MEAN-SQUARE-VOLTAGE (MSV) METHODS[15]

5- 5.1 Basis of Method

The MSV method depends on the fact that, if the time distribution of pulses from a nuclear radiation sensor is a Poisson distribution, the variance (mean of the squares of the deviations from the mean) is a direct measure of the mean. (See Table 5.1 for relevant definitions and formulas ) For all practical purposes this condition is met by boron and fission counting chambers

There are at least three advantages to be gained from using MSV methods increased gamma discrimination (com­pared to compensation), improved operation when cham­bers and cables are exposed to elevated temperatures, and more efficient use of chambers (sensors).

So that the advantages of the method can be realized, a measure of a quantity proportional to the square of the charge (or current) is made. One way to do this is to subtract the mean signal with a differentiator and measure the temperature rise in a resistor, as is done in a true root-mean-square meter commonly used in the shop or laboratory Another way is to pass the variable (a-c) signal through a half — or full-wave rectifier measuring, as a result, the average magnitude or average magnitude squared This latter technique is accurate at only one frequency for which a correction factor can be applied More generally, the pulses can be passed through an electronic squaring amplifier and the output read without correction as a linear measure of the mean square If a mean-square signal is sent to a log converter circuit, the output is again proportional to the log of the mean.

5- 5.2 Gamma Discrimination

Gamma discrimination must be compared with “com pensation” for gammas as accomplished in the CIC dis­cussed in Sec 2-2 2 of Chap 2. In a CIC a compensating signal generated in a volume not sensitive to neutrons is subtracted electrically from the gamma-plus-neutron signal In practice the compensating volume and the mass of material forming the neutron and compensating volumes cannot be matched exactly, through engineering com­promise the compensation is usually between 95 and 99% of the gamma signal Although m theory the compensation could be much better, it just cannot be achieved Commer­cial units use two concentric volumes that are adjusted so that overcompensation in some gamma range is avoided. Overcompensation would result in negative readings and confusion to control-system functions Manufacturers usu-

Table 5.1—Poisson Distribution Definitions and Formulas

Definitions

n = number of events observed n = average (mean) number of events observed n — n = deviation from mean

= deviation of the observed number of events from the

average

(n — n)2 = a2

= variance

= mean of the squares of the deviations

Formulas

Poisson distribution

e"nn

P(n)=————

n1

L p(n)= і

n=0

(2)

For Poisson distribution

n = Г nP(n) = n n=0

(3)

n2 = £ n2P(n) = n2 +n n=0

(4)

o2 = £ (n — n)2 P(n) = n2 — n2 n=0

Substitute (4) into (5) and obtain

(5)

a2 = n

(6)

Note If n is the number of counts indicated by a sensing device in a given time interval, then n = count rate x time interval____________________________

ally guarantee a gamma/neutron signal ratio of 1/20 and a maximum of 1/100, the latter to avoid overcompensation With MSV methods the compensation or discrimination is not dependent on the mechanical construction of the chamber Only one ionization volume is involved, arj advantage is taken of the charge ratio of a fission fragment to a gamma-scattered beta particle If the number of events is N per unit time and the charge collected per event is Q, then an average voltage Ej c is developed

Ed-c = NQ/0 h(t) dt (5.4)

where N is the mean number of events, Q is the mean charge per event, and h(t) is the circuit response to a single pulse of unit charge. By definition the mean-square voltage is

Ems = (Ed-c)2 +NQ2 /„ [h(t)l 2 dt (5 5)

The voltage E<j. c is made zero if h(t), the circuit response, is limited to acceptance of a-c signals alone In this case

Ems = N Q2 /о [h(t)] 2 dt (5 6)

Подпись: (5.7)Подпись: (5.8)Подпись:Подпись: DmsIt is not difficult, as indicated earlier, to make the circuit such that Ems is the lone acceptable result. A differentia­tion circuit at the input of the squaring circuit will do the job.

The relation between the resulting signals can be established if a chamber operating in the d-c mode is compared to a similar chamber operating in the MSV mode. If a subscript n is used for neutron events and a subscript (3 for gamma effects (since gammas scatter /3 particles or electrons into the chamber), the discrimination in the d-c mode for gammas is (from Eq. 5.4)

NnQn

КрЦз and the discrimination for the MSV mode is

NnQn

ЩЩ

The ratio of the discriminations is thus

Dms _ Qn Off ~ Qn (5

Dd-c Qn Q/3 0)3

The ratio Qn/Q| has been set equal to (Qn)2/(О/з)2 m deriving Eq 5.9 since it can be shown that in practical cases this is a good approximation.

The ratio Qn/Qd is about 103 for a fission chamber Compared to a compensated chamber, this means an assured 103 discrimination against gammas instead of the 20 to 100 In practice, experimental results show a nearly hundredfold improvement in gamma discrimination, mainly because the 1/20 ratio of gamma to neutron signal is more realistic for a CIC than the 1/100 ratio.

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