110
M. Yamanaka
β
PARTISN
eff
=
φ
+
(g
) χ d (g
) ν d (g) Σ f (g) φ (g)
φ + (g ) χ(g ) ν(g) Σ f (g) φ (g)
,
(4.47)
Λ
PARTISN
=
1
v (g)
φ
+
(g) φ (g)
φ + (g ) χ(g ) ν(g) Σ f (g) φ(g)
,
(4.48)
where φ and φ
+ are the forward and adjoint fluxes in λ-mode or ω-mode calculations,
respectively, χ and χ d the total and delayed neutron fission spectra, respectively, ν
and ν d the number of total and delayed neutrons by fission reaction, respectively,
f the effective fission cross section, v the neutron velocity, < > the integration over
energy group and phase space, and g and g
the energy groups. Here, χ d (g
) was
obtained by the extraction of nuclear data of
235 U from ENDF/B-VII.1 by NJOY99
[22]. Also, ν d (g) was defined as follows:
ν d (g) = ν (g) − ν p (g),
(4.49)
where ν p (g), which was obtained as in the procedure for χ d (g
), is the number
of prompt neutrons by the fission reaction. Furthermore, β eff / values by using
MCNP6.1 were obtained by combining kinetics parameters (evaluated with KOPT
option in MCNP6.1).
By varying subcriticality, the value of β eff / tended to decrease with deep subcriticality as shown in Fig. 4.11. Interestingly, β eff / differed even when subcriticality was the same, although the core size was different in Cases I-2 and III.
Also, the nonsignificant difference of β eff / values was observed indicated between
14 MeV and spallation neutron sources in measurements. Thus, β eff / was considered independent of any external neutron source, indicating that the measurement
was conducted correctly to extract fundamental-mode components in the time evolution of neutron flux. In the comparison between calculations, the λ-mode calculation
by PARTISN showed a bias compared with that by MCNP6.1, and the results were
Fig. 4.11 β eff / value for α
value in ω-mode for
subcriticality variation (Ref.
[15])
140
180
220
260
300
I-1
(523)
I-2
(607)
I-3
(910)
I-4
(673)
I-5
(1051)
II
(378)
III
(690)
IV
(1026)
V
(1159)
VI
(1238)
VII
(1669)
eff / [1/s]
Case
(α value in ω-mode by PARTISN)
14 MeV neutron
Spallation neutrons
MCNP6.1
λ-mode in PARTISN
ω-mode in PARTISN
M. Yamanaka
β
PARTISN
eff
=
φ
+
(g
) χ d (g
) ν d (g) Σ f (g) φ (g)
φ + (g ) χ(g ) ν(g) Σ f (g) φ (g)
,
(4.47)
Λ
PARTISN
=
1
v (g)
φ
+
(g) φ (g)
φ + (g ) χ(g ) ν(g) Σ f (g) φ(g)
,
(4.48)
where φ and φ
+ are the forward and adjoint fluxes in λ-mode or ω-mode calculations,
respectively, χ and χ d the total and delayed neutron fission spectra, respectively, ν
and ν d the number of total and delayed neutrons by fission reaction, respectively,
f the effective fission cross section, v the neutron velocity, < > the integration over
energy group and phase space, and g and g
the energy groups. Here, χ d (g
) was
obtained by the extraction of nuclear data of
235 U from ENDF/B-VII.1 by NJOY99
[22]. Also, ν d (g) was defined as follows:
ν d (g) = ν (g) − ν p (g),
(4.49)
where ν p (g), which was obtained as in the procedure for χ d (g
), is the number
of prompt neutrons by the fission reaction. Furthermore, β eff / values by using
MCNP6.1 were obtained by combining kinetics parameters (evaluated with KOPT
option in MCNP6.1).
By varying subcriticality, the value of β eff / tended to decrease with deep subcriticality as shown in Fig. 4.11. Interestingly, β eff / differed even when subcriticality was the same, although the core size was different in Cases I-2 and III.
Also, the nonsignificant difference of β eff / values was observed indicated between
14 MeV and spallation neutron sources in measurements. Thus, β eff / was considered independent of any external neutron source, indicating that the measurement
was conducted correctly to extract fundamental-mode components in the time evolution of neutron flux. In the comparison between calculations, the λ-mode calculation
by PARTISN showed a bias compared with that by MCNP6.1, and the results were
Fig. 4.11 β eff / value for α
value in ω-mode for
subcriticality variation (Ref.
[15])
140
180
220
260
300
I-1
(523)
I-2
(607)
I-3
(910)
I-4
(673)
I-5
(1051)
II
(378)
III
(690)
IV
(1026)
V
(1159)
VI
(1238)
VII
(1669)
eff / [1/s]
Case
(α value in ω-mode by PARTISN)
14 MeV neutron
Spallation neutrons
MCNP6.1
λ-mode in PARTISN
ω-mode in PARTISN