-zero, the homogeneous flux is obtained using the Built-in diffusion flux solver.
• The calculation currently supports only a limited number of surface types: infinite planes and square and hexagonal prisms.
• The order of surface and mid-point values for square prisms is: $X_{\mathrm{W},1} \, X_{\mathrm{W},2} \, ... \, X_{\mathrm{S},1} \, X_{\mathrm{S},2} \, ... \, X_{\mathrm{E},1} \, X_{\mathrm{E},2} \, ... \, X_{\mathrm{N},1} \, X_{\mathrm{N},2} \, ...$ and the order of corner values: $X_{\mathrm{NW},1} \, X_{\mathrm{NW},2} \, ... \, X_{\mathrm{NE},1} \, X_{\mathrm{NE},2} \, ... \, X_{\mathrm{SE},1} \, X_{\mathrm{SE},2} \, ... \, X_{\mathrm{SW},1} \, X_{\mathrm{SW},2} \, ...$ where $X_{k,g}$ refers to parameter $X$ on surface/corner k and energy group g.
• The order of surface and mid-point values for Y-type hexagonal prims runs clockwise starting from the north. The corner values start from the next corner in clockwise direction.
• The order of surface and mid-point values for X-type hexagonal prims runs counterclockwise starting from the east. The corner values start from the next corner in clockwise direction.
• Note that one should confirm the order of values in the hexagonal prisms.

Parameter	Size	Description
DF_SURFACE	(string)	Name of the surface used for the calculation
DF_SYM	1	Symmetry option defined in the input
DF_N_SURF	1	Number of surface values (denoted as NS below)
DF_N_CORN	1	Number of corner values (denoted as NC below)
DF_VOLUME	1	Volume (3D) or cross sectional area (2D) of the homogenized cell
DF_SURF_AREA	NS	Area (3D) or perimeter length (2D) of the surface region
DF_MID_AREA	NS	Area (3D) or perimeter length (2D) of the mid-point region
DF_CORN_AREA	NS	Area (3D) or perimeter length (2D) of the corner region
DF_SURF_IN_CURR	2G $\times$ NS	Inward surface currents
DF_SURF_OUT_CURR	2G $\times$ NS	Outward surface currents
DF_SURF_NET_CURR	2G $\times$ NS	Net surface currents
DF_MID_IN_CURR	2G $\times$ NS	Inward mid-point currents
DF_MID_OUT_CURR	2G $\times$ NS	Outward mid-point currents
DF_MID_NET_CURR	2G $\times$ NS	Net mid-point currents
DF_CORN_IN_CURR	2G $\times$ NC	Inward corner currents
DF_CORN_OUT_CURR	2G $\times$ NC	Outward corner currents
DF_CORN_NET_CURR	2G $\times$ NC	Net corner currents
DF_HET_VOL_FLUX	2G	Heterogeneous flux over homogenized cell
DF_HET_SURF_FLUX	2G $\times$ NS	Heterogeneous surface flux
DF_HET_CORN_FLUX	2G $\times$ NC	Heterogeneous corner flux
DF_HOM_VOL_FLUX	2G	Homogeneous flux over homogenized cell
DF_HOM_SURF_FLUX	2G $\times$ NC	Homogeneous surface flux
DF_HOM_CORN_FLUX	2G $\times$ NC	Homogeneous corner flux
DF_SURF_DF	2G $\times$ NC	Surface discontinuity factors
DF_CORN_DF	2G $\times$ NC	Corner discontinuity factors

Pin-power form factors

Notes:

• Calculation of pin-power form factors requires the set ppw option.
• The power distribution is calculated by tallying the few-group fission energy deposition in each lattice position and dividing the values with the total energy produced in the universe (sum over all values of PPW_POW equals 1).
• The calculation of form factors depends on the boundary conditions:
  1. If the homogenized region is surrounded by reflective boundary conditions (zero net-current), the homogeneous flux becomes flat and equal to the volume-averaged heterogeneous flux. Variables PPW_HOM_FLUX and PPW_FF are then omitted.
  2. When the net currents are non-zero, the homogeneous flux is obtained using the built-in diffusion flux solver. The form-factors (PPW_FF) are obtained by dividing the pin- and group-wise powers with the corresponding homogeneous diffusion flux (PPW_HOM_FLUX).
• Running the diffusion flux solver currently requires ADF calculation.
• The order of values is: $X_{1,1} \, X_{1,2} \, ... \, X_{2,1} \, X_{2,2} \, ...$ where $X_{n,g}$ refers to parameter $X$ of pin n and energy group g. For example, two-group power distributions in a 17$\times$17 lattice can be converted into matrix form using the reshape-command in Matlab:

P1 = reshape(PPW_POW(1,1:4:end), 17, 17);
P2 = reshape(PPW_POW(1,3:4:end), 17, 17);

Parameter	Size	Description
PPW_LATTICE	(string)	Name of the lattice used for the calculation
PPW_LATTICE_TYPE	1	Lattice type (corresponds to the lat-card)
PPW_PINS	1	Number of pin positions in the lattice (denoted as NP below)
PPW_POW	2G $\times$ NP	Pin-wise power distribution
PPW_HOM_FLUX	2G $\times$ NP	Pin-wise homogeneous flux distribution
PPW_FF	2G $\times$ NP	Pin-wise form factors

Albedos

Notes:

• Calculation of albedos requires the set alb option.
• The order of the surfaces should be the same as for the ADFs.
• The order of ALB_IN_CURR is $J_{1,1} , J_{1,2} , \ldots , J_{2,1} , J_{2,2} , \ldots$ where $J_{k,g}$ refers to incoming partial current of surface k of group g'.
• The order of ALB_OUT_CURR is $J_{1,1,1,1} , J_{1,1,1,2} , \ldots , J_{1,1,2,1} , J_{1,1,2,2} , \ldots , J_{1,2,1,1} , J_{1,2,1,2} , \ldots , J_{2,1,1,1} , J_{2,1,1,2} , \ldots$ where $J_{k,g,k',g'}$ refers to outgoing partial current of surface k of group g which has entered the albedo surface through surface k and group g.
• The order of ALB_TOT_ALB is $\alpha_{1,1} , \alpha_{1,2} , \ldots , \alpha_{2,1} , \alpha_{2,2} , \ldots$ where $\alpha_{g,g'}$ refers to albedo from group g to g'.
• The order of ALB_PART_ALB is $\alpha_{1,1,1,1} , \alpha_{1,1,1,2} , \ldots , \alpha_{1,1,2,1} , \alpha_{1,1,2,2} , \ldots , \alpha_{1,2,1,1} , \alpha_{1,2,1,2} , \ldots , \alpha_{2,1,1,1} , \alpha_{2,1,1,2} , \ldots$ where $\alpha_{k,g,k',g'}$ refers to albedo of surface k of group g which has entered the albedo surface through surface k and group g.
• For example, two-group hexagonal partial albedos can be converted into matrix form using the reshape-command in Matlab with the notation part_alb(g', k', g, k) $= \alpha_{k,g,k',g'}$ as

part_alb = reshape(ALB_PART_ALB(1, 1:2:end), 2, 6, 2, 6)

Parameter	Size	Description
ALB_SURFACE	(string)	Name of the surface used for the calculation
ALB_FLIP_DIR	1
ALB_N_SURF	1	Number of albedo surface faces (denoted as NS below)
ALB_IN_CURR	2G $\times$ NS	Groupwise incoming partial currents of albedo surface faces
ALB_OUT_CURR	2G2 $\times$ NS2	Outgoing group to group and face to face outgoing partial currents
ALB_TOT_ALB	2G2	Total group to group albedos for the entire albedo surface
ALB_PART_ALB	2G2 $\times$ NS2	Partial group to group and face to face albedos

Miscellaneous notes for other outputs

Delayed neutrons accounted for in ANA_KEFF

Since Serpent 2.1.23, ANA_KEFF estimator is calculated separately for delayed neutrons. The first two values are total, 3-4 are prompt neutron multiplication only and 5-6 delayed neutron multiplication only.