Special XSDRNPM Files

Three special files that can be optionally produced by XSDRNPM are described in this appendix. (See Sect. 9.1.5 and the discussion of the logical units in the 0$ array.) The files will be created with file names of the form ftNNfXXX.EXT where NN is the 2 digit logical unit number (from the 0$$ array), XXX is a 3 digit number which is incremented by one starting with one to make the name unique, and EXT is an extension identifying which type of file it is (acf for activity file, btf for balance table file, and idf for input and derived data file). Activity file

The data on the activity file depends on what input options are specified. The data is in ASCII sets, which consist of a label record followed by the record(s) of the activity. There will be at most IAZ sets ordered as the 49$ and 50$ arrays. The first sets of data will be the activities by interval (if the input parameter IAI was specified). A set will be formatted as below.

activity by interval for nuclide nnnnnnnn reaction type rrrrrrrr

Activity(first interval)





Activity(last interval)

The preceding set will be repeated IAZ times. Then sets giving the activities by zone will be given. They will be formatted as below.

activity by zone for nuclide nnnnnnnn reaction rrrrrrrr
Activity(first zone)





Activity(last zone) Balance table file

The contents of the balance table are defined in Table 9.1.3 and Table 9.1.4. The structure of the “balance table file” written to LBTF is:

Record 1 KEFF, SP

KEFF - keffective for problem

SP - search parameter for case

Record 2 - Sets of ASCII data consisting of a label record followed by data records.

Record last

A set of data is as follows (igp is the total number of groups plus one):

fine(few) group summary for zone zzzzz set type

Set type data(group 1)

Set type data(group 2)





Set type data(group igp)

The data for a set type will be written for each zone of the problem, plus a system summary if there is more than one zone. After one set type is finished, the next set type will be written. The order of the set types is as follows:

fixed source

fission source

absorption rate

total leakage

fission rate


<n,2n> rate

buckling loss

right current

left current

right leakage

left leakage

The fine group summary data will be written if LBTF is > 0. After the fine group data is finished, the few group summary data will follow if a weighting calculation is specified with a broad group collapse. Input and derived data file

The contents of the input and derived data file (specified by LIDF) is as follows:

Record 1 – title (80 characters)

Record 2 – 1$$ array (label)

Record 3,4 – data from 1$ array

Record 5 – 2$$ array (label)

Record 6 – data from 2$ array

Record 7 – 3$$ array (label)

Record 8,9 – data from 3$ array

Record 10 – 4$$ array (label)

Record 11 – data from 4$ array

Record 12 – 5** array (label)

Record 13,14 – data from the 5* array

Record 15 – cross section parameters (label)

Record 16 – total groups, neutron groups, gamma groups, first thermal group

Record 17 – nuclides on library (label)

Records 17a – list of nuclides on the cross section library

Record 18 – mixture numbers (label)

Records 18a – data from the 13$ array

Record 19 – component numbers (label)

Records 19a – data from the 14$ array

Record 20 – densities (label)

Records 20a – data from the 15* array

Record 21 – cccc identifiers (label)

Records 21a – data from the 16$ array

Record 22 – neutron energy group boundaries (label)

Records 22a — list of the energy boundaries for the neutron groups

Record 23 – neutron lethargy group boundaries (label)

Records 23a – list of the lethargy boundaries for the neutron groups

Record 24 – neutron weighted velocities (label)

Record 24a – list of the neutron average velocities

Record 25 – gamma energy group boundaries (label)

Record 25a – list of the energy boundaries for the gamma groups

Record 26 – gamma lethargy group boundaries (label)

Records 26a – list of the lethargy boundaries for the gamma groups

Record 27 – gamma weighted velocities (label)

Records 27a – list of the gamma velocities

Record 28 – broad group numbers (label)

Records 28a – list of the broad group numbers by fine group - 51$ array

Record 29 – group band (label)

Records 29a – group band numbers by fine group

Record 30 – calculation type (label)

Records 30a – calculation type by fine group

Record 31 – right albedo (label)

Records 31a – list of the right boundary albedos by group - 47* array

Record 32 – left albedo (label)

Records 32a – list of the left boundary albedos by group - 48* array

Record 34 – mixture by zone (label)

Records 34a – data from the 39$ array

Record 35 – order of scattering by zone (label)

Records 35a – data from the 40$ array

Record 36 – activity materials (label)

Records 36a – data from the 49$ array

Record 37 – activity reaction types (label)

Records 37a – data from the 50$ array

Record 38 – quadrature weights (label)

Records 38a – data from the 43* array

Record 39 – quadrature cosines (label)

Records 39a – data from the 42* array

Record 40 – weights x cosines (label)

Records 40a – product of quadrature weights times quadrature

Record 41 – reflected directions (label)

Records 41a – reflected direction index array

Record 42 – pl scattering constants (label)

Records 42a – constants for converting from discrete angles to Legendre moments

Record 43 – interval boundaries (label)

Records 43a – data from the 35* array

Record 44 – interval midpoints (label)

Records 44a – array containing the midpoints of each interval

Record 45 – zone by interval (label)

Records 45a – data from the 36$ array

Record 46 – interval boundary areas (label)

Records 46a – area of each interval boundary

Record 47 – interval volumes (label)

Records 47a – volume of each interval

Record 48 – interval density factors (label)

Records 48a – data from the 38* array

Record 49 – zone width modifiers (label)

Records 49a – data from the 41* array

Record 50 – source spectrum by interval (label)

Records 50a – data from the 30$ array

Table 9.1.3 Balance table definitions.

FS = Fission Sourcegrp,zone = \(1 / \lambda \Sigma_{\text {i} \subset \text{zone}}\left[X_{i, \operatorname{grp}} \Sigma_{\operatorname{grp}^{\prime}}\left(v \Sigma_{\text {fgrp }^{\prime}, i} \varphi_{\text {grp }^{\prime}, \mathrm{i}}\right) V_{i}\right]\)

XS = Fixed Sourcegrp,zone = \(\Sigma_{1 \subset \text{zone} \text{}}\left[Q_{\text {grp }, i} V_{i}+A_{i} \Sigma_{\mu m>0} B S_{i, \text { grp, } m} \mu_{m} w_{m}-A_{i+1} \Sigma_{\mu m<0} B S_{i, \text { grp }, m} \mu_{m} w_{m}\right]\)

IS = Inscattergrp,zone = \(\Sigma_{\text {i} \subset \text{zone}} \sum_{j \neq \operatorname{grp}}\left[\Sigma_{j \rightarrow \operatorname{grp}, i} \varphi_{j, i} V_{i}\right]\)

SS = Selfscattergrp,zone = \(\Sigma_{\text {i} \subset \text{zone}}\left[\Sigma_{\text {grp } \rightarrow \operatorname{grp}} \varphi_{\text {grp }, \mathrm{i}} \mathrm{V}_{\mathrm{i}}\right]\)

OS = Outscattergrp,zone = \(\Sigma_{\text {i} \subset \text{zone}} \sum_{j \neq \operatorname{grp}}\left[\sum_{\operatorname{grp} \rightarrow j} \varphi_{\text {grp }, i} V_{i}\right]\)

AB = Absorptiongrp,zone = \(\Sigma_{\text {i} \subset \text{zone}}\left[\Sigma_{\text {abs grp }, i} \varphi_{\text {grp }, \mathrm{i}} \mathrm{V}_{\mathrm{i}}\right]\)

LK = Leakagegrp,zone = \(\left\lbrack A_{\text{zr}}\Sigma_{m}\left( \psi_{m,\mathrm{\mspace{6mu}}\text{zr}}\mu_{m}w_{m} \right)\mathrm{\quad} - \mathrm{\quad}A_{z1}\Sigma_{m}\left( \psi_{m,\mathrm{\mspace{6mu}}z1}\mu_{m}w_{m} \right) \right\rbrack\)

RF = Right Boundary Fluxgrp,zone = \(\Sigma_{\mathrm{m}}\left(\psi_{\mathrm{m}, \mathrm{zr}, \mathrm{grp}} \mathrm{W}_{\mathrm{m}}\right)\)

LF = Left Boundary Fluxgrp,zone = \(\Sigma_{\mathrm{m}}\left(\psi_{\mathrm{m}, \mathrm{zr}, \mathrm{grp}} \mathrm{W}_{\mathrm{m}}\right)\)

RL = Right Leakagegrp,zone = \(\mathrm{A}_{\mathrm{zr}} \Sigma_{\mathrm{m}}\left(\psi_{\mathrm{m}, \mathrm{zr}, \mathrm{grp}} \mu_{\mathrm{m}} \mathrm{W}_{\mathrm{m}}\right)\)

LL = Left Leakagegrp,zone = \(A_{z l} \Sigma_{m}\left(\psi_{m, z l, g r p} \mu_{m} W_{m}\right)\)

NN = n,2n Rategrp,zone = \(\Sigma_{i \subset \text { zone }} \Sigma_{p \geq 2}\left[p / 2 \Sigma_{n, p n} \varphi_{g r p, i} V_{i}\right]\)

FR = Fission Rategrp,zone = \(\sum_{i \subset \text { zone }}\left[\Sigma_{f g r p, i} \varphi_{g r p, i} V_{i}\right]\)

DB = DB2 Fluxgrp,zone = \(\sum_{i \subset zone}\left[D_{g r p, i} B_{g r p, i}^{2} \varphi_{g r p, i} V_{i}\right]\)

TF = Total Fluxgrp,zone = \(\sum_{i \subset z o n e}\left[\varphi_{g r p, i} V_{i}\right]\)

BAL = {FS+XS+IS+NN+max(LL,0)-min(RL,0)} / {OS+AB+max(RL,0)-min(LL,0)}

Table 9.1.4 Balance table definition symbols.

\(\sum_{\mathrm{i} \subset \mathrm{zone}}\) is the sum over all intervals i in the zone

\(\sum_{\mathrm{grp}}\) is the sum over all groups grp

\(\sum_{j \neq g r p}\) is the sum over all groups j not equal to group grp

\(\sum_{\mathrm{m}}\) is the sum over the quadrature

\(\sum_{\mathrm{p} \geq 2}\) is the sum over all processes \(\sum_{\mathrm{n}, \mathrm{pn}}\)

\(\lambda \quad=\text { the eigenvalue }\)

\(\chi \quad=\text { the fission spectrum }\)

\(\mathbf{V}\) = the average number of neutrons produced in a fission

\(\sum_{\mathrm{f}}\) = the fission cross section

\(\varphi\) = the scalar flux

V = the volume of a mesh interval

Q = the volumetric external source in a mesh interval

A = the area of a boundary of a mesh interval

BS = the angular flux boundary source on an interval boundary

\(\mu_{\mathrm{m}}\) = the mth discrete angle of the quadrature

\(\mathrm{W}_{\mathrm{m}}\) = the mth weight of the quadrature

\(\sum_{j \rightarrow g r p}\) = the scattering cross section for scattering from group j to group grp

\(\sum_{\mathrm{grp} \rightarrow \mathrm{j}}\) = the scattering cross section for scattering from group grp to group j

\(\sum_{\operatorname{grp} \rightarrow \operatorname{grp}}\) = the scattering cross section for within-group scattering (i.e., from group grp to the same group grp)

\(\sum_{\mathrm{abs}}\) = the absorption cross section

\(\psi\) = the angular flux

Azr = the area of the right-hand boundary of the zone

Azl = the area of the left-hand boundary of the zone

\(\sum_{\mathrm{n}, \mathrm{pn}}\) = the cross section for producing p neutrons, p=2,3,…,p an integer

D = the diffusion coefficient (used in providing a buckling correction for 2 and 3 dimensions)

B2 = the buckling for the second and third dimensions (includes an extrapolation distance)

max(LL,0) means that a positive Left Leakage is a source into the zone

min(RL,0) means that a negative Right Leakage is a source into the zone. It is included with a minus sign to make it a positive source

max(RL,0) means that a positive Right Leakage is a loss from the zone

min(LL,0) means that a negative Left Leakage is a loss from the zone. It is included with a minus sign to make it a positive loss XSDRNPM Mixed Cross Sections

When IPRT (2$$ array) is set > -1, XSDRNPM prints the mixed reaction rate cross sections that are used in its calculations. The order of the cross sections for each group is given below in Table 9.1.5. The diffusion coefficient is used in computing buckling corrections, and in some of the options for computing the current used in weighting the transport cross section. The upscatter cross section is used to checking upscatter convergence. The <n,2n> cross section is used in computing the balance for the balance tables. It is actually a weighted sum of all the multiple neutron exit reactions other than fission. These are all treated in XSDRNPM as scattering reactions. Chi is the fission spectrum, and is used to distribute the fission source in energy space. The fission cross section is used to compute the fission rate reported in the balance tables. The absorption cross section is used to compute the absorptions in the balance tables, and to compute the absorption term in the eigenvalue. Nu*fission cross section is used to generate the source term for all except a fixed source calculation. The total cross section is used to determine the neutron transport.

Table 9.1.5 Order of mixed reaction cross sections

1. Diffusion coefficient (for use in buckling corrections)

2. Upscatter cross section

3. <n,2n> cross section

4. Chi (fission spectrun)

5. Fission cross section

6. Absorption cross section

7. Nu*Fission cross section

8. Total cross section