Radioactive decay source, practical example
The radioactive decay source mode was implemented in Serpent 2.1.24 for the purpose of radiation transport calculations involving activated materials. The source term is determined by:
- Isotopic material compositions, either user-defined or obtained from a previous burnup / activation calculation
- Decay constants of radioactive nuclides read from ENDF format decay data file
- Emission spectra read from ENDF format decay data file
The radiation types in version 2.1.28 and earlier are limited to discrete photon emitting reactions. Work on continuum reactions, neutron emission and bremsstrahlung from beta decay is under way.
The radioactive decay source mode is most conveniently used with burnup or activation calculation, in which case the radioactive material compositions can be read from a binary restart file (see the set rfw and set rfr options). In such case the same input can be used for both calculations without major modifications. Serpent converts the isotopic material compositions in the neutron transport calculation into elemental compositions for the following photon transport calculation, and source rate normalization is carried out automatically based on the total emission rate.
There are two sampling modes for selecting the position of emitted particles:
- Analog sampling mode -- Source points are sampled uniformly throughout the geometry and each point accepted or rejected based on the ratio of local to maximum emission rate
- Implicit sampling mode -- Source points are sampled uniformly throughout the geometry and the weight of the emitted photon adjusted according to the ratio of local to average emission rate.
Efficiency of analog sampling may become poor when most (but not all) of the activity is concentrated on local hot spots. Implicit sampling allows covering the geometry uniformly with source points, but may lead to sparse distribution of weights and lead to problems with tally statistics.
The radioactive decay source mode has been tested in radiation shielding calculations involving a transport cask containing irradiated fuel and shut-down dose rate calculations for the ITER fusion reactor. Below is a simple example demonstrating the two-stage procedure.
Production of decay source from burnup calculation
The first calculation involves a conventional burnup calculation. The example input below is a 2D pin-cell calculation. The binary restart file used by the radioactive decay source mode is produced using the set rfw option.
% --- Pin-cell burnup calculation ---------------------------- set title "Pin-cell burnup calculation" % --- Pin definition: pin 1 fuel 0.412 clad 0.475 water % --- Geometry: surf 1 sqc 0.0 0.0 0.665 cell 1 0 fill 1 -1 cell 2 0 outside 1 % --- Periodic boundary condition: set bc 3 % --- Fuel (composition given in atomic densities): mat fuel -10.045 vol 5.33267E-01 burn 1 92234.09c 6.15169E+18 92235.09c 6.89220E+20 92236.09c 3.16265E+18 92238.09c 2.17103E+22 6012.09c 9.13357E+18 7014.09c 1.04072E+19 8016.09c 4.48178E+22 % --- Zircalloy cladding: mat clad -6.560 vol 1.75555E-01 40000.06c -0.9791 50000.06c -0.0159 26000.06c -0.0050 % --- Water (composition given in atomic densities): mat water -0.7569 vol 1.06008E+00 moder lwtr 1001 1001.06c 5.06153E+22 8016.06c 2.53076E+22 5010.06c 2.75612E+18 5011.06c 1.11890E+19 % --- Thermal scattering data for light water: therm lwtr lwj3.11t % --- Data libraries: set acelib "/xs/sss_jeff31u.xsdata" set declib "/xs/sss_jeff31.dec" set nfylib "/xs/sss_jeff31.nfy" % --- Options: set gcu -1 set pop 2000 500 20 % --- Write binary restart file: set rfw 1 % --- Burnup calculation: set powdens 40.0E-3 dep butot 0.1 0.5 1 5 10 15 20 25 30 35 40 % ------------------------------------------------------------
Photon transport simulation using radioactive decay source
The second calculation reads the binary restart file with the set rfr option. The other modification in the input are:
- The burn entry after definition of material "fuel" is omitted (the div-cards must remain in place, if any)
- The source is defined using the src card and the sg entry
- Calculation mode is set to external source simulation by replacing the set pop card with the set nps card
- The normalization option is omitted
- Photon transport library is added in the set acelib card (this example uses the mcnp5 library)
- Photon data directory is defined using the set pdatadir card
- Depletion history is omitted
Serpent automatically converts the isotopic material compositions used in the neutron transport calculation into elemental compositions and finds the corresponding photon interaction data from the library directory files. The total source rate is automatically set equal to the emission rate of photons in radioactive decay. The material volumes, consistent with the div-card, must be provided if Serpent is unable to calculate them to evaluate the source material-wise emission rate. The modified input is listed below.
% --- Pin-cell photon transport calculation ------------------ set title "Pin-cell photon transport calculation" % --- Pin definition: pin 1 fuel 0.412 clad 0.475 water % --- Geometry: surf 1 sqc 0.0 0.0 0.665 cell 1 0 fill 1 -1 cell 2 0 outside 1 % --- Periodic boundary condition: set bc 3 % --- Fuel (composition given in atomic densities): mat fuel -10.045 vol 5.33267E-01 92234.09c 6.15169E+18 92235.09c 6.89220E+20 92236.09c 3.16265E+18 92238.09c 2.17103E+22 6012.09c 9.13357E+18 7014.09c 1.04072E+19 8016.09c 4.48178E+22 % --- Zircalloy cladding: mat clad -6.560 vol 1.75555E-01 40000.06c -0.9791 50000.06c -0.0159 26000.06c -0.0050 % --- Water (composition given in atomic densities): mat water -0.7569 vol 1.06008E+00 moder lwtr 1001 1001.06c 5.06153E+22 8016.06c 2.53076E+22 5010.06c 2.75612E+18 5011.06c 1.11890E+19 % --- Thermal scattering data for light water: therm lwtr lwj3.11t % --- Data libraries: (use photon data from mcnp5) set acelib "/xs/sss_jeff31u.xsdata" "mcnp5.xsdata" set declib "/xs/sss_jeff31.dec" set pdatadir "/xs/photon_data" % --- Options: set gcu -1 set nps 10000 % --- Read binary restart file (10 MWd/kgU burnup) set rfr 10.0 "pc0.wrk" % --- Radioactive decay source: src 1 g sg -1 1 % ------------------------------------------------------------
When the calculation is run, Serpent produces an additional output file [input]_gsrc.m that contains the source spectra. The data is listed separately for each radioactive material, and it contains the emission lines of each discrete photon-producing reaction. The columns are:
- Nuclide ZAI
- Specific intensity (photons per decay)
- Total emission rate (photons/s)
- Cumulative fraction of material total
- Emission line energy
- Relative intensity (photons per decay)
- Cumulative fraction of nuclide total
The first four column contain nuclide-specific and the last three columns emission line-specific data. The specific intensity refers to the number of photons emitted per decay of the given isotope. The total emission rate is the total number of photons emitted per second in the decay of the isotope in the material. Relative intensity refers to the number of photons emitted at the given energy per decay.
mat_fuel = [ % --- Np-239 : 932390 1.82250E+00 5.96906E+12 1.40817E-01 1.47920E-02 5.07619E-01 2.78529E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 1.06123E-01 2.72130E-01 4.27845E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 1.03760E-01 2.51087E-01 5.65616E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 4.75600E-03 1.58734E-01 6.52712E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 9.95500E-02 1.56930E-01 7.38819E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 2.77599E-01 1.43820E-01 8.17733E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 2.28184E-01 1.12800E-01 8.79626E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 1.17260E-01 5.57414E-02 9.10211E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 2.09753E-01 3.42631E-02 9.29011E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 1.20600E-01 3.13859E-02 9.46232E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 1.16270E-01 2.93772E-02 9.62351E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 3.34310E-01 2.07270E-02 9.73724E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 3.15880E-01 1.59330E-02 9.82467E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 6.14600E-02 1.29015E-02 9.89546E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 2.85460E-01 7.89599E-03 9.93878E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 2.26400E-01 2.82000E-03 9.95425E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 5.72700E-02 1.50870E-03 9.96253E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 4.94100E-02 1.17030E-03 9.96895E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 2.54410E-01 1.09980E-03 9.97499E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 4.46630E-02 9.02399E-04 9.97994E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 6.78400E-02 9.02399E-04 9.98489E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 1.81710E-01 8.03701E-04 9.98930E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 2.72840E-01 7.75500E-04 9.99356E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 1.06480E-01 4.79401E-04 9.99619E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 1.66390E-01 1.69200E-04 9.99711E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 4.34700E-01 1.22670E-04 9.99779E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 1.24400E-01 1.12800E-04 9.99841E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 8.80500E-02 5.92201E-05 9.99873E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 4.92300E-01 5.92201E-05 9.99906E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 4.29500E-01 3.80699E-05 9.99926E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 4.97600E-01 3.10201E-05 9.99944E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 4.97700E-01 3.10201E-05 9.99961E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 3.91300E-01 1.55100E-05 9.99969E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 4.61900E-01 1.55100E-05 9.99978E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 4.69800E-01 1.05750E-05 9.99983E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 1.84300E-02 1.02930E-05 9.99989E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 4.84300E-01 1.02930E-05 9.99995E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 5.73000E-02 5.92201E-06 9.99998E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 4.47600E-01 2.53800E-06 9.99999E-01 932390 1.82250E+00 5.96906E+12 1.40817E-01 7.86000E-03 1.29720E-06 1.00000E+00 % --- U-239 : 922390 7.03465E-01 2.30761E+12 1.95256E-01 7.46640E-02 4.81000E-01 6.83758E-01 922390 7.03465E-01 2.30761E+12 1.95256E-01 1.44400E-02 1.33667E-01 8.73771E-01 922390 7.03465E-01 2.30761E+12 1.95256E-01 4.35330E-02 4.16065E-02 9.32916E-01 922390 7.03465E-01 2.30761E+12 1.95256E-01 4.60800E-03 2.81389E-02 9.72916E-01 922390 7.03465E-01 2.30761E+12 1.95256E-01 6.62240E-01 1.77970E-03 9.75446E-01 ...
- ^ Sirén, P. and Leppänen, J. "Expanding the Use of Serpent 2 to Fusion Applications: Development of a Plasma Neutron Source." In proc. PHYSOR 2016. Sun Valley, ID, May 1-6, 2016.
- ^ Leppänen, J. and Kaltiaisenaho, T. "Expanding the Use of Serpent 2 to Fusion Applications: Shut-down Dose Rate Calculations." In proc. PHYSOR 2016. Sun Valley, ID, May 1-6, 2016.