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 multigroup structure with H energy groups. The data is then collapsed into the final fewgroup structure with G groups using the infinite and leakagecorrected flux spectra.
 The methodology used in Serpent for spatial homogenization is described in a paper published in Annals of Nuclear Energy in 2016.^{[1]}
 The fundamental mode calculation is off by default, and invoked by the set fum option. Otherwise all values with B1 prefix are printed as zeros.
 The intermediate multigroup structure is defined using option set micro or set fum.
 The fewgroup 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 twodimensional data (scattering matrices, ADF and pinpower 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 multigroup structure (referred to as H below)

MICRO_E

H + 1

Group boundaries in the intermediate multigroup structure (in ascending order)

MACRO_NG

1

Number of energy groups in the final fewgroup structure (referred to as G below)

MACRO_E

G + 1

Group boundaries in the final fewgroup structure (in descending order)

Group constants homogenized in infinite spectrum
Parameter

Size

Description

INF_MICRO_FLX

2H

Multigroup flux spectrum (integral, unnormalized)

INF_FLX

2G

Fewgroup 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 (groupremoval + 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 P_{0} scattering cross section

INF_SCATT1

2G

Total P_{1} scattering cross section

INF_SCATT2

2G

Total P_{2} scattering cross section

INF_SCATT3

2G

Total P_{3} scattering cross section

INF_SCATT4

2G

Total P_{4} scattering cross section

INF_SCATT5

2G

Total P_{5} scattering cross section

INF_SCATT6

2G

Total P_{6} scattering cross section

INF_SCATT7

2G

Total P_{7} scattering cross section

INF_SCATTP0

2G

Total P_{0} scattering production cross section

INF_SCATTP1

2G

Total P_{1} scattering production cross section

INF_SCATTP2

2G

Total P_{2} scattering production cross section

INF_SCATTP3

2G

Total P_{3} scattering production cross section

INF_SCATTP4

2G

Total P_{4} scattering production cross section

INF_SCATTP5

2G

Total P_{5} scattering production cross section

INF_SCATTP6

2G

Total P_{6} scattering production cross section

INF_SCATTP7

2G

Total P_{7} 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: where 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 reshapecommand, for example:
reshape(INF_S0(idx,1:2:end), G, G);
Parameter

Size

Description

INF_S0

4G^{2}

P_{0} scattering matrix

INF_S1

4G^{2}

P_{1} scattering matrix

INF_S2

4G^{2}

P_{2} scattering matrix

INF_S3

4G^{2}

P_{3} scattering matrix

INF_S4

4G^{2}

P_{4} scattering matrix

INF_S5

4G^{2}

P_{5} scattering matrix

INF_S6

4G^{2}

P_{6} scattering matrix

INF_S7

4G^{2}

P_{7} scattering matrix

INF_SP0

4G^{2}

P_{0} scattering production matrix

INF_SP1

4G^{2}

P_{1} scattering production matrix

INF_SP2

4G^{2}

P_{2} scattering production matrix

INF_SP3

4G^{2}

P_{3} scattering production matrix

INF_SP4

4G^{2}

P_{4} scattering production matrix

INF_SP5

4G^{2}

P_{5} scattering production matrix

INF_SP6

4G^{2}

P_{6} scattering production matrix

INF_SP7

4G^{2}

P_{7} scattering production matrix

Diffusion parameters
Notes:
 Calculation of sensible values for INF_TRANSPXS and INF_DIFFCOEF requires fine enough intermediate multigroup structure.
 The cumulative migration method ^{[2]} 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 energydependent 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 outscattering approximation)

INF_DIFFCOEF

2G

Diffusion coefficient (calculated using the outscattering approximation)

CMM_TRANSPXS

2G

Transport cross section calculated using the cumulative migration method (equivalent with the inscattering approximation)

CMM_TRANSPXS_X

2G

Xcomponent of the directional transport cross section calculated using the cumulative migration method (equivalent with the inscattering approximation)

CMM_TRANSPXS_Y

2G

Ycomponent of the directional transport cross section calculated using the cumulative migration method (equivalent with the inscattering approximation)

CMM_TRANSPXS_Z

2G

Zcomponent of the directional transport cross section calculated using the cumulative migration method (equivalent with the inscattering approximation)

CMM_DIFFCOEF

2G

Diffusion coefficient calculated using the cumulative migration method (equivalent with the inscattering approximation)

CMM_DIFFCOEF_X

2G

Xcomponent of the directional diffusion coefficient calculated using the cumulative migration method (equivalent with the inscattering approximation)

CMM_DIFFCOEF_Y

2G

Ycomponent of the directional diffusion coefficient calculated using the cumulative migration method (equivalent with the inscattering approximation)

CMM_DIFFCOEF_Z

2G

Zcomponent of the directional diffusion coefficient calculated using the cumulative migration method (equivalent with the inscattering approximation)

TRC_TRANSPXS

2G

Transport cross section calculated by applying userdefined transport correction factors to total cross section

TRC_DIFFCOEF

2G

Diffusion coefficient calculated by applying userdefined 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 I135 (cumulative, includes all precursors)

INF_XE135_YIELD

2G

Fission yield of Xe135

INF_PM149_YIELD

2G

Fission yield of Pm149 (cumulative, includes all precursors)

INF_SM149_YIELD

2G

Fission yield of Sm149

INF_I135_MICRO_ABS

2G

Microscopic absorption cross section of I135

INF_XE135_MICRO_ABS

2G

Microscopic absorption cross section of Xe135

INF_PM149_MICRO_ABS

2G

Microscopic absorption cross section of Pm149

INF_SM149_MICRO_ABS

2G

Microscopic absorption cross section of Sm149

INF_XE135_MACRO_ABS

2G

Macroscopic absorption cross section of Xe135

INF_SM149_MACRO_ABS

2G

Macroscopic absorption cross section of Sm149

Group constants homogenized in leakagecorrected spectrum
Parameter

Size

Description

B1_MICRO_FLX

2H

Multigroup flux spectrum (integral, unnormalized)

B1_FLX

2G

Fewgroup 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 k_{eff} 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 (groupremoval + 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 P_{0} scattering cross section

B1_SCATT1

2G

Total P_{1} scattering cross section

B1_SCATT2

2G

Total P_{2} scattering cross section

B1_SCATT3

2G

Total P_{3} scattering cross section

B1_SCATT4

2G

Total P_{4} scattering cross section

B1_SCATT5

2G

Total P_{5} scattering cross section

B1_SCATT6

2G

Total P_{6} scattering cross section

B1_SCATT7

2G

Total P_{7} scattering cross section

B1_SCATTP0

2G

Total P_{0} scattering production cross section

B1_SCATTP1

2G

Total P_{1} scattering production cross section

B1_SCATTP2

2G

Total P_{2} scattering production cross section

B1_SCATTP3

2G

Total P_{3} scattering production cross section

B1_SCATTP4

2G

Total P_{4} scattering production cross section

B1_SCATTP5

2G

Total P_{5} scattering production cross section

B1_SCATTP6

2G

Total P_{6} scattering production cross section

B1_SCATTP7

2G

Total P_{7} 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: where 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 reshapecommand, for example:
reshape(B1_S0(idx,1:2:end), G, G).
Parameter

Size

Description

B1_S0

4G^{2}

P_{0} scattering matrix

B1_S1

4G^{2}

P_{1} scattering matrix

B1_S2

4G^{2}

P_{2} scattering matrix

B1_S3

4G^{2}

P_{3} scattering matrix

B1_S4

4G^{2}

P_{4} scattering matrix

B1_S5

4G^{2}

P_{5} scattering matrix

B1_S6

4G^{2}

P_{6} scattering matrix

B1_S7

4G^{2}

P_{7} scattering matrix

B1_SP0

4G^{2}

P_{0} scattering production matrix

B1_SP1

4G^{2}

P_{1} scattering production matrix

B1_SP2

4G^{2}

P_{2} scattering production matrix

B1_SP3

4G^{2}

P_{3} scattering production matrix

B1_SP4

4G^{2}

P_{4} scattering production matrix

B1_SP5

4G^{2}

P_{5} scattering production matrix

B1_SP6

4G^{2}

P_{6} scattering production matrix

B1_SP7

4G^{2}

P_{7} scattering production matrix

Diffusion parameters
Parameter

Size

Description

B1_TRANSPXS

2G

Transport cross section (outscattering transport cross section collapsed with the critical spectrum when old B_{1} calculation mode is used, otherwise calculated from B1_DIFFCOEF)

B1_DIFFCOEF

2G

Diffusion coefficient calculated from during the fundamental mode calculation (old and new B_{1} and P_{1} calculation modes, or flux collapsed during the FM calculation mode)

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 I135 (cumulative, includes all precursors)

B1_XE135_YIELD

2G

Fission yield of Xe135

B1_PM149_YIELD

2G

Fission yield of Pm149 (cumulative, includes all precursors)

B1_SM149_YIELD

2G

Fission yield of Sm149

B1_I135_MICRO_ABS

2G

Microscopic absorption cross section of I135

B1_XE135_MICRO_ABS

2G

Microscopic absorption cross section of Xe135

B1_PM149_MICRO_ABS

2G

Microscopic absorption cross section of Pm149

B1_SM149_MICRO_ABS

2G

Microscopic absorption cross section of Sm149

B1_XE135_MACRO_ABS

2G

Macroscopic absorption cross section of Xe135

B1_SM149_MACRO_ABS

2G

Macroscopic absorption cross section of Sm149

Delayed neutron data
Notes:
 The output always consists of 9 values: total, followed by precursor groupwise 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. JEFF3.1, 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. Midpoint and corner values are approximated by integrating over a small surface segment.
 The surface and volume fluxes are flux densities, i.e. they are surface or volume integrated fluxes divided by the respective surface area or volume.
 The currents are surface integrated values.
 The net current is defined as current in subtracted with current out.
 When the homogenized region is surrounded by reflective boundary conditions (zero netcurrent) the homogeneous flux becomes flat and equal to the volumeaveraged heterogeneous flux. When the net currents are nonzero, the homogeneous flux is obtained using the Builtin 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 midpoint values for square prisms is: and the order of corner values: where refers to parameter on surface/corner k and energy group g.
 The order of surface values for Ytype hexagonal prims runs clockwise starting from the north, i.e. N, NE, SE, S, SW, NW. The corner values run counterclockwise starting from east, i.e. E, NE, NW, W, SW, SE.
 The order of surface values for Xtype hexagonal prims runs counterclockwise starting from the east, i.e. E, NE, NW, W, SW, SE. The corner values run clockwise starting from north, i.e. N, NE, SE, S, SW, NW.
 The sign moment weighted parameters are calculated only for surface types sqc, rect and hexxc.
 The convention of sign moment directions follows that of the nodal neutronics program Ants.
 The ADF symmetry options on set adf card are currently not used for sign moment weighted parameters.
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 N_{S} below)

DF_N_CORN

1

Number of corner values (denoted as N_{C} below)

DF_VOLUME

1

Volume (3D) or cross sectional area (2D) of the homogenized cell

DF_SURF_AREA

N_{S}

Area (3D) or perimeter length (2D) of the surface region

DF_MID_AREA

N_{S}

Area (3D) or perimeter length (2D) of the midpoint region

DF_CORN_AREA

N_{C}

Area (3D) or perimeter length (2D) of the corner region

DF_SURF_IN_CURR

2G N_{S}

Inward surface currents

DF_SURF_OUT_CURR

2G N_{S}

Outward surface currents

DF_SURF_NET_CURR

2G N_{S}

Net surface currents

DF_MID_IN_CURR

2G N_{S}

Inward midpoint currents

DF_MID_OUT_CURR

2G N_{S}

Outward midpoint currents

DF_MID_NET_CURR

2G N_{S}

Net midpoint currents

DF_CORN_IN_CURR

2G N_{C}

Inward corner currents

DF_CORN_OUT_CURR

2G N_{C}

Outward corner currents

DF_CORN_NET_CURR

2G N_{C}

Net corner currents

DF_HET_VOL_FLUX

2G

Heterogeneous flux over homogenized cell

DF_HET_SURF_FLUX

2G N_{S}

Heterogeneous surface fluxes

DF_HET_CORN_FLUX

2G N_{C}

Heterogeneous corner fluxes

DF_HOM_VOL_FLUX

2G

Homogeneous flux over homogenized cell

DF_HOM_SURF_FLUX

2G N_{S}

Homogeneous surface fluxes

DF_HOM_CORN_FLUX

2G N_{C}

Homogeneous corner fluxes

DF_SURF_DF

2G N_{S}

Surface discontinuity factors

DF_CORN_DF

2G N_{C}

Corner discontinuity factors

DF_SGN_SURF_IN_CURR

2G N_{S}

Inward sign moment weighted currents

DF_SGN_SURF_OUT_CURR

2G N_{S}

Outward sign moment weighted currents

DF_SGN_SURF_NET_CURR

2G N_{S}

Net sign moment weighted currents

DF_SGN_HET_SURF_FLUX

2G N_{S}

Heterogeneous sign moment weighted surface fluxes

DF_SGN_HOM_SURF_FLUX

2G N_{S}

Homogeneous sign moment weighted surface fluxes

DF_SGN_SURF_DF

2G N_{S}

Sign moment weighted surface discontinuity factors

Pinpower form factors
Notes:
 Calculation of pinpower form factors requires the set ppw option.
 The power distribution is calculated by tallying the fewgroup 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:
 If the homogenized region is surrounded by reflective boundary conditions (zero netcurrent), the homogeneous flux becomes flat and equal to the volumeaveraged heterogeneous flux.
 When the net currents are nonzero, the homogeneous flux is obtained using the builtin diffusion flux solver. The formfactors (PPW_FF) are obtained by dividing the pin and groupwise powers with the corresponding homogeneous diffusion flux (PPW_HOM_FLUX).
 However, if the net currents are nonzero, but the sum of the net currents is equal to zero, the volumeaveraged heterogeneous flux is used as the homogeneous flux, which is not an accurate approximation. This case is for example when modeling hexagonal fuel assemblies with other than 30 or 60 degree symmetries with periodic boundary conditions.
 Running the diffusion flux solver currently requires ADF calculation.
 The order of values is: where refers to parameter of pin n and energy group g. For example, twogroup power distributions in a 17 x 17 lattice can be converted into matrix form using the reshapecommand in Matlab:
P1 = reshape(PPW_POW(1, 1:4:end), 17, 17);
P2 = reshape(PPW_POW(1, 3:4:end), 17, 17);
 Symmetry used in the lattice may result in some pin powers and form factors to be for example 1/2, 1/4 or 1/8 of their true value, which have to be corrected during post processing of the values.
Parameter

Size

Description

PPW_LATTICE

(string)

Name of the lattice used for the calculation

PPW_LATTICE_TYPE

1

Lattice type (corresponds to the latcard)

PPW_PINS

1

Number of pin positions in the lattice (denoted as N_{P} below)

PPW_POW

2G N_{P}

Pin and groupwise power distribution normalized to unity sum

PPW_HOM_FLUX

2G N_{P}

Pin and groupwise homogeneous flux distribution

PPW_FF

2G N_{P}

Pin and groupwise 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 where refers to incoming partial current of surface k of group g.
 The order of ALB_OUT_CURR is where 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 where refers to albedo from group g to g'.
 The order of ALB_PART_ALB is where refers to albedo of surface k' of group g' which has entered the albedo surface through surface k and group g.
 For example, twogroup hexagonal partial albedos can be converted into matrix form using the reshapecommand in Matlab with the notation part_alb(g', k', g, k) 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 N_{S} below)

ALB_IN_CURR

2G N_{S}

Groupwise incoming partial currents of albedo surface faces

ALB_OUT_CURR

2G^{2} N_{S}^{2}

Outgoing group to group and face to face outgoing partial currents

ALB_TOT_ALB

2G^{2}

Total group to group albedos for the entire albedo surface

ALB_PART_ALB

2G^{2} N_{S}^{2}

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, 34 are prompt neutron multiplication only and 56 delayed neutron multiplication only. ^{[3]}
References
 ^ Leppänen, J., Pusa, M. and Fridman, E. "Overview of methodology for spatial homogenization in the Serpent 2 Monte Carlo code." Ann. Nucl. Energy, 96 (2016) 126136.
 ^ Liu, Z., Smith, K., Forget, B. and Ortensi, J."Cumulative migration method for computing rigorous diffusion coefficients and transport cross sections from Monte Carlo." Ann. Nucl. Energy, 118 (2018) 507516.
 ^
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