correlated component. In the nearly critical system, we obtain α ¼ 172 (s
À1 ) and
178 (s
À1 ) from the uncorrelated and correlated component, respectively, for the true
fundamental mode α value of 179 (s
À1 ) [15].
12.4 Conclusions
In a subcriticality measurement for an ADS, the Feynman Y function in general
appears as the sum of the correlated and uncorrelated components. The highermode effect in the correlated component is less significant than in the uncorrelated
component. Thus, a relatively good approximation of the true fundamental mode α
can be obtained by using the correlated component. However, it is not necessarily
easy to separate the correlated component from the measured Feynman Y function.
Considering the difficulty of separating the correlated component, the Feynman-α
method is not always suitable as a subcriticality measurement technique for ADSs.
In an ADS that is nearly critical, the uncorrelated component is very minor. Thus,
by fitting the measured Feynman Y function to the correlated component, the
fundamental mode α can be accurately estimated.
In a subcriticality measurement using the power spectral density method, the
uncorrelated component emerges at the integer multiples of the pulse frequency as
delta-function-like peaks. Thus, the uncorrelated component can be easily discriminated from the correlated component. The correlated component is less contaminated by the higher-order modes. An approximate fundamental mode α can be
obtained by fitting the Feynman Y function to the correlated component of the
power spectral density. The use of the uncorrelated component is not always
recommended, because the higher-order modes are more significant in the
uncorrelated component.
–1.0E+05
0.0E+00
1.0E+05
2.0E+05
3.0E+05
4.0E+05
5.0E+05
1
10
100
1000
Frequency (Hz)
Fundamental
1st higher
2nd higher
Re[CPSD
C (w) + CPSD
CS (w)] (/s)
Fig. 12.8 Mode components of the correlated component in the CPSD in the nearly critical
system (real part)
12 Theory of Power Spectral Density and Feynman-Alpha Method. . .
127
À1 ) and
178 (s
À1 ) from the uncorrelated and correlated component, respectively, for the true
fundamental mode α value of 179 (s
À1 ) [15].
12.4 Conclusions
In a subcriticality measurement for an ADS, the Feynman Y function in general
appears as the sum of the correlated and uncorrelated components. The highermode effect in the correlated component is less significant than in the uncorrelated
component. Thus, a relatively good approximation of the true fundamental mode α
can be obtained by using the correlated component. However, it is not necessarily
easy to separate the correlated component from the measured Feynman Y function.
Considering the difficulty of separating the correlated component, the Feynman-α
method is not always suitable as a subcriticality measurement technique for ADSs.
In an ADS that is nearly critical, the uncorrelated component is very minor. Thus,
by fitting the measured Feynman Y function to the correlated component, the
fundamental mode α can be accurately estimated.
In a subcriticality measurement using the power spectral density method, the
uncorrelated component emerges at the integer multiples of the pulse frequency as
delta-function-like peaks. Thus, the uncorrelated component can be easily discriminated from the correlated component. The correlated component is less contaminated by the higher-order modes. An approximate fundamental mode α can be
obtained by fitting the Feynman Y function to the correlated component of the
power spectral density. The use of the uncorrelated component is not always
recommended, because the higher-order modes are more significant in the
uncorrelated component.
–1.0E+05
0.0E+00
1.0E+05
2.0E+05
3.0E+05
4.0E+05
5.0E+05
1
10
100
1000
Frequency (Hz)
Fundamental
1st higher
2nd higher
Re[CPSD
C (w) + CPSD
CS (w)] (/s)
Fig. 12.8 Mode components of the correlated component in the CPSD in the nearly critical
system (real part)
12 Theory of Power Spectral Density and Feynman-Alpha Method. . .
127