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M
dN i ( t)
M
= ∑ f j→iλ
j N i ( t)
+ ∑{
g
dt
j≠i
− [ λ + ( σ
i
M
a,
i
+ σ
M
n2n,
i
k ≠i
) ϕ
M
k→i
σ
M
c,
k
Fact(
t)]
N
+ γ
M
i
k→i
( t)
σ
M
f , k
+ h
k→i
σ
M
n2n,
k
} ϕ
M
Fact(
t)
N
M
k
( t)
(7.7-1)
where i, j, k : depleting nuclides
M : depleting zone, which corresponds to the M-Region in the SRAC code.
N : atomic number density
λ, f : decay constant and branching ratio
γ, g, h : yield fraction of each transmutation,
ϕ : relative flux obtained by eigenvalue calculation
Fact(t) : Normalization factor to convert relative flux to absolute one
If we assume the thermal power over the cell under consideration is constant (P) during [t n-1 , t n ], the
normalization factor Fact(t) for the interval of the m-th sub-step [t m-1 , t m ]∈[t n-1 , t n ] is given by
∑∑
M
M
Fact ( tm−1 ≤ t ≤ tm
) = P(
tm−1
≤ t ≤ tm
) /
i N i ( tm−1
) σ f , i
M i
where P : Constant power in [t n-1 , t n ] given by input data
κ i
: Energy release per fission of the i-th nuclide
M
κ V
(7.7-2)
Then, Eq. (7.7-1) can be solved analytically by the method of the DCHAIN code 75) for each sub-step.
The method of DCHAIN is based on Bateman’s method with a modification for more accurate
treatment of cyclic burn-up chain caused by α-decay and so on.
The burn-up chain model and parameters such as decay constants and fission yields are installed
in the burn-up libraries equipped in the SRAC system. The decay constants are taken from the “Chart
of Nuclides 2004” 76) . The fission yields are based on the second version of the JNDC nuclear data
library of fission products 77) . Several burn-up chain models 29) are available to be selected by the
purpose of the calculation. The library data of each chain model is written in a file of text format,
which helps the understanding of the user. The contents can be easily replaced, if necessary (cf. Sect.
3.3).
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