M. E. Farrar
Westinghouse Savannah River Company
Aiken, SC 29808

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The HBL NaI Monitoring system was developed and installed in the mid 1980’s by Los Alamos National Laboratory (LANL) for monitoring of plutonium solutions in various location throughout HBL Phase II. The system was put in a state of warm standby when the decision not to start Phase II was made and has remained in that state ever since. HBL Phase II Engineering group requested the Instrumentation & Examination Systems group (I&ES) upgrade the system to be Y2K compliant and Windows compatible. This document describes the equations and algorithms to be used to calculate plutonium mass or concentration as a function of the count rate in the region of 375 KeV – 425 KeV.

The NaI Monitoring system provides information on the amount of plutonium present in various vessels when the vessels are fully charged or emptied down to the heels. Assays of the various vessels are made using 15 NaI detectors distributed throughout the facility, each one mounted and shielded to monitor a specific vessel. In certain cases the vessels being monitored are piping, in which case the concentration of solution is measured and reported. NaI detectors are used to monitor the following locations:

In the Phase III Control Room are located three racks of instrumentation. Two of the racks consist of a high voltage power supply, stabilized amplifier, single channel analyzer (SCA), and count rate meter (CRM) for each detector. The high voltage power supply provides bias voltage to the detector. The signal from the detector is fed into the stabilized amplifier; stabilization is performed on the alpha decay peak of a ²⁴¹Am seed on the NaI crystal. The output of the stabilized amplifier feeds the SCA and a multi-channel buffer (MCB) in parallel. The SCA is set to pass pulses in the region of interest corresponding to ²³⁹Pu (375 – 425 keV). The pulses passed by the SCA go to the CRM, which alarms when the rate exceeds the setpoint. The MCB collects and processes the gamma ray spectra from each detector, under the control of a Windows compatible computer. The computer acts as an operator interface to the MCB, analyzes the spectra from each detector, and calculates the gram mass or concentration of plutonium in the vessel.

Gamma rays from the vessel solution are counted by the MCB and sorted by energy into channels. Regions of interest are defined in the software in areas where gamma rays of interest are predominant. For ²³⁹Pu, the region of interest is in the 375 keV to 425 keV range. Additional regions of interest used for analysis include ²⁴¹Am (60 keV), ²⁴¹Am (1.3 MeV alpha-equivalent gamma peak), and ¹³⁷Cs (662 keV). The cesium peak is used only with the Transfer Line where a cesium source is installed as a transmission source. The transmission source is used in the analysis to correct for voids in the liquid, which will reduce the apparent concentration.

The spectral data collected by the MCB is transferred to the computer. Compton background radiation is subtracted from each region of interest on a channel by channel basis. The background is calculated by taking the average of two small background regions of interest on each side of the peak. These background regions are defined in the parameter database along with the regions of interest for each peak. The plutonium peak is an exception to this in that there is only one background region of interest used. Corrections are then made for dead time and pulse pile up. The alpha decay peak of the ²⁴¹Am seed is used to determine the dead time correction factor. The parameter database contains the net area (after background correction), centroid, and FWHM for the ²⁴¹Am seed for an assay. These values are used to evaluate the validity of the data collected. Values outside the limits set by engineering could indicate a shift in amplifier gain or some other electronic failure.

All of the algorithms described here are derived from the General Process description given in Appendix A of the "HB-Line NaI Monitor Array System User Manual", LA-UR0870187. Additionally, the processes used here are described in detail in "Passive Nondestructive Assay of Nuclear Materials", NUREG/CR-5550. Except for the deviations defined below, differences in the calculations from the process described in HB-Line NaI Monitor Array System User Manual, Appendix A are due to differences in approach and do not affect the final determination of plutonium mass or concentration.

The original process description included subtraction of "physical background". This background is defined as background due to other sources of radiation in the vicinity of the detector. This background is not used because it requires that the radiation sources in the vicinity of the detector are characterized and fossilized prior to introducing materials to the vessel in question. Performing this characterization anytime after introduction of radioactive materials to the vessels would necessarily introduce more error than it corrected because it would include any material not previously flushed from the vessel being monitored. In addition, the background sources in an operating facility can change on a daily basis causing the background subtraction to introduce another additional error source. Therefore, although the subtraction of a well-characterized physical background would improve the calculation, determination of that background to any degree of certainty is not practical.

The original process description included using a three-point curve smoothing prior to calculating the centroid. It was determined that even though analytically it is obvious that smoothing the curve will result in a more precise determination of the centroid of a peak, from a practical standpoint the additional precision is not significant. In addition, although Appendix A of the User Manual does not explicitly describe it, the software calculates and reports the centroid for all ROI’s. Since the ²⁴¹Am seed peak is the only centroid that is used in the analysis, calculation of all centroids was dropped from this version of the software.

Although the area of a ROI is not used in the analysis, the equation is generic and is used in several places where it may be labeled as NetArea, NetArea_Corrected, etc.

[1] Area =

Where P_LC = Left most channel number of peak ROI
           P_RC = Right most channel number of peak ROI
   Counts(i) = Number of counts in absolute channel i

The background is the region in the peak ROI below the line defined by the average counts/channel in the high and low background ROI’s. The Pu²³⁹ background is a special case of this in that it is a horizontal line through the average counts/channel of only the high background ROI.

Calculate average counts/channel in background ROI’s.

[2] Avg =

Where LC = Left most channel of background ROI
           RC = Right most channel of background ROI

[3] Background =

Where Avg_High = Average counts/channel in background ROI above peak ROI
               Avg_Low = Average counts/channel in background ROI below peak ROI

The background is then subtracted from each channel in the peak ROI.

[4] Netcounts(i) = Counts(i) – Background

Where i = Absolute channel number within span of peak ROI
Background = Average background for peak ROI

2.2.3 Calculate Decay Correction Factor

The Decay Correction Factor (DCF) adjusts the count rate of a given source for decay of the source since a reference assay has been performed. As a result, the DCF serves to normalize assay data prior to calculating dead time or attenuation factors.

[5] DCF =

Where DCF = Decay Correction Factor
l = Decay constant for given source
T = Elapsed time since reference assay in days

Because the process is random, gamma rays may enter the NaI crystal at the same time or close enough to each other that the electronics will not be able to process both pulses. The effect is a net loss in the number of counts detected. A correction for this loss can be made by taking the ratio of the count rate of your measurement at a reference source peak to the count rate of the reference source peak when no other source is present. The reference source peak used in this application is the ²⁴¹Am alpha-equivalent peak. For this equation to be explicitly correct, the DCF for the reference assay, when no other source is present, must be included. However, the reference assay used here is also the reference assay for calculation of decay correction; therefore, the DCF for the reference assay is by definition 1.

[6] DTC =

Where NetArea_Ref(AmSeed) = The net area, after subtracting background, of the Am²⁴¹
Seed taken during a reference assay
NetArea (AmSeed) = The net area, after subtracting background, of the Am²⁴¹
Seed taken during the measurement assay
RT = The actual elapsed assay time

[7] NetArea_Corrected(Peak) = NetArea(Peak)*DTC

Where NetArea(Peak) = Background subtracted area for a given peak ROI

[8] CountRate(Pu) = NetArea(Pu)/RealTime_Assay

Where RealTime_Assay = Elapsed time during which data was taken.

[9] Pu²³⁹ = A*CountRate(Pu)² + B*CountRate(Pu) + C

Where A, B, and C = Calibration constants determined by Monte Carlo simulation and/or experimentation.

If the vessel being assayed is a tank there are two sets of valid calibration constants, one for a full tank and one for empty. Full and empty are defined here as the high and low limits, respectively, for each vessel. Note that these calibration constants are not valid for any other level in the vessels because the calibration constants take into account the volume of the tank at the given level.

To calculate the total Pu mass the isotopic ratios, by weight, must be known. These values will be determined by sampling each batch. The operator will be prompted to input the batch id and the ratio of Pu²³⁹ to total Pu. The calculation of total Pu is then:

[10] PuMass_Total = Pu²³⁹/%Pu²³⁹

Where %Pu²³⁹ = Pu²³⁹/Pu_Total

The calculation of Pu mass in tanks and transfer lines are identical up to equation [7]. Calculation of the concentration of PU in the transfer line requires the following additional corrections.

Am²⁴¹ has a small gamma peak within the Cs¹³⁷ ROI. The actual number of counts can be estimated as a fraction of the Am²⁴¹ 60 KeV peak. The fractional value, f_A, is dependent on the relative intensity of the two gammas and the relative attenuation factors. The value of the fraction will be calculated using Monte Carlo and maintained in the parameter file.

[11] CsNoAm = NetArea_Corrected(Cs) – f_A * NetArea_Corrected(Am)

Where CsNoAm = Cs¹³⁷ peak corrected for Am²⁴¹ contribution.
NetArea_Corrected(Am) = Am²⁴¹ 60 KeV peak area corrected for background and dead time.

Because of the large background in the vicinity of the Am²⁴¹ 60 KeV peak the minimum level detectable (MLD) in that area is very large and, in fact, negative peak areas may be calculated. The result of a negative peak area is that correcting for Am²⁴¹ in the CS peak could cause an increase in Cs¹³⁷ net area. Since this situation is not physically possible, for any case in which the Am²⁴¹ 60 KeV peak is negative, the peak area will automatically be set to zero.

The Pu²³⁹ self-attenuation is calculated based on the attenuation of Cs¹³⁷ using the relationship described in the PANDA manual, pages 186-187, eq. 6-23. The first step is to calculate the transmission of Cs¹³⁷ through an empty pipe. The calculation is based on experimental data from a Cs¹³⁷ source through an empty pipe of the same configuration as that used in the facility and without the pipe attenuation.

[12] T_Pipe[Cs] =

Where Area_Pipe(Cs) = The net area of the Cs peak when attenuated by the empty pipe.
Area_NoPipe(Cs) = The net area of the Cs peak when the empty pipe is removed and all other aspects of the geometry are maintained constant.
Area_Pipe(Cs) and Area_NoPipe(Cs) will be maintained in the parameter file.

The transmission through the solution and pipe is calculated using the following equation.

[13] T_t(Cs) =

Where = Net area, corrected for background and dead time, of the Cs¹³⁷ peak. This value will be determined based on a reference assay taken in the facility when the pipe is empty.
RealTime_CsReference = Real time of reference assay discussed above.

The transmission through the solution only is then the ratio of total transmission to the transmission of the pipe only.

[14] T_Sol[Cs] =

The transmission of Pu²³⁹ can be found by raising the transmission factor of Cs¹³⁷ to the ratio of the linear coefficients of Pu²³⁹ and Cs¹³⁷ in nitric acid solution.

[15] T_Sol(Pu) =

Where µ_Sol = Linear attenuation coefficient in nitric acid solution for Cs¹³⁷ and Pu²³⁹, respectively.

Experimental values for the linear attenuation coefficients are readily available in the literature and will be maintained in the parameter file.

[16] T_Pipe(Pu) =

Where µ_Pipe = Linear attenuation coefficient of the stainless steel pipe for Cs¹³⁷ and Pu²³⁹, respectively.

The self attenuation correction factor can now be calculated using the following equation.

[17] CF(att) =

Where k = Pi/4

The Transfer Line total corrected area then becomes;

[18] TCA = CF(att) * NetArea_Corrected(Pu)

The total Pu concentration is calculated using equations [9] and [10] substituting TCA for NetArea_Corrected[Pu].

Perform a 3 point average of the spectrum. This will smooth the data minimizing the possibility of skewing the FWHM or centroid.

Find the maxima in netcounts(i) for the AmSeed ROI.

Calculate the half-maxima as:

[19] HM = Maxima/2

Compare HM to the counts in each channel to the left of the maxima until the netcount(i) drops below HM. Interpolate position of HM and label the channel number as LHMC.

Compare HM to the counts in each channel to the right of the maxima until the netcount(i) drops below HM. Interpolate position of HM and label the channel number as RHMC.

[20] FWHM = RHMC – LHMC

The centroid calculation is performed using the same smoothed data used for the FWHM calculation.

[21] Centroid =

Where channel (i) = Absolute channel number
netcounts (i) = Counts in channel i
LC = LHMC rounded down to the nearest integer
RC = RHMC rounded up to the nearest integer

The equations documented in this report will be used to calculate the concentrations and/or mass of plutonium as a function of count rate for the NaI Monitoring System in HBL. The software developed using these equations will also be adapted for the Portable NaI Monitoring System, which is used to monitor other locations in HBL that do not require monitoring on as frequent a basis as the locations in the permanent detector locations. These equations are based on the equations used in the original version of the NaI Monitoring System software which was provided by Los Alamos and is described in references 1 – 3. Additional details of the measurement and analysis techniques used can be found in references 4, 5, and 6.

1. Simmonds, Stanley M. and Rinard, Phillip M., HB-Line NaI Monitor Array System Users Manual, LA-UR-87-387, November 25, 1986.
2. Simmonds, Stanley M., et al, HB-Line Sodium Iodide Monitor Assay Hardware Manual, LA-UR-87-386, November 26, 1986.
3. Schneider, Constance M., HB-Line NaI Monitor System Software Manual.
4. Reilly, Doug, et al, editors, Passive Nondestructive Assay of Nuclear Materials, NUREG/CR-5550, March 1991.
5. Knoll, Glenn F., Radiation Detection and Measurement, Second Edition, 1988.
6. Auguston, R. H. and Reilly, T. D, Fundamentals of Passive Nondestructive Assay of Fissionable Material, LA-5651-M, June 1974.