4 Effective Delayed Neutron Fraction
115
effective multiplication factors k critical and k super-critical , in critical and super-critical
(clean) cores, respectively, as follows:
ρ
cal
excess =
1
k critical
−
1
k super−critical
.
(4.53)
Also, control rod worth was numerically deduced by the difference between the
critical and the subcritical (rod insertion) cores, as in Eq. (4.53).
Using the kinetics parameters obtained by MCNP6.1, experimental reactivity
ρ
exp was deduced and compared with numerical reactivity ρ
cal obtained by JENDL4.0 and ENDF/B-VII.1, as shown in Tables 4.16 and 4.17, with the consideration of
statistical errors of neutron counts obtained from the neutron detectors and processing
of error propagation caused by experimental analyses. For the critical cores (3016 and
3008 HEU plates in Tables 4.14 and 4.15) shown in Figs. A4.1 and A4.4, respectively,
numerical reactivity obtained by JENDL-4.0 revealed a fairly good agreement with
the experimental reactivity within a relative difference of around 5% through the C/E
(calculation/experiment) value of excess reactivity and control rod worth, as shown
in Tables 4.16 and 4.18. In terms of ENDF/B-VII.1, the difference between numerical
and experimental reactivity was relatively large over 10%, as shown in Tables 4.17
and 4.19. The difference between β eff values by JENDL-4.0 and ENDF/B-VII.1 was
attributable to numerical results by the MCNP calculations in fraction β i (i = 1–6:
precursor group of delayed neutrons) and decay constant λ i of delayed neutrons, as
shown in Figs. 4.13 and 4.14, respectively.
Table 4.16 Comparison between measured and calculated reactivity [pcm] with JENDL-4.0 (# of
HEU plates: 3016; critical core in Fig. A4.1 and Table 4.14) (Ref. [23])
ρ cal
J40
ρ
exp
J40
C/E (ρ cal
J40 /ρ
exp
J40 )
Excess reactivity
259.9 ± 5.7
271.7 ± 0.1
0.96 ± 0.02
C1 rod worth
876.1 ± 5.7
867.4 ± 3.9
1.01 ± 0.01
C2 rod worth
154.8 ± 5.7
142.8 ± 3.5
1.08 ± 0.05
C3 rod worth
529.2 ± 5.7
506.4 ± 4.1
1.05 ± 0.01
MCNP6.1 with JENDL-4.0: β eff = 813 ± 10 [pcm], = 31.67 ± 0.07 [μs]
Table 4.17 Comparison between measured and calculated reactivity [pcm] with ENDF/B-VII.1 (#
of HEU plates: 3016; critical core in Fig. A4.1 and Table 4.14) (Ref. [23])
ρ cal
E71
ρ
exp
E71
C/E (ρ cal
E71 /ρ
exp
E71 )
Excess reactivity
253.9 ± 5.6
229.8 ± 0.3
1.10 ± 0.02
C1 rod worth
862.5 ± 5.7
718.8 ± 3.2
1.20 ± 0.01
C2 rod worth
138.2 ± 5.6
118.3 ± 2.9
1.17 ± 0.05
C3 rod worth
513.1 ± 5.7
419.6 ± 4.5
1.22 ± 0.01
MCNP6.1 with ENDF/B-VII.1: β eff = 801 ± 10 [pcm], = 31.26 ± 0.07 [μs]
115
effective multiplication factors k critical and k super-critical , in critical and super-critical
(clean) cores, respectively, as follows:
ρ
cal
excess =
1
k critical
−
1
k super−critical
.
(4.53)
Also, control rod worth was numerically deduced by the difference between the
critical and the subcritical (rod insertion) cores, as in Eq. (4.53).
Using the kinetics parameters obtained by MCNP6.1, experimental reactivity
ρ
exp was deduced and compared with numerical reactivity ρ
cal obtained by JENDL4.0 and ENDF/B-VII.1, as shown in Tables 4.16 and 4.17, with the consideration of
statistical errors of neutron counts obtained from the neutron detectors and processing
of error propagation caused by experimental analyses. For the critical cores (3016 and
3008 HEU plates in Tables 4.14 and 4.15) shown in Figs. A4.1 and A4.4, respectively,
numerical reactivity obtained by JENDL-4.0 revealed a fairly good agreement with
the experimental reactivity within a relative difference of around 5% through the C/E
(calculation/experiment) value of excess reactivity and control rod worth, as shown
in Tables 4.16 and 4.18. In terms of ENDF/B-VII.1, the difference between numerical
and experimental reactivity was relatively large over 10%, as shown in Tables 4.17
and 4.19. The difference between β eff values by JENDL-4.0 and ENDF/B-VII.1 was
attributable to numerical results by the MCNP calculations in fraction β i (i = 1–6:
precursor group of delayed neutrons) and decay constant λ i of delayed neutrons, as
shown in Figs. 4.13 and 4.14, respectively.
Table 4.16 Comparison between measured and calculated reactivity [pcm] with JENDL-4.0 (# of
HEU plates: 3016; critical core in Fig. A4.1 and Table 4.14) (Ref. [23])
ρ cal
J40
ρ
exp
J40
C/E (ρ cal
J40 /ρ
exp
J40 )
Excess reactivity
259.9 ± 5.7
271.7 ± 0.1
0.96 ± 0.02
C1 rod worth
876.1 ± 5.7
867.4 ± 3.9
1.01 ± 0.01
C2 rod worth
154.8 ± 5.7
142.8 ± 3.5
1.08 ± 0.05
C3 rod worth
529.2 ± 5.7
506.4 ± 4.1
1.05 ± 0.01
MCNP6.1 with JENDL-4.0: β eff = 813 ± 10 [pcm], = 31.67 ± 0.07 [μs]
Table 4.17 Comparison between measured and calculated reactivity [pcm] with ENDF/B-VII.1 (#
of HEU plates: 3016; critical core in Fig. A4.1 and Table 4.14) (Ref. [23])
ρ cal
E71
ρ
exp
E71
C/E (ρ cal
E71 /ρ
exp
E71 )
Excess reactivity
253.9 ± 5.6
229.8 ± 0.3
1.10 ± 0.02
C1 rod worth
862.5 ± 5.7
718.8 ± 3.2
1.20 ± 0.01
C2 rod worth
138.2 ± 5.6
118.3 ± 2.9
1.17 ± 0.05
C3 rod worth
513.1 ± 5.7
419.6 ± 4.5
1.22 ± 0.01
MCNP6.1 with ENDF/B-VII.1: β eff = 801 ± 10 [pcm], = 31.26 ± 0.07 [μs]