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:

1. 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
2. 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  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
40000.06c  -0.9791
50000.06c  -0.0159
26000.06c  -0.0050

% --- Water (composition given in atomic densities):

mat water  -0.7569   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

% --- 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
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
40000.06c  -0.9791
50000.06c  -0.0159
26000.06c  -0.0050

% --- Water (composition given in atomic densities):

mat water  -0.7569   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

% ------------------------------------------------------------