86
M. Yamanaka
Table 4.2 Subcriticality deduced by excess reactivity and control rod worth in the experiments and
by MCNPX-2.5.0 in Fig. A2.1 (Ref. [2])
Case # of fuel rods Rod insertion pattern Subcriticality [pcm]
C/E
MCNPX-2.5.0 Experiment
I-1
25
C1, C2, C3
1258 ± 11
1200 ± 36
1.05 ± 0.02
I-2
25
C1, C2, C3, S4
2099 ± 11
2011 ± 60
1.04 ± 0.01
I-3
25
C1, C2, C3,
S4, S5, S6
2774 ± 11
2657 ± 80
1.04 ± 0.01
I-4
21
–
2737 ± 11
–
–
I-5
21
C1, C2, S4, S6
4858 ± 11
–
–
I-6
19
–
5299 ± 11
–
–
I-7
19
C1, C2, S4, S6
7457 ± 12
–
–
4.1.2.2 Reaction Rates
The delayed neutron fraction is defined as the ratio of the delayed neutron generation
to the total neutron generation as follows:
β =
F
d
φ
Fφ
,
(4.1)
where φ is forward angular flux, < > the integration over angle, space, and energy,
respectively. F, F
d , and F
p are production operators of total, delayed, and prompt
neutron generations by fission reactions, respectively, as follows:
F =
d E
χ (E
→ E) ν (E
) Σ f (E
),
(4.2)
F
d
=
d E
χ
d
(E
→ E) ν
d
(E
) Σ f (E
),
(4.3)
F
p
= F − F
d
,
(4.4)
where χ and χ
d are the energy spectra of total and delayed neutrons, respectively; ν
and ν
d the neutron yields for total and delayed neutrons, respectively; E the energy
of scattered neutrons; E
induced neutron energy; and f the macroscopic fission
cross sections. And β eff is defined as the ratio of the contribution of delayed neutrons
to total neutrons for reactivity with the use of adjoint angular flux φ
+ for weighting
function as follows:
β eff =
φ
+
, F
d
φ
φ + , F φ
.
(4.5)