96
M. Yamanaka
N =
2
√
2 π σg ∗ S
ν p
g
ν p
ν p − 1
T 0
C
α B
=
(1 − β eff ) (− ρ $ )
β eff (1 − ρ $ )
2
,
(4.34)
and correction factors g and g* were obtained with the following calculations [6]:
g =
P(r) dr
P(r) I
2
(r)dr
P(r) I(r)dr
2
,
(4.35)
g∗ =
S(r) I q (r) dr
P(r) dr
P(r) I(r) dr
S(r) dr
,
(4.36)
P(r) =
Σ f (r, E) φ(r, E) d E,
(4.37)
I(r) =
χ(r, E) φ
+
(r, E) d E,
(4.38)
I q (r) =
χ q (r, E) φ
+
(r, E) d E,
(4.39)
where φ and φ
+ are the forward and adjoint fluxes, respectively, f the macroscopic
fission cross section, and χ and χ q the fission spectrum and the spectrum of the
external neutron source, respectively. From the relation between N and β eff shown
in Eq. (4.24), β eff is obtained experimentally as follows:
β eff =
−ρ $
N (1 − ρ $ )
2
− ρ $
.
(4.40)
The procedure for the deduction of β eff in the PNS experiments is shown in
Fig. 4.1.
Area ratio method
ρ $
Fitting PNS Histogram
α
Rossi-α method
C, B
PNS experiment
S, <ν p (ν p -1)>, σ
Experimental condition
Core analysis
Correction factors
Calculation
Fig. 4.1 Procedure for deduction of β eff in PNS experiments (Ref. [12])