JAEA-Conf 2011-002 - 日本原子力研究開発機構

Sensitivities of curium isotope concentrations to nuclear data of major and minor actinides are
calculated in order to specify the important nuclear data for accurate prediction of the curium
isotope concentrations after burn-up.
2. Brief description of the depletion perturbation theory
In the present section, the depletion perturbation theory for the nuclide field is briefly
described. Its detail can be found in the literatures [3][4][6].
The nuclide densities of a reactor are expressed using the following nuclide density vector:
N( t),
N ( t),...,
N ( t)
N ( t) 1 2
n ,
where N i (t)
is the number density of nuclide i at time t . We denote the initial time as t 0
and the final time as t T . The number density vector satisfies the following burn-up equation:
d
N( t)
MN(
t)
,
dt
where M is the so-called burn-up matrix.
In the present study, we calculate the sensitivity of the nuclide concentrations after burn-up to
nuclear data. The sensitivity is defined as
i dN i ( t)
N i ( t)
dN i ( t)
S
,
d
N i ( t)
d
where denotes nuclear data such as reaction cross sections and half-lives Using the depletion
perturbation theory, the derivative term in the above equation can be calculated as
where
dN i ( t)
d
JAEA-Conf 2011-002
T
0
dt
N
*
dM
d
t N
t
*
N is the adjoint number density vector which satisfies the following equation:
d *
* *
N ( t)
M N ( t)
,
dt
*
where M is a transposed matrix of M . In this adjoint burn-up equation, an appropriate
initial vector is given at t T according to the target nuclide for which the sensitivity is
calculated.
In the depletion perturbation theory for the neutron flux and nuclide density coupled field,
the generalized adjoint flux and the adjoint power are introduced in order to consider a neutron
flux spatial/energetical distribution effect and a power normalization effect.
3. Numerical procedure
The present study treats a light water mixed-oxide fuel pin cell model, which is made to
represent a 17 17 pressurized water reactor fuel assembly [7]. This model and a calculation
condition are almost same as those used in the previous sensitivity study for fission product
concentrations [6]. The uranium-235 concentration and the plutonium content of the fuel are 0.2
wt% and 10.0 wt%, respectively. The initial number densities of the fuel are shown in Table 1.
The geometrical parameters of this pin cell are:
,