- Email: [email protected]
Negative reactivity measurements using random source excitation and autocorrelation techniques
Transactions
of the symposium on noise analysis
17
in nuclear systems
Paper No. 3-2
NEGATIVE REACTIVITY MEASUREMENTS USING RANDOM SOURCE EXCITATION AND AUTOCORRELATION TECHNIQUES J. VALAT* Centre d’Etudes Nuckaires de Saclay, Saclay, France THE object of this work is to obtain a smaller statistical error compared to that of previously used methods. In the previous work efforts have been made to obtain a higher correlation function for a given correlation technique, that is, the crosscorrelation between the input and the output. In this abstract a better use of a given random excitation (random square waves, rectangular Poissonian pulses) has been presented. First, the auto-correlation of the output (counting rate) when the reactor is excited by a given random input is suggested. The auto-correlation of the output without excitation is not practicable if the negative reactivity is less than about five dollars. By computing the variance of the square of a Poissonian counting rate, it is possible to find, for strong external sources, that R,,, the relative statistical error in case of auto-correlation, is related to Rio, the relative statistical error in case of cross-correlation by R=-
M*Rio A4
where MOis the total counting rate and M is the counting rate due to the mean value of the excitation. Unfortunately, this method is not satisfactory for reactors with strong internal sources. By applying the classical cross-correlation technique, where the results obtained, for instance the impulse response, are auto-correlated, we may obtain smaller statistical errors. Let us suppose for simplicity the cross-correlation gives the impulse response h(u) M l?(u) exp [-MU] with a large statistical error but no systematic error. impulse response, we find
If we auto-correlate
AA7) = $ exp (--ET) (1 - exp [-24T
the true
- T)]}
which gives a smaller statistical error, but extracting the information is more difficult. Experiments are under way and encouraging. * Presented by T. STERN. 2
of the symposium on noise analysis
17
in nuclear systems
Paper No. 3-2
NEGATIVE REACTIVITY MEASUREMENTS USING RANDOM SOURCE EXCITATION AND AUTOCORRELATION TECHNIQUES J. VALAT* Centre d’Etudes Nuckaires de Saclay, Saclay, France THE object of this work is to obtain a smaller statistical error compared to that of previously used methods. In the previous work efforts have been made to obtain a higher correlation function for a given correlation technique, that is, the crosscorrelation between the input and the output. In this abstract a better use of a given random excitation (random square waves, rectangular Poissonian pulses) has been presented. First, the auto-correlation of the output (counting rate) when the reactor is excited by a given random input is suggested. The auto-correlation of the output without excitation is not practicable if the negative reactivity is less than about five dollars. By computing the variance of the square of a Poissonian counting rate, it is possible to find, for strong external sources, that R,,, the relative statistical error in case of auto-correlation, is related to Rio, the relative statistical error in case of cross-correlation by R=-
M*Rio A4
where MOis the total counting rate and M is the counting rate due to the mean value of the excitation. Unfortunately, this method is not satisfactory for reactors with strong internal sources. By applying the classical cross-correlation technique, where the results obtained, for instance the impulse response, are auto-correlated, we may obtain smaller statistical errors. Let us suppose for simplicity the cross-correlation gives the impulse response h(u) M l?(u) exp [-MU] with a large statistical error but no systematic error. impulse response, we find
If we auto-correlate
AA7) = $ exp (--ET) (1 - exp [-24T
the true
- T)]}
which gives a smaller statistical error, but extracting the information is more difficult. Experiments are under way and encouraging. * Presented by T. STERN. 2