JAEA-Data/Code 2007-004 - Welcome to Research Group for ...

7.5.2 Spectrum for Collapsing
The fluxes thus used are however not taken account of the neutron leakage from the system
under study. So these fluxes should be renormalized to take account of the leakage. For this purpose,
the homogenized effective cross-sections are at first calculated without any group collapsing for the
whole energy range to obtain the homogeneous P 1 or B 1 spectrum.
The P 1 or B 1 equation in multigroup form can be written in the conventional and unified way as
F
1, g
3α
Σ
g
+ Σ
t,
g
tg
F
F
1g
0g
=
G
∑
g ' = 1
2
− B F
Σ
0g
s0g
' →g
=
G
∑
g ' = 1
F
Σ
0g
'
+ Χ
s1g
' →g
F
0g
1g
'
,
(7.5-14)
where α g equals unity for the P 1 approximation and is given for the B 1 approximation by
α
α
g
g
= ( x
= ( x
g
g
tan
−1
tanh
x
−1
g
x
)
g
)
−1
{ − (tan x ) / x }
3 1
−1
2
{ − (tanh x ) / x } for B ≤ 0
3 1
g
g
g
g
for
B
2
≥ 0
(7.5-15)
with
2
x g B Σt,
g
= ,
where the quantity B 2 is the value entered in Block-4 of Sect.2.2.
Assuming a fission spectrum as the source term. Eq.(7.5-2) is solved by the P 1 or B 1
approximation for the fast energy range, while the solution is obtained in the thermal energy range
assuming a slowing-down source. The linked spectrum for the whole energy range is optionally used
to replace the spectrum of the flux of the cell calculation obtained by assuming an infinite array of
lattice cell.
Using the solution, ϕ i,g , of Eq.(7.4.1-1), the spatially averaged fluxes are calculated by
Φ
g
=
∑
i
i∈cell
V ϕ / V .
(7.5-16)
i,
g
cell
Then, the spectrum which includes the leakage effect can be given by
ϕ ' i, g = ϕi,
g F0
g / Φ g .
(7.5-17)
The resultant spectrum ϕ ’ i,g replaces the infinite spectrum ϕ i,g , if the minus sign of IC9 is entered, and
is used to give the microscopic effective cross-section σ
procedure is executed in the HOMOSP routine.
n
z , m,
G
to the cell burn-up routine. Above
For the isolated mixture which is not used in the cell calculation, either of the spectra on the
items (a), (b) and (c) in the second paragraph of Sec.7.5 will be chosen for the weight.
283