40
K. Hashimoto
dC k (t)
dt
=
β k
Λ
N (t) − λ k C k (t),
(2.52)
where N(t) is the neutron density, C k (t) the concentration of k-th-group precursor,
and S the neutron source strength. Other notations are conventional. As the above
neutron density, usually, time-sequence count-rate data can be employed to determine
the reactivity ρ. The differential term of Eq. (2.51) is usually neglected to simplify
the analysis. The assumption is applicable to the KUCA system. Consequently, the
discrete form of Eq. (2.51) on time domain is described as
N (t j ) =
Λ
β − ρ
Q (t j ) +
Λ S
β − ρ
,
(2.53)
Q (t j ) =
6
k = 1
λ k C k (t j ),
(2.54)
where t j is the jth discrete time. As the time-dependent neutron density N(t j ), the timesequence count data were employed. The time-dependent precursor density C k (t j )
of delayed neutrons can be obtained by solving numerically Eq. (2.52). In this study,
the implicit time-integration method was employed to obtain the precursor density.
When the time-sequence data N(t j ) and Q(t j ) are plotted on the x-y coordinate, two
unknown constants, i.e., the reactivity and the source strength, can be determined
from the least-squares fitting of Eq. (2.53) to these data. By applying the LSIKM to
beam trip data, Eq. (2.53) is reduced to
N (t j ) =
Λ
β − ρ
Q (t j ),
(2.55)
where the source strength is set to zero.
The delayed neutron data and prompt-neutron generation time of the present
reactor system were generated using the SRAC code system [34], where a threedimensional, 19-energy-group diffusion calculation was done with JENDL-3.2
nuclear library [35].
2.3.2.2 Integral Count Technique
The integral count technique has been frequently employed to determine the subcriticality from a source jerk experiment and a rod drop one [31, 36]. When a neutron
source is rapidly taken out of a subcritical reactor core or a control rod is dropped
into a critical core at t = 0, the reactivity of the core can be expressed as
ρ = −
6
k = 1
β k
λ k
N (0)
∫
∞
0 N (t) dt
.
(2.56)
K. Hashimoto
dC k (t)
dt
=
β k
Λ
N (t) − λ k C k (t),
(2.52)
where N(t) is the neutron density, C k (t) the concentration of k-th-group precursor,
and S the neutron source strength. Other notations are conventional. As the above
neutron density, usually, time-sequence count-rate data can be employed to determine
the reactivity ρ. The differential term of Eq. (2.51) is usually neglected to simplify
the analysis. The assumption is applicable to the KUCA system. Consequently, the
discrete form of Eq. (2.51) on time domain is described as
N (t j ) =
Λ
β − ρ
Q (t j ) +
Λ S
β − ρ
,
(2.53)
Q (t j ) =
6
k = 1
λ k C k (t j ),
(2.54)
where t j is the jth discrete time. As the time-dependent neutron density N(t j ), the timesequence count data were employed. The time-dependent precursor density C k (t j )
of delayed neutrons can be obtained by solving numerically Eq. (2.52). In this study,
the implicit time-integration method was employed to obtain the precursor density.
When the time-sequence data N(t j ) and Q(t j ) are plotted on the x-y coordinate, two
unknown constants, i.e., the reactivity and the source strength, can be determined
from the least-squares fitting of Eq. (2.53) to these data. By applying the LSIKM to
beam trip data, Eq. (2.53) is reduced to
N (t j ) =
Λ
β − ρ
Q (t j ),
(2.55)
where the source strength is set to zero.
The delayed neutron data and prompt-neutron generation time of the present
reactor system were generated using the SRAC code system [34], where a threedimensional, 19-energy-group diffusion calculation was done with JENDL-3.2
nuclear library [35].
2.3.2.2 Integral Count Technique
The integral count technique has been frequently employed to determine the subcriticality from a source jerk experiment and a rod drop one [31, 36]. When a neutron
source is rapidly taken out of a subcritical reactor core or a control rod is dropped
into a critical core at t = 0, the reactivity of the core can be expressed as
ρ = −
6
k = 1
β k
λ k
N (0)
∫
∞
0 N (t) dt
.
(2.56)