32
K. Hashimoto
From a least-squares fit of Eq. (2.47) to peak data at frequency of the integral
multiple of f R , the prompt-neutron decay constant α and coefficient C 2 can be
determined.
Next, a well-known effect of a higher mode excited by the injection of pulsed
neutrons [10–12] should be considered. Sakon et al. employed the following equation
to consider the effect successfully [12, 23].
Φ 12 (n f R )
C 2
(2 π n f R )
2
+ α 2 +
C 2H
(2 π n f R )
2
+ α
2
H
, n = 1, 2, 3, . . . . (2.48)
When certain a higher prompt mode as well as a fundamental prompt mode are
excited, such a higher term as the second term of the above equation can be added
to the fundamental term of the power spectral density [25–27]. The prompt-neutron
decay constant of the higher mode is represented by α H . The coefficient C 2H includes
the eigenfunction and the adjoint eigenfunction of the higher prompt mode. We try
to apply Eq. (2.48) as well as Eq. (2.47) to derive the fundamental decay constant α
from the uncorrelated peaks.
When the uncorrelated peaks of the cross-power spectral density are masked,
Eq. (2.45) can be reduced to the following equation for the remaining data unmasked:
Φ 12 ( f ) =
C 1
(2 π f )
2
+ α 2 .
(2.49)
From a least-squares fit of Eq. (2.49) to the unmasked data, the prompt neutron
decay constant α and coefficient C 1 can be also determined. The above equation
gives an expression to the correlated noise component and is identical to the familiar
formula for a stationary neutron source.
2.2.3 Results and Discussion
2.2.3.1 Power Spectral Density
Figure 2.15a, b show measured auto-power spectral density of counter B1 and crosspower spectral density between neutron detector B1 and B2, respectively, where
subcritical pattern is F. The auto-power spectral density is composed of a continuous
correlated component, another constant chamber noise and many delta-function-like
peaks at the integral multiple of the repetition frequency, as expected by Eq. (2.41).
The correlated component tends to be hidden by the white chamber noise with an
increase in frequency and this feature suggests a difficulty in estimating the break
frequency, i.e., the prompt-neutron decay constant.
On the other hand, the cross-power spectral density has no white chamber noise,
expected by Eq. (2.37). The correlated component is larger than one decade (20 dB).
This feature is significantly different from that of the auto-power spectral density as
K. Hashimoto
From a least-squares fit of Eq. (2.47) to peak data at frequency of the integral
multiple of f R , the prompt-neutron decay constant α and coefficient C 2 can be
determined.
Next, a well-known effect of a higher mode excited by the injection of pulsed
neutrons [10–12] should be considered. Sakon et al. employed the following equation
to consider the effect successfully [12, 23].
Φ 12 (n f R )
C 2
(2 π n f R )
2
+ α 2 +
C 2H
(2 π n f R )
2
+ α
2
H
, n = 1, 2, 3, . . . . (2.48)
When certain a higher prompt mode as well as a fundamental prompt mode are
excited, such a higher term as the second term of the above equation can be added
to the fundamental term of the power spectral density [25–27]. The prompt-neutron
decay constant of the higher mode is represented by α H . The coefficient C 2H includes
the eigenfunction and the adjoint eigenfunction of the higher prompt mode. We try
to apply Eq. (2.48) as well as Eq. (2.47) to derive the fundamental decay constant α
from the uncorrelated peaks.
When the uncorrelated peaks of the cross-power spectral density are masked,
Eq. (2.45) can be reduced to the following equation for the remaining data unmasked:
Φ 12 ( f ) =
C 1
(2 π f )
2
+ α 2 .
(2.49)
From a least-squares fit of Eq. (2.49) to the unmasked data, the prompt neutron
decay constant α and coefficient C 1 can be also determined. The above equation
gives an expression to the correlated noise component and is identical to the familiar
formula for a stationary neutron source.
2.2.3 Results and Discussion
2.2.3.1 Power Spectral Density
Figure 2.15a, b show measured auto-power spectral density of counter B1 and crosspower spectral density between neutron detector B1 and B2, respectively, where
subcritical pattern is F. The auto-power spectral density is composed of a continuous
correlated component, another constant chamber noise and many delta-function-like
peaks at the integral multiple of the repetition frequency, as expected by Eq. (2.41).
The correlated component tends to be hidden by the white chamber noise with an
increase in frequency and this feature suggests a difficulty in estimating the break
frequency, i.e., the prompt-neutron decay constant.
On the other hand, the cross-power spectral density has no white chamber noise,
expected by Eq. (2.37). The correlated component is larger than one decade (20 dB).
This feature is significantly different from that of the auto-power spectral density as