4 Effective Delayed Neutron Fraction
91
4.1.3.3 Results and Discussion
Fixed-source calculations were performed by MCNPX-2.5.0 with 1E + 09 total
histories with nuclear data libraries of ENDF/B-VII.0 and JENDL/HE-2007 [8] as
shown in Table 4.5. For the case of the spallation neutrons, since neutrons over
20 MeV neutrons could be produced by the 100 MeV proton injections into the W
target, JENDL/HE-2007 has a full advantage in the accuracy of the particle transport
for neutrons over the energy of 20 MeV. However, because the yields for total and
prompt neutrons are not provided in JENDL/HE-2007, ENDF/B-VII.0 was used for
fissile and fissionable nuclei. β values calculated with the fluxes by eigenvalue and
fixed-source calculations showed independency on the subcriticality, as shown in
Table 4.4. However, the β values were decreased by the flux in fixed-source calculation. Then, β
RR
source in Eq. (4.20) deduced by the fixed-source calculations indicated
different values from β (fixed-source calculation), and these values were varied larger
than those of β eff by the eigenvalue calculations (MCNP6.1). In Cases I-1 to I-7, the
increase of buckling in the core can be the reason to increase β eff and β
RR
source by the
fuel rod replacement (Cases I-1, I-4, and I-6) and by the control rod insertion (Cases
I-3, I-5, and I-7) because of especially increasing the leakage of prompt neutrons
having higher energy compared to delayed neutrons. The neutron flux distribution
was distorted by the injection of spallation neutrons having dominantly lower energy
with the comparison of 14 MeV neutrons in Case II-1. This distorted flux distribution was considered to be induced by the leakage of prompt neutrons, resulting in
the increase of β
RR
source .
The target results of the measured subcriticality (pcm units) in the uranium-fueled
core were obtained from measured subcriticality in dollar unit multiplied by β eff
(MCNP6.1), β
RR
eigen , and β
RR
source in Eqs. (4.11) and (4.19) (Table 4.4), respectively, as
shown in Table 4.6. The measured subcriticality with the use of β
RR
source in Eq. (4.20) for
conversion from dollar units into pcm units by the fixed-source calculations showed
good agreement with the reference subcriticality within a relative difference of 10%
in the variation of the subcriticality level. And, β
RR
source worked well for the results of
measured subcriticality, comparing those of reference subcriticality. In Cases I-4 to
I-7 (Table 4.6), there was a slight difference between β eff and β
RR
source .
In deep subcritical cores, the measured subcriticality in the area ratio method is
generally considered inaccurately obtained in pcm units to compare with reference
one because an assumption is imposed on the measurements: all source neutrons
induce the fission reactions and neuron signals originate from correlated neutrons to
Table 4.5 List of nuclear data libraries for calculation of β RR
source in particle transport simulations
of the ADS experiments (Ref. [2])
Neutrons
Protons
Spallation neutrons JENDL/HE-2007 and ENDF/B-VII.0 (for U and Th
only)
JENDL/HE-2007
14 MeV neutrons
ENDF/B-VII.0
–
91
4.1.3.3 Results and Discussion
Fixed-source calculations were performed by MCNPX-2.5.0 with 1E + 09 total
histories with nuclear data libraries of ENDF/B-VII.0 and JENDL/HE-2007 [8] as
shown in Table 4.5. For the case of the spallation neutrons, since neutrons over
20 MeV neutrons could be produced by the 100 MeV proton injections into the W
target, JENDL/HE-2007 has a full advantage in the accuracy of the particle transport
for neutrons over the energy of 20 MeV. However, because the yields for total and
prompt neutrons are not provided in JENDL/HE-2007, ENDF/B-VII.0 was used for
fissile and fissionable nuclei. β values calculated with the fluxes by eigenvalue and
fixed-source calculations showed independency on the subcriticality, as shown in
Table 4.4. However, the β values were decreased by the flux in fixed-source calculation. Then, β
RR
source in Eq. (4.20) deduced by the fixed-source calculations indicated
different values from β (fixed-source calculation), and these values were varied larger
than those of β eff by the eigenvalue calculations (MCNP6.1). In Cases I-1 to I-7, the
increase of buckling in the core can be the reason to increase β eff and β
RR
source by the
fuel rod replacement (Cases I-1, I-4, and I-6) and by the control rod insertion (Cases
I-3, I-5, and I-7) because of especially increasing the leakage of prompt neutrons
having higher energy compared to delayed neutrons. The neutron flux distribution
was distorted by the injection of spallation neutrons having dominantly lower energy
with the comparison of 14 MeV neutrons in Case II-1. This distorted flux distribution was considered to be induced by the leakage of prompt neutrons, resulting in
the increase of β
RR
source .
The target results of the measured subcriticality (pcm units) in the uranium-fueled
core were obtained from measured subcriticality in dollar unit multiplied by β eff
(MCNP6.1), β
RR
eigen , and β
RR
source in Eqs. (4.11) and (4.19) (Table 4.4), respectively, as
shown in Table 4.6. The measured subcriticality with the use of β
RR
source in Eq. (4.20) for
conversion from dollar units into pcm units by the fixed-source calculations showed
good agreement with the reference subcriticality within a relative difference of 10%
in the variation of the subcriticality level. And, β
RR
source worked well for the results of
measured subcriticality, comparing those of reference subcriticality. In Cases I-4 to
I-7 (Table 4.6), there was a slight difference between β eff and β
RR
source .
In deep subcritical cores, the measured subcriticality in the area ratio method is
generally considered inaccurately obtained in pcm units to compare with reference
one because an assumption is imposed on the measurements: all source neutrons
induce the fission reactions and neuron signals originate from correlated neutrons to
Table 4.5 List of nuclear data libraries for calculation of β RR
source in particle transport simulations
of the ADS experiments (Ref. [2])
Neutrons
Protons
Spallation neutrons JENDL/HE-2007 and ENDF/B-VII.0 (for U and Th
only)
JENDL/HE-2007
14 MeV neutrons
ENDF/B-VII.0
–