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Gamma spectrometry of short living fission products in fuel pins
Nuclear Instruments and Methods in Physics Research A 739 (2014) 55–62
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Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Gamma spectrometry of short living fission products in fuel pins Marie Švadlenková a,n, Lenka Heraltová b, Vlastimil Juříček a, Michal Košťál a, Evžen Novák a a b
Research Centre Rez, Ltd., Hlavni 130, 250 68 Husinec-Rez, Czech Republic Czech Technical University, Faculty of Nuclear Sciences and Physical Engineering, Brehova 7, 115 19 Prague 1, Czech Republic
art ic l e i nf o
a b s t r a c t
Article history: Received 12 November 2013 Received in revised form 6 December 2013 Accepted 7 December 2013 Available online 21 December 2013
A method of measurement and analysis of gamma spectra of short living fission products of lightly irradiated fuel pins has been developed at facilities at the LR-0 zero-power experimental reactor. Experimental and computational methods of the peak area correction for radioactive decay are described. Selection of energy peaks suitable for deriving power distribution in the core was performed. & 2013 Elsevier B.V. All rights reserved.
Keywords: Gamma spectrometry Research reactor Fuel pin Fission products MCNPX
1. Introduction The zero-power light-water research reactor LR-0 is used mainly for measurements of physical neutron characteristic of VVER and PWR-type reactors (see a scheme of the LR-0 reactor in Fig. 1). The advantage of the LR-0 is in its versatility, which allows carry out experiments with variable numbers of fuel assemblies in reactor core, variable fuel enrichment or variable concentration of H3BO3 in moderator and many others [1]. One of the main tasks of the LR-0 is the measurement of parameters that can be used in reactor dosimetry. It is similar to the using of other low power reactors, e.g., [2–5]. Reactor dosimetry topics demand a correct description of the power distribution in the reactor, especially in its marginal parts. For this reason the LR-0 is used for the determination of neutron fluence distribution in fuel pins and fuel assemblies through measurements of the fission products activity induced in the fuel. The increase of the induced activity in a particular region of the reactor is directly related to the density of uranium fission in the same region and therefore to the fuel pin activity increasing. The determination of neutron fluence and power distribution in the reactor core is possible by means of axial and radial measurements of fuel pin gamma activity. The distribution of fission products activities in fuel pins is measured by two methods at LR-0:
Integral method—in a specific energy interval, using a scintillation detector with one-channel analyzer [6] n
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Spectrometric method—where the spectrum of gamma radiation is measured, while individual energy peaks and radionuclides are analyzed.
The spectrometric method described here uses an HPGe semiconductor detector with multi-channel analyzer and the analysis of gamma spectra after short-time fuel pin irradiation in the LR-0 reactor is performed.
2. Materials and methods 2.1. Fuels pins Fuel pin cladding is an alloy composed of zirconium (98.97%), niobium (1%) and hafnium (0.03%) with average density of 6.44 g cm 3. Fuel column (inside the cladding) with length of 1250 mm is composed of uranium pellets of cylindrical annulus shape with inner radius of 1.4 mm and with outer radius of 7.5 mm. The height of the pellet is about 9.7 mm. The uranium fuel is enriched by 235U in the range from 1.6 to 4.4 wt%. The corresponding fuel density is between 10.33 and 10.35 g cm 3. A diagram of the fuel pin is in Fig. 2. After the reactor shut-down, selected irradiated fuel pins are transferred (under the radiation protection measure for handling with irradiated pins) to a fuel pin workplace. The place is located close to a laboratory for gamma scanning of the fuel pins and is not influenced by the radiation of the reactor.
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Fig. 1. The scheme of the LR-0 reactor—horizontal cross-section.
2.2. Equipment for gamma scanning of fuel pins A spectrometric device with coaxial high purity germanium detector HPGe (Ortec, GEM70) and multichannel analyzer DSA 2000 (Canberra) is used for the measurement of fuel pins. HPGe crystal has diameter of 74.6 mm and length of 87.9 mm, FWHM resolution at 1.33 MeV is about 2 keV and the Peak-to-Compton ratio for 60Co is approximately 75:1. The DSA-2000 analyzer is 100% controlled by computer using Genie 2000 [7] spectroscopy software platforms via the in-built Ethernet interface. The HPGe detector is horizontally attached to a cryostat (resp. Dewar vessel) and is inserted into a massive lead shielding with a collimator. The width of the collimator window is of 1 cm and the height is adjustable to 2, 3, or 5 cm, which makes it possible to measure gamma radiation from a specific part of the fuel pin. In some cases, a two-layer plate (lead with thickness of 3.3 mm and copper with thickness of 1 mm) is inserted between the fuel pin and the collimator window. The plate absorbs mainly low energy component of gamma spectrum and thus reduces the number of photons incident on the detector. As a result, the dead time of the detector is decreased which is desirable for more irradiated pins. The position of the HPGe detector in the shielding is depicted in Fig. 3. The shielding with collimator was optimized, so that only the gamma photons of the fuel pin part that faces directly the collimator window are registered. Nevertheless, since the shielding is not ideal and its throughput is not zero, the gamma radiation from fuel pin parts above and below the collimator window still falls partly on the detector. Therefore, experiments and MCNP calculations were performed in order to determine the extent of throughput of the shielding and the corresponding correction coefficients (see below). The experimental arrangement for scanning of fuel pins is shown in Fig. 4. The equipment consists of stand, precise helices, stepper motor, coupling and special fixing for fuel pin. Fuel pin is
Fig. 2. Diagram of the LR-0 fuel pin of VVER type; three times shortened in comparison with real VVER pin.
Fig. 3. The position of the HPGe detector in the shielding.
hung on a holder and can perform sequential axial movement around the collimator window. Fuel pin movement and positioning are controlled by special software DASAVR (RC Rez) with an accuracy of 0.5 mm. Fuel pin measured in a given position performs a rotary movement to average possible inhomogeneity of irradiation in its cross-section. This inhomogeneity plays a role for fuel pins at the periphery of the core. The calculation result for peripheral pins is in Fig. 5
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The GammaScan software (based on Delphi 6PE platform) was developed for automatic measurement of fuel pins. It collaborates with programs DASAVR and Genie-2000 (including its superstructure Batch Tools). 2.3. Fuel pins measurement and gamma spectra analysis
Fig. 4. The experimental arrangement for gamma scanning of fuel pins.
Fig. 5. Inhomogeneity of the fuel pins for four 90º circular arcs in the radial section.
where the relative detector response for four 901 circular arcs in the radial section of fuel pins is shown. The DASAVR data acquisition system installed on host PC allows to control up to three spectrometric devices and performs the following basic operations:
Loading of gamma spectra into the analyzer (e.g., DSA 2000) Storing the gamma spectra into a separate directory with other
information about the single measurement, e.g., position of pin, time, name of spectra Generating of commands for stepper motors Kinex control device, setting the step rate and start acceleration.
Parameters of measurement were set in such a way that the energy range and the shape of the spectrum were optimal for the performed experiments. The measurements were performed in energy range from 60 to 2500 keV. The point standard sources (type EG3, Eurostandard-Praha) with activity of the order of 105 Bq (60Co, 88Y, 133B, 137Cs, 152Eu and 241Am) were used for energy calibration. The efficiency calibration of HPGe detector for given measurement geometry was calculated. An experimental determination of efficiency would be costly and inefficient due to the complex geometry of fuel pin. The calculation was performed using the code MCNPX (Monte Carlo N-Particle transport code) [8] and also the software module ISOCS [9]. If the technical data of the detector (dimensions, material, etc.) are sufficiently accurate, the result of our MCNPX calculation is more precise in comparison with ISOCS. The reason is that the ISOCS program has a limited number of templates to model the geometry, while MCNPX can model the geometry of the sample (i.e., fuel pin) and the detector with shielding in detail practically without limits. Prior to selected fuel pin irradiation in the LR-0 reactor the residual activity (of the previous irradiation) of each fuel pin is measured. The pins are selected to have sufficiently long interval between irradiation. Then only radionuclides 235U, 234mPa, 226Ra, 137 Cs, 40K and K-line of Pb are present in the residual spectra. Fuel pins are then put into selected positions in the fuel assembly placed in the reactor core. The irradiation time is in the order of hours. The reactor power is roughly in the range from 1 to 10 W. An evaluation of measured spectra was carried out with the software GENIE 2000. To describe the fission density distribution in the core either values of Net Peak Area – NPA (counts) of selected energy peaks in the spectrum or activities – A (Bq) of radionuclides found in spectrum were used. For our calculation, the variable NPA proved more appropriate results because of their greater accuracy. Nevertheless, both values of the NPA and of the A had to be corrected for radioactive decay and possible residual activity. The aim was to select energy lines (peaks) in the spectrum that will be suitable for determining of the reactor core characteristics. First, these were the energy lines or peaks with the highest value of the NPA and with sufficiently long half-live. Then, there were selected either single peaks (that do not form multiplets and could likely belong only to the one radionuclide) or multiplets whose composition can be uniquely determined. 2.4. Correction for radioactive decay Correction for radioactive decay was necessary because the time between reactor shutdown and the end of measurements of irradiated pins was comparable with a half-life of selected fission products, i.e., tens to hundreds of minutes. The correction was performed by experiment or calculation. The experimental method of decay correction used for the determination of relative power distribution in the reactor is based on simultaneous measurement of irradiated pins and so called “monitoring pin” (monitor). The monitor is not different from the fuel pins. It is irradiated together with the other pins under the same conditions and then a time series of spectra is measured at one and the same appropriate position of the monitor. Based on the monitor measurements, the decrease rate of the area of a
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selected peak can be calculated and then the decay correction factor derived (see below). Through that factor the area of the same peak in the fuel pin spectra measured at a known time can be then corrected. This method is suitable for the decay correction of all peaks in the irradiated fuel pin spectra because the radionuclides induced in the fuel pins and the monitor are the same. Parallel measurement of monitor and fuel pin is possible, if two independent measurement devices are available. In case, we have just one, it is necessary to interrupt the measurement of the fuel pins at certain time intervals and switch to the measurement of the monitor. Replacement of the monitor for measuring the fuel pin has to be done manually. The procedure described above extends the time of measurement, which is disadvantage for short-lived radionuclides measurement. Decay correction coefficient is related to a reference time, which is usually the time of reactor shutdown or the start of pin series measurement. In the case the count rate is the quotient of the NPA and the time of measurement t, the following relations (1)–(6) can be used for the count rate decay correction of a specific peak in the gamma spectrum. Interpolated count rate of the corresponding peak monitor at time t is: mt ¼ k m2 þð1 kÞ m1 ;
ð1Þ
where k ¼(t t1)/(t2 t1), m1 and m2 are monitor count rates peak areas (closest in time) measured at times t1 and t2. Then, the correction factor CF at time t is CF ¼
mt ; m0
ð2Þ
where m0 is the first measured (reference) count rate of the monitor. Generally, CF can be larger than 1, smaller than 1 or equal to 1 for a specific energy peak, depending on the time course of monitor. The corrected count rate nkt of the peak in the fuel pin spectrum equals: nkt ¼
nt ; CF
ð3Þ
where nt is the uncorrected (measured) count rate of fuel pin. An uncertainty estimation of the corrected count rate was based on the equation for standard deviation of variable y¼ f (x1, x2,…, xn) depending on mutually independent variables ti with standard deviations ϑxi , sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 n ∂y ϑxi : ϑy ¼ ð4Þ ∑ i ¼ 1 ∂xi Then, for the standard deviation of the calculated monitor at time t holds qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ð5Þ ϑmt ¼ k ϑ2m2 þ ð1 kÞ2 ϑ2m1 and for the standard deviation of the fuel pin value nkt the following relationship is valid sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 m0 nt nt m0 ϑnt þ ϑm0 þ ϑ ϑnk ¼ : ð6Þ mt t mt mt m2t Schematic diagram of the experimental arrangement for correction by monitoring pin is in Fig. 6. On the other hand, the theoretical calculation of decay correction requires the assignment of a particular unique radionuclide to a selected energy peak in the spectrum. The possibility of such an assignment was studied by regression analysis where the match of the NPA decreasing rate and of the half-life of anticipated radionuclide was estimated. Four time series of pin spectra irradiated in independent irradiation campaigns were analyzed for this purpose.
Fig. 6. Schematic diagram of the experimental arrangement for correction by monitoring pin: 1- pin line, 2-monitor line.
The selected radionuclide may be the ith member (i¼1, 2,…, n) of a series of n genetically related radionuclides. Correction for decay for such a nuclide can be calculated by solving a system of ordinary first-degree differential equations whose ith term is of the form: dN i ¼ ðλi 1 N i 1 –λi N i Þdt
ð7Þ
The solution of (7) has a form i
Ni ¼ ∑ N ji ; j¼1
ð8Þ
where i1
Nji ¼ N0j ∑ K ir expð λr tÞ þK ii expð λi tÞ r¼j
and N 0j is the number of atoms of the radionuclide j at the time t¼0. In our case, series with up to two radionuclides were selected, i.e., mother and daughter radionuclide. Therefore, one-exponential or two-exponential regression functions were parameterized.
2.5. Correction for shielding throughput Throughput of the lead shielding of the detector for gamma radiation was estimated experimentally and by MCNP calculation. Axial gamma-spectrometric measurements of two pins with either cesium 137Cs or irradiated uranium pellets were performed. The range of axial distance of centre of the pellet from the collimator window was between 8 cm below and 8 cm above the centre of the window. The dimensions of the collimator were 1 2 cm (width height). The uranium pellet with a height of 1 cm was of the same type as pellets in the fuel pins. The cesium pellet of known composition was stored in a case with the dimensions similar to those of uranium pellets, but the active portion had a height of 0.6 cm. The detector response to gamma photons was calculated using the MCNPX code, for the energies of 662 keV (137Cs) and 307, 847, 1384 and 1435 keV (selected from the spectrum of fission products of an irradiated U-pellet) and in different positions of the pellet against the collimator window.
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Results from MCNPX were compared with experimental results. An algorithm for calculating the throughput correction of axial fuel pin measurements was designed.
3. Results and discussion 3.1. Efficiency calibration of measuring system An example of the detector calibration curves calculated by MCNPX for the collimator window of size 1 5 cm (w h) and 1 2 cm is in Fig. 7. The calculation was performed for inserted or ejected absorption plate. It takes also into account the nonuniform axial distribution of activity in the fuel pin after irradiation. The axial distribution calculated by MCNPX for fuel pin irradiated in the center of the LR-0 core is in Fig. 8. The MCNPX calculations show that the height of the window changes not only the maximum of the efficiency curve, but also its shape. For instance, for the window of height 5 cm the maximum is approximately twice as large as that for the window of height 2 cm and is shifted by 0.2 MeV towards lower energies.
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3.2. Throughput of detector shielding The comparison of calculation with experiment for gamma photons with energies of 662 and 1384 keV and for collimator window with a size of 1 2 cm is in Fig. 9. Experimental and calculated values of the shielding throughput are in relatively good agreement. Deviations are within the uncertainties of measured values of the NPA or count rate corrected for decay according to the relation (6). As expected, the throughput of gamma radiation through Pb shielding increases with increasing gamma rays energy. Once the radioactive source reaches the axial edge of the window, i.e. 71 cm from the collimator center, the detected count rate dropped to 80–90% relative to the value in the central position. At a distance of 72 cm the count rate is only about 10% and decreases rapidly with further increasing distance. Let the following conditions apply:
The length of the fuel column in fuel pin is s (cm) The continuous distribution of fuel in the fuel pin is approxi-
mated with equidistant point sources of ionizing radiation, the axial distance of which is d (cm), and therefore we have [s/d] ¼ m point sources along the pin ([s/d] is the integer part of the fraction s/d); let the point 1 lie at the bottom and the point m in the upper part of fuel pin The pin position is such that the jth point source (j ¼1,…,m) is at the center of the collimator window of the detector shielding (x ¼0)
Fig. 7. Detector calibration curves calculated with MCNPX for collimator window of size 1 5 cm and 1 2 cm.
Fig. 9. The comparison of C/E for Eg¼ 662 and 1384 keV and for collimator window with size of 1 2 cm.
Table 1 Values of the shielding throughput correction coefficients CC for several gammaray energies E and distances x from the center of the collimator window.
Fig. 8. Relative count rate axial distribution calculated by MCNPX for fuel pin irradiated in the center of LR-0 core.
E (keV) x (cm) ↓
307 U
662 Cs
847 U
1384 U
1435 U
4 3 2 1 0.5 0 0.5 1 2 3 4
o MDA o MDA 0.0267 0.6929 0.9683 1.0000 0.9728 0.6887 0.0259 o MDA o MDA
0.0017 0.0121 0.1009 0.7030 0.9746 1.0000 0.9990 0.8546 0.1637 0.0194 0.0028
0.0068 0.0283 0.1631 0.7806 0.9078 1.0000 0.9809 0.7770 0.1608 0.0272 0.0068
0.0285 0.0712 0.2459 0.8042 0.9782 1.0000 0.9861 0.8036 0.2417 0.0695 0.0276
0.0299 0.0731 0.2495 0.8053 0.9790 1.0000 0.9879 0.8068 0.2486 0.0734 0.0302
MDA ¼ minimum detectable activity; CC ¼cEði jÞd .
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Fig. 10. Gamma spectrum of a fuel pin irradiated in the LR-0 and measured 1.2 h after the reactor shutdown. Measured without Pb þ Cu plate. Time of irradiation ¼2.5 h, reactor power ¼ 9.5 W.
Table 2 Radionuclides selected from fuel pin gamma spectra measured 1.2 h after irradiation (irradiation period ¼ 2.5 h, reactor power E9.5 W). Radioisotope
Activity (%) Uncert. (%) Key line (keV) T1/2 (h) Decay scheme
134
100.0 98.5 68.2 44.1 29.1
1.0 0.8 1.1 0.9 1.3
847.0 1435.8 767.2 641.3 912.7
0.88 0.56 0.70 1.52 0.92
25.1 19.2 13.9 13.6 8.5 8.4 3.5 5.7 4.9 3.2
0.8 3.9 2.1 1.2 2.0 2.2 5.9 2.1 2.2 5.7
1383.9 402.6 2392.1 1260.4 1024.3 657.9 228.2 743.4 529.9 249.8
2.71 1.27 2.84 6.57 9.63 1.20 3.2 16.9 20.8 9.14
I Cs 134 Te 142 La 133m Te 138
92
Sr Kr Kr 135 I 91 Sr 97 Nb 132 Te 97 Zr 133 I 135 Xe 87 88
134
Te- 134I Xe- 138Cs 134 Te- 134I 142 Ba- 142La 133m Te133 Te 92 Sr- 92Y 87 Kr- 87Rb 88 Kr- 88Rb 135 I- 135Xe 91 Sr- 91Y 97 Zr- 97Nb 132 Te-132I 97 Zr- 97Nb 133 Te-133I 135 I- 135Xe 138
Activity values were corrected for radioactive decay to the time of reactor shutdown; T1/2 ¼ Half-Life.
Fig. 11. The comparison of calculated and measured count rate for pins adjacent to baffle model of LR-0 reactor [11].
Fig. 12. Time series of a fuel pin spectrum. Measured with Pb þ Cu plate.
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The count rate corrected for radioactive decay in the peak of gamma energy E (keV) and at the jth pin position is rj,E (cps). Then, the following relation holds for the correction factor of the throughput of analyzed shielding: ! E
kj ¼ r Ejm =r Ej ¼ 1 þ
m
∑
i ¼ 1;i a j
r Ei cEði jÞd
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point source i which is located at a distance x¼ (i j)d (cm) from the source j. If (i j) o0, the ith source is located under the jth source and if (i j)40 it is located above it. Some values of the CC obtained by MCNP calculation are listed in Table 1. Standard deviation of the calculated values is o 1% (1s).
ð9Þ
where r Ejm and r Ej (cps) are count rates at point j without and with the throughput correction, respectively; cEði jÞd is a dimensionless coefficient (CC) that corrects the count rate for the influence of
3.3. Analysis of gamma spectra A typical spectrum of the fuel pin shortly irradiated in the LR-0 reactor and measured 1.2 h after the reactor shutdown is in Fig. 10. Radionuclides marked in the spectrum (evaluated by the program Genie) correspond to energy peaks whose the NPA value was sufficiently high. Radionuclides found in the spectrum, which can be useful for the fuel fission density distribution determining in the LR-0 are in Table 2. It can be seen that the most intensive radionuclides are 134 138 I, Cs and 134Te. However, their half-life is shorter than 1 h, and therefore they are useful only for measurement about two hours after irradiation at power up to 10 W, i.e., when relatively small number of axial or radial spectra is measured. In terms of activity and half-life, radionuclides 92Sr and 142La meet best the requirements. An example of the application of 92Sr for the experimental verification of radial power distribution in the reactor LR-0 calculated using MCNPX and MOBY DICK codes is shown in Fig. 11 [10]. A verification of the half-lives for significant energy peaks was performed using the regression analysis of 4 time series of spectra. Each series contains from 20 to 40 consecutive measurements of one fuel pin. An example of the time series is in Fig. 12, where only three spectra are plotted for clarity reasons. An example of regression curves for the peaks of 1384, 847 and 767 keV are in Fig. 13. Regression functions have the general form y ¼ a þ b expð c xÞ þ d expð e xÞ;
ð10Þ
where parameters c, e are positive. The shape of the function depends on the conditions of pin irradiation, on the starting time of its measurement and on the analyzed peak in the spectrum. A sufficiently accurate estimation of initial parameter values is important for correct results of nonlinear regression. The results of regression analysis are in Table 3. The count rate of most energy peaks changes with the speed λn that is equal to Table 3 Kinetics of the count rate n change for significant energy peaks in the spectrum.
Fig. 13. Time trend of the count rate decrease for selected energy peak. Points – measurement, line – regression curve.
Peak energy
Average λn
SD
(keV)
(h 1)
(%)
278 530 641 658 743 767 847 884 1024 1260 1384 1436
1.028 0.034 0.466 0.598 0.039 0.950 0.802 0.790 0.070 0.095 0.262 1.236
9.04 5.56 1.81 22.34 5.97 5.04 3.76 3.29 4.91 10.85 2.71 8.78
Assigned RN
134
Te I La 97 Nb 97 Zr 134 Te 134 I 134 I 91 Sr 135 I 92 Sr 138 Cs 133 142
RN decay constant Difference λ λ λn (h 1)
(%)
0.995 0.033 0.457 0.577 0.041 0.995 0.792 0.792 0.072 0.105 0.265 1.245
3.29 2.82 2.08 3.75 6.87 4.51 1.29 0.27 2.84 9.66 1.49 0.71
Estimated from the analysis of 4 time series of spectra. Compared with half-lives of assigned radionuclides. SD ¼Standard Deviation, λn ¼ speed of count rate change in the peak, RN¼ radionuclide.
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the decay constant λ of the associated radionuclide in the range of 75%. A larger deviation is at energies 1260 and 743 keV. However, the standard deviations of the λn average value are relatively large. The increase of (λ λn) difference for some energy peaks may be caused by the fact that more than one radionuclide may contribute to an energy peak. For instance, 134I, 134Te contribute to the peak 767 keV, 97Zr, 134Te and 234mPm contribute to the peak 743 keV, 134Te, 239Np contribute to the peak 278 keV, 91Y, 90Y contribute to the peak 1024 keV. This is due to the non-zero width of peaks, which increases with energy and is in the range from 1 to 2.2 keV for our spectrometry system. Overall, the following energy-radionuclide pairs are burdened with the smallest uncertainties: 1384 keV–92Sr, 641 keV–142La, 847 and 884 keV–134I. A detail analysis of the peak 743 keV has shown that it is also suitable for the determination of absolute power density, if the share of fission origin 97Zr in the peak is quantified [11].
be identified with these peaks are 92Sr, 142La, 134I, 91Sr, and 138Cs, respectively. The analysis of the throughput of the detector shielding has been performed and correction algorithm was implemented to get more precise measurement results.
4. Conclusion
[1] V. Rypar, J. Kyncl, E., Novak, VVER Physics Experiments: Hexagonal Lattices (1.22 cm Pitch) of Low Enriched U(3.6, 4.4 wt% U235)O2 Fuel Assemblies in Light Water with Variable Fuel Assemblies Pitch, Report UJV Rez, Z2030, 2007, ICSBEP Handbook—LEU-COMP-THERM-087, 2007. [2] J..J. Peir, T.-K. Wang, C.-C. Liu, Appl. Radiat. Isot. 50 (1999) 1085. [3] F. Jatuffa, P. Grimma, R. van Geemerta, et al., Ann. Nucl. Energy 30 (2003) 911. [4] U.C. Bergmann, R. Chawla, F. Jatuff, M.F. Murphy, Nucl. Instrum. Methods Phys. Res., Sect. A 556 (2006) 331. [5] H. Krőhnert, G. Perret, M.F. Murphy, R. Chawla, Nucl. Instrum. Methods Phys. Res., Sect. A 624 (2010) 101. [6] F. Hudec, V. Rypar, E. Novák, Experimental Verification of Fission Density Distribution Around VVER-440 Control Assembly Model in LR-0 Reactor, Report 12203, NRI Rez, 2005. [7] Genie TM 2000 Spectroscopy Software, v. 3.2.2, Canberra Industries, Inc., 2009. [8] D.B. Pellowitz, MCNPX User0 s Manual, Version 2.6.0, Los Alamos Report No. LA CP 02 408, 2007. [9] ISOCS Model S573 Calibration Software, Canberra Industries, Inc., 2009. GenieTM2000 Spectroscopy software, v. 3.2.2, Canberra Industries, Inc., 2009. [10] M. Kostal, M. Svadlenkova, J. Milcak, Appl. Radiat. Isot. 78 (2013) 38. [11] M. Kostal, M. Svadlenkova, J. Milcak, Application of 97Zr on Absolute Determination of Power Density and Cladding Activation Contribution in the VVER-1000 Mock-Up on the LR-0 Research Reactor, Nucl. Instrum. Methods Phys. Res. Sect. A 738 (2014) 87–92.
A suitable method for power distribution determination in reactor core based on measurement and analysis of the short living fission products in lightly irradiated fuel pins has been developed on the experimental facility for gamma scanning at the LR-0 experimental reactor. The method includes the energy peak area correction to the radioactive decay. It has been done both by monitoring pin measurement and by computation method based on half-life of the radionuclide that is correctly assigned to the energy peak. The first (experimental) method is used for the determination of relative power distribution; the second one is useful also for absolute power density determination. As for the second method, selection of energy peaks suitable for the evaluation of power distribution in the experimental zeropower reactor LR-0 was made. The energies 1384, 641, 884, 847, 1024, and 1436 keV are the optimal ones. Radionuclides that can
Acknowledgments The experiments and calculations were funded by the Research Centre Rez Ltd. within Ministry of Education, Youth and Sport Czech Republic project MSM2672244501, and by the SUSEN Project CZ.1.05/ 2.1.00/03.0108 realized in the framework of the European Regional Development Fund (ERDF). References
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Gamma spectrometry of short living fission products in fuel pins Marie Švadlenková a,n, Lenka Heraltová b, Vlastimil Juříček a, Michal Košťál a, Evžen Novák a a b
Research Centre Rez, Ltd., Hlavni 130, 250 68 Husinec-Rez, Czech Republic Czech Technical University, Faculty of Nuclear Sciences and Physical Engineering, Brehova 7, 115 19 Prague 1, Czech Republic
art ic l e i nf o
a b s t r a c t
Article history: Received 12 November 2013 Received in revised form 6 December 2013 Accepted 7 December 2013 Available online 21 December 2013
A method of measurement and analysis of gamma spectra of short living fission products of lightly irradiated fuel pins has been developed at facilities at the LR-0 zero-power experimental reactor. Experimental and computational methods of the peak area correction for radioactive decay are described. Selection of energy peaks suitable for deriving power distribution in the core was performed. & 2013 Elsevier B.V. All rights reserved.
Keywords: Gamma spectrometry Research reactor Fuel pin Fission products MCNPX
1. Introduction The zero-power light-water research reactor LR-0 is used mainly for measurements of physical neutron characteristic of VVER and PWR-type reactors (see a scheme of the LR-0 reactor in Fig. 1). The advantage of the LR-0 is in its versatility, which allows carry out experiments with variable numbers of fuel assemblies in reactor core, variable fuel enrichment or variable concentration of H3BO3 in moderator and many others [1]. One of the main tasks of the LR-0 is the measurement of parameters that can be used in reactor dosimetry. It is similar to the using of other low power reactors, e.g., [2–5]. Reactor dosimetry topics demand a correct description of the power distribution in the reactor, especially in its marginal parts. For this reason the LR-0 is used for the determination of neutron fluence distribution in fuel pins and fuel assemblies through measurements of the fission products activity induced in the fuel. The increase of the induced activity in a particular region of the reactor is directly related to the density of uranium fission in the same region and therefore to the fuel pin activity increasing. The determination of neutron fluence and power distribution in the reactor core is possible by means of axial and radial measurements of fuel pin gamma activity. The distribution of fission products activities in fuel pins is measured by two methods at LR-0:
Integral method—in a specific energy interval, using a scintillation detector with one-channel analyzer [6] n
Corresponding author. Tel.: þ 420 2661 725 79. E-mail address: [email protected] (M. Švadlenková).
0168-9002/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nima.2013.12.019
Spectrometric method—where the spectrum of gamma radiation is measured, while individual energy peaks and radionuclides are analyzed.
The spectrometric method described here uses an HPGe semiconductor detector with multi-channel analyzer and the analysis of gamma spectra after short-time fuel pin irradiation in the LR-0 reactor is performed.
2. Materials and methods 2.1. Fuels pins Fuel pin cladding is an alloy composed of zirconium (98.97%), niobium (1%) and hafnium (0.03%) with average density of 6.44 g cm 3. Fuel column (inside the cladding) with length of 1250 mm is composed of uranium pellets of cylindrical annulus shape with inner radius of 1.4 mm and with outer radius of 7.5 mm. The height of the pellet is about 9.7 mm. The uranium fuel is enriched by 235U in the range from 1.6 to 4.4 wt%. The corresponding fuel density is between 10.33 and 10.35 g cm 3. A diagram of the fuel pin is in Fig. 2. After the reactor shut-down, selected irradiated fuel pins are transferred (under the radiation protection measure for handling with irradiated pins) to a fuel pin workplace. The place is located close to a laboratory for gamma scanning of the fuel pins and is not influenced by the radiation of the reactor.
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Fig. 1. The scheme of the LR-0 reactor—horizontal cross-section.
2.2. Equipment for gamma scanning of fuel pins A spectrometric device with coaxial high purity germanium detector HPGe (Ortec, GEM70) and multichannel analyzer DSA 2000 (Canberra) is used for the measurement of fuel pins. HPGe crystal has diameter of 74.6 mm and length of 87.9 mm, FWHM resolution at 1.33 MeV is about 2 keV and the Peak-to-Compton ratio for 60Co is approximately 75:1. The DSA-2000 analyzer is 100% controlled by computer using Genie 2000 [7] spectroscopy software platforms via the in-built Ethernet interface. The HPGe detector is horizontally attached to a cryostat (resp. Dewar vessel) and is inserted into a massive lead shielding with a collimator. The width of the collimator window is of 1 cm and the height is adjustable to 2, 3, or 5 cm, which makes it possible to measure gamma radiation from a specific part of the fuel pin. In some cases, a two-layer plate (lead with thickness of 3.3 mm and copper with thickness of 1 mm) is inserted between the fuel pin and the collimator window. The plate absorbs mainly low energy component of gamma spectrum and thus reduces the number of photons incident on the detector. As a result, the dead time of the detector is decreased which is desirable for more irradiated pins. The position of the HPGe detector in the shielding is depicted in Fig. 3. The shielding with collimator was optimized, so that only the gamma photons of the fuel pin part that faces directly the collimator window are registered. Nevertheless, since the shielding is not ideal and its throughput is not zero, the gamma radiation from fuel pin parts above and below the collimator window still falls partly on the detector. Therefore, experiments and MCNP calculations were performed in order to determine the extent of throughput of the shielding and the corresponding correction coefficients (see below). The experimental arrangement for scanning of fuel pins is shown in Fig. 4. The equipment consists of stand, precise helices, stepper motor, coupling and special fixing for fuel pin. Fuel pin is
Fig. 2. Diagram of the LR-0 fuel pin of VVER type; three times shortened in comparison with real VVER pin.
Fig. 3. The position of the HPGe detector in the shielding.
hung on a holder and can perform sequential axial movement around the collimator window. Fuel pin movement and positioning are controlled by special software DASAVR (RC Rez) with an accuracy of 0.5 mm. Fuel pin measured in a given position performs a rotary movement to average possible inhomogeneity of irradiation in its cross-section. This inhomogeneity plays a role for fuel pins at the periphery of the core. The calculation result for peripheral pins is in Fig. 5
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The GammaScan software (based on Delphi 6PE platform) was developed for automatic measurement of fuel pins. It collaborates with programs DASAVR and Genie-2000 (including its superstructure Batch Tools). 2.3. Fuel pins measurement and gamma spectra analysis
Fig. 4. The experimental arrangement for gamma scanning of fuel pins.
Fig. 5. Inhomogeneity of the fuel pins for four 90º circular arcs in the radial section.
where the relative detector response for four 901 circular arcs in the radial section of fuel pins is shown. The DASAVR data acquisition system installed on host PC allows to control up to three spectrometric devices and performs the following basic operations:
Loading of gamma spectra into the analyzer (e.g., DSA 2000) Storing the gamma spectra into a separate directory with other
information about the single measurement, e.g., position of pin, time, name of spectra Generating of commands for stepper motors Kinex control device, setting the step rate and start acceleration.
Parameters of measurement were set in such a way that the energy range and the shape of the spectrum were optimal for the performed experiments. The measurements were performed in energy range from 60 to 2500 keV. The point standard sources (type EG3, Eurostandard-Praha) with activity of the order of 105 Bq (60Co, 88Y, 133B, 137Cs, 152Eu and 241Am) were used for energy calibration. The efficiency calibration of HPGe detector for given measurement geometry was calculated. An experimental determination of efficiency would be costly and inefficient due to the complex geometry of fuel pin. The calculation was performed using the code MCNPX (Monte Carlo N-Particle transport code) [8] and also the software module ISOCS [9]. If the technical data of the detector (dimensions, material, etc.) are sufficiently accurate, the result of our MCNPX calculation is more precise in comparison with ISOCS. The reason is that the ISOCS program has a limited number of templates to model the geometry, while MCNPX can model the geometry of the sample (i.e., fuel pin) and the detector with shielding in detail practically without limits. Prior to selected fuel pin irradiation in the LR-0 reactor the residual activity (of the previous irradiation) of each fuel pin is measured. The pins are selected to have sufficiently long interval between irradiation. Then only radionuclides 235U, 234mPa, 226Ra, 137 Cs, 40K and K-line of Pb are present in the residual spectra. Fuel pins are then put into selected positions in the fuel assembly placed in the reactor core. The irradiation time is in the order of hours. The reactor power is roughly in the range from 1 to 10 W. An evaluation of measured spectra was carried out with the software GENIE 2000. To describe the fission density distribution in the core either values of Net Peak Area – NPA (counts) of selected energy peaks in the spectrum or activities – A (Bq) of radionuclides found in spectrum were used. For our calculation, the variable NPA proved more appropriate results because of their greater accuracy. Nevertheless, both values of the NPA and of the A had to be corrected for radioactive decay and possible residual activity. The aim was to select energy lines (peaks) in the spectrum that will be suitable for determining of the reactor core characteristics. First, these were the energy lines or peaks with the highest value of the NPA and with sufficiently long half-live. Then, there were selected either single peaks (that do not form multiplets and could likely belong only to the one radionuclide) or multiplets whose composition can be uniquely determined. 2.4. Correction for radioactive decay Correction for radioactive decay was necessary because the time between reactor shutdown and the end of measurements of irradiated pins was comparable with a half-life of selected fission products, i.e., tens to hundreds of minutes. The correction was performed by experiment or calculation. The experimental method of decay correction used for the determination of relative power distribution in the reactor is based on simultaneous measurement of irradiated pins and so called “monitoring pin” (monitor). The monitor is not different from the fuel pins. It is irradiated together with the other pins under the same conditions and then a time series of spectra is measured at one and the same appropriate position of the monitor. Based on the monitor measurements, the decrease rate of the area of a
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selected peak can be calculated and then the decay correction factor derived (see below). Through that factor the area of the same peak in the fuel pin spectra measured at a known time can be then corrected. This method is suitable for the decay correction of all peaks in the irradiated fuel pin spectra because the radionuclides induced in the fuel pins and the monitor are the same. Parallel measurement of monitor and fuel pin is possible, if two independent measurement devices are available. In case, we have just one, it is necessary to interrupt the measurement of the fuel pins at certain time intervals and switch to the measurement of the monitor. Replacement of the monitor for measuring the fuel pin has to be done manually. The procedure described above extends the time of measurement, which is disadvantage for short-lived radionuclides measurement. Decay correction coefficient is related to a reference time, which is usually the time of reactor shutdown or the start of pin series measurement. In the case the count rate is the quotient of the NPA and the time of measurement t, the following relations (1)–(6) can be used for the count rate decay correction of a specific peak in the gamma spectrum. Interpolated count rate of the corresponding peak monitor at time t is: mt ¼ k m2 þð1 kÞ m1 ;
ð1Þ
where k ¼(t t1)/(t2 t1), m1 and m2 are monitor count rates peak areas (closest in time) measured at times t1 and t2. Then, the correction factor CF at time t is CF ¼
mt ; m0
ð2Þ
where m0 is the first measured (reference) count rate of the monitor. Generally, CF can be larger than 1, smaller than 1 or equal to 1 for a specific energy peak, depending on the time course of monitor. The corrected count rate nkt of the peak in the fuel pin spectrum equals: nkt ¼
nt ; CF
ð3Þ
where nt is the uncorrected (measured) count rate of fuel pin. An uncertainty estimation of the corrected count rate was based on the equation for standard deviation of variable y¼ f (x1, x2,…, xn) depending on mutually independent variables ti with standard deviations ϑxi , sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 n ∂y ϑxi : ϑy ¼ ð4Þ ∑ i ¼ 1 ∂xi Then, for the standard deviation of the calculated monitor at time t holds qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ð5Þ ϑmt ¼ k ϑ2m2 þ ð1 kÞ2 ϑ2m1 and for the standard deviation of the fuel pin value nkt the following relationship is valid sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 m0 nt nt m0 ϑnt þ ϑm0 þ ϑ ϑnk ¼ : ð6Þ mt t mt mt m2t Schematic diagram of the experimental arrangement for correction by monitoring pin is in Fig. 6. On the other hand, the theoretical calculation of decay correction requires the assignment of a particular unique radionuclide to a selected energy peak in the spectrum. The possibility of such an assignment was studied by regression analysis where the match of the NPA decreasing rate and of the half-life of anticipated radionuclide was estimated. Four time series of pin spectra irradiated in independent irradiation campaigns were analyzed for this purpose.
Fig. 6. Schematic diagram of the experimental arrangement for correction by monitoring pin: 1- pin line, 2-monitor line.
The selected radionuclide may be the ith member (i¼1, 2,…, n) of a series of n genetically related radionuclides. Correction for decay for such a nuclide can be calculated by solving a system of ordinary first-degree differential equations whose ith term is of the form: dN i ¼ ðλi 1 N i 1 –λi N i Þdt
ð7Þ
The solution of (7) has a form i
Ni ¼ ∑ N ji ; j¼1
ð8Þ
where i1
Nji ¼ N0j ∑ K ir expð λr tÞ þK ii expð λi tÞ r¼j
and N 0j is the number of atoms of the radionuclide j at the time t¼0. In our case, series with up to two radionuclides were selected, i.e., mother and daughter radionuclide. Therefore, one-exponential or two-exponential regression functions were parameterized.
2.5. Correction for shielding throughput Throughput of the lead shielding of the detector for gamma radiation was estimated experimentally and by MCNP calculation. Axial gamma-spectrometric measurements of two pins with either cesium 137Cs or irradiated uranium pellets were performed. The range of axial distance of centre of the pellet from the collimator window was between 8 cm below and 8 cm above the centre of the window. The dimensions of the collimator were 1 2 cm (width height). The uranium pellet with a height of 1 cm was of the same type as pellets in the fuel pins. The cesium pellet of known composition was stored in a case with the dimensions similar to those of uranium pellets, but the active portion had a height of 0.6 cm. The detector response to gamma photons was calculated using the MCNPX code, for the energies of 662 keV (137Cs) and 307, 847, 1384 and 1435 keV (selected from the spectrum of fission products of an irradiated U-pellet) and in different positions of the pellet against the collimator window.
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Results from MCNPX were compared with experimental results. An algorithm for calculating the throughput correction of axial fuel pin measurements was designed.
3. Results and discussion 3.1. Efficiency calibration of measuring system An example of the detector calibration curves calculated by MCNPX for the collimator window of size 1 5 cm (w h) and 1 2 cm is in Fig. 7. The calculation was performed for inserted or ejected absorption plate. It takes also into account the nonuniform axial distribution of activity in the fuel pin after irradiation. The axial distribution calculated by MCNPX for fuel pin irradiated in the center of the LR-0 core is in Fig. 8. The MCNPX calculations show that the height of the window changes not only the maximum of the efficiency curve, but also its shape. For instance, for the window of height 5 cm the maximum is approximately twice as large as that for the window of height 2 cm and is shifted by 0.2 MeV towards lower energies.
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3.2. Throughput of detector shielding The comparison of calculation with experiment for gamma photons with energies of 662 and 1384 keV and for collimator window with a size of 1 2 cm is in Fig. 9. Experimental and calculated values of the shielding throughput are in relatively good agreement. Deviations are within the uncertainties of measured values of the NPA or count rate corrected for decay according to the relation (6). As expected, the throughput of gamma radiation through Pb shielding increases with increasing gamma rays energy. Once the radioactive source reaches the axial edge of the window, i.e. 71 cm from the collimator center, the detected count rate dropped to 80–90% relative to the value in the central position. At a distance of 72 cm the count rate is only about 10% and decreases rapidly with further increasing distance. Let the following conditions apply:
The length of the fuel column in fuel pin is s (cm) The continuous distribution of fuel in the fuel pin is approxi-
mated with equidistant point sources of ionizing radiation, the axial distance of which is d (cm), and therefore we have [s/d] ¼ m point sources along the pin ([s/d] is the integer part of the fraction s/d); let the point 1 lie at the bottom and the point m in the upper part of fuel pin The pin position is such that the jth point source (j ¼1,…,m) is at the center of the collimator window of the detector shielding (x ¼0)
Fig. 7. Detector calibration curves calculated with MCNPX for collimator window of size 1 5 cm and 1 2 cm.
Fig. 9. The comparison of C/E for Eg¼ 662 and 1384 keV and for collimator window with size of 1 2 cm.
Table 1 Values of the shielding throughput correction coefficients CC for several gammaray energies E and distances x from the center of the collimator window.
Fig. 8. Relative count rate axial distribution calculated by MCNPX for fuel pin irradiated in the center of LR-0 core.
E (keV) x (cm) ↓
307 U
662 Cs
847 U
1384 U
1435 U
4 3 2 1 0.5 0 0.5 1 2 3 4
o MDA o MDA 0.0267 0.6929 0.9683 1.0000 0.9728 0.6887 0.0259 o MDA o MDA
0.0017 0.0121 0.1009 0.7030 0.9746 1.0000 0.9990 0.8546 0.1637 0.0194 0.0028
0.0068 0.0283 0.1631 0.7806 0.9078 1.0000 0.9809 0.7770 0.1608 0.0272 0.0068
0.0285 0.0712 0.2459 0.8042 0.9782 1.0000 0.9861 0.8036 0.2417 0.0695 0.0276
0.0299 0.0731 0.2495 0.8053 0.9790 1.0000 0.9879 0.8068 0.2486 0.0734 0.0302
MDA ¼ minimum detectable activity; CC ¼cEði jÞd .
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Fig. 10. Gamma spectrum of a fuel pin irradiated in the LR-0 and measured 1.2 h after the reactor shutdown. Measured without Pb þ Cu plate. Time of irradiation ¼2.5 h, reactor power ¼ 9.5 W.
Table 2 Radionuclides selected from fuel pin gamma spectra measured 1.2 h after irradiation (irradiation period ¼ 2.5 h, reactor power E9.5 W). Radioisotope
Activity (%) Uncert. (%) Key line (keV) T1/2 (h) Decay scheme
134
100.0 98.5 68.2 44.1 29.1
1.0 0.8 1.1 0.9 1.3
847.0 1435.8 767.2 641.3 912.7
0.88 0.56 0.70 1.52 0.92
25.1 19.2 13.9 13.6 8.5 8.4 3.5 5.7 4.9 3.2
0.8 3.9 2.1 1.2 2.0 2.2 5.9 2.1 2.2 5.7
1383.9 402.6 2392.1 1260.4 1024.3 657.9 228.2 743.4 529.9 249.8
2.71 1.27 2.84 6.57 9.63 1.20 3.2 16.9 20.8 9.14
I Cs 134 Te 142 La 133m Te 138
92
Sr Kr Kr 135 I 91 Sr 97 Nb 132 Te 97 Zr 133 I 135 Xe 87 88
134
Te- 134I Xe- 138Cs 134 Te- 134I 142 Ba- 142La 133m Te133 Te 92 Sr- 92Y 87 Kr- 87Rb 88 Kr- 88Rb 135 I- 135Xe 91 Sr- 91Y 97 Zr- 97Nb 132 Te-132I 97 Zr- 97Nb 133 Te-133I 135 I- 135Xe 138
Activity values were corrected for radioactive decay to the time of reactor shutdown; T1/2 ¼ Half-Life.
Fig. 11. The comparison of calculated and measured count rate for pins adjacent to baffle model of LR-0 reactor [11].
Fig. 12. Time series of a fuel pin spectrum. Measured with Pb þ Cu plate.
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The count rate corrected for radioactive decay in the peak of gamma energy E (keV) and at the jth pin position is rj,E (cps). Then, the following relation holds for the correction factor of the throughput of analyzed shielding: ! E
kj ¼ r Ejm =r Ej ¼ 1 þ
m
∑
i ¼ 1;i a j
r Ei cEði jÞd
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point source i which is located at a distance x¼ (i j)d (cm) from the source j. If (i j) o0, the ith source is located under the jth source and if (i j)40 it is located above it. Some values of the CC obtained by MCNP calculation are listed in Table 1. Standard deviation of the calculated values is o 1% (1s).
ð9Þ
where r Ejm and r Ej (cps) are count rates at point j without and with the throughput correction, respectively; cEði jÞd is a dimensionless coefficient (CC) that corrects the count rate for the influence of
3.3. Analysis of gamma spectra A typical spectrum of the fuel pin shortly irradiated in the LR-0 reactor and measured 1.2 h after the reactor shutdown is in Fig. 10. Radionuclides marked in the spectrum (evaluated by the program Genie) correspond to energy peaks whose the NPA value was sufficiently high. Radionuclides found in the spectrum, which can be useful for the fuel fission density distribution determining in the LR-0 are in Table 2. It can be seen that the most intensive radionuclides are 134 138 I, Cs and 134Te. However, their half-life is shorter than 1 h, and therefore they are useful only for measurement about two hours after irradiation at power up to 10 W, i.e., when relatively small number of axial or radial spectra is measured. In terms of activity and half-life, radionuclides 92Sr and 142La meet best the requirements. An example of the application of 92Sr for the experimental verification of radial power distribution in the reactor LR-0 calculated using MCNPX and MOBY DICK codes is shown in Fig. 11 [10]. A verification of the half-lives for significant energy peaks was performed using the regression analysis of 4 time series of spectra. Each series contains from 20 to 40 consecutive measurements of one fuel pin. An example of the time series is in Fig. 12, where only three spectra are plotted for clarity reasons. An example of regression curves for the peaks of 1384, 847 and 767 keV are in Fig. 13. Regression functions have the general form y ¼ a þ b expð c xÞ þ d expð e xÞ;
ð10Þ
where parameters c, e are positive. The shape of the function depends on the conditions of pin irradiation, on the starting time of its measurement and on the analyzed peak in the spectrum. A sufficiently accurate estimation of initial parameter values is important for correct results of nonlinear regression. The results of regression analysis are in Table 3. The count rate of most energy peaks changes with the speed λn that is equal to Table 3 Kinetics of the count rate n change for significant energy peaks in the spectrum.
Fig. 13. Time trend of the count rate decrease for selected energy peak. Points – measurement, line – regression curve.
Peak energy
Average λn
SD
(keV)
(h 1)
(%)
278 530 641 658 743 767 847 884 1024 1260 1384 1436
1.028 0.034 0.466 0.598 0.039 0.950 0.802 0.790 0.070 0.095 0.262 1.236
9.04 5.56 1.81 22.34 5.97 5.04 3.76 3.29 4.91 10.85 2.71 8.78
Assigned RN
134
Te I La 97 Nb 97 Zr 134 Te 134 I 134 I 91 Sr 135 I 92 Sr 138 Cs 133 142
RN decay constant Difference λ λ λn (h 1)
(%)
0.995 0.033 0.457 0.577 0.041 0.995 0.792 0.792 0.072 0.105 0.265 1.245
3.29 2.82 2.08 3.75 6.87 4.51 1.29 0.27 2.84 9.66 1.49 0.71
Estimated from the analysis of 4 time series of spectra. Compared with half-lives of assigned radionuclides. SD ¼Standard Deviation, λn ¼ speed of count rate change in the peak, RN¼ radionuclide.
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the decay constant λ of the associated radionuclide in the range of 75%. A larger deviation is at energies 1260 and 743 keV. However, the standard deviations of the λn average value are relatively large. The increase of (λ λn) difference for some energy peaks may be caused by the fact that more than one radionuclide may contribute to an energy peak. For instance, 134I, 134Te contribute to the peak 767 keV, 97Zr, 134Te and 234mPm contribute to the peak 743 keV, 134Te, 239Np contribute to the peak 278 keV, 91Y, 90Y contribute to the peak 1024 keV. This is due to the non-zero width of peaks, which increases with energy and is in the range from 1 to 2.2 keV for our spectrometry system. Overall, the following energy-radionuclide pairs are burdened with the smallest uncertainties: 1384 keV–92Sr, 641 keV–142La, 847 and 884 keV–134I. A detail analysis of the peak 743 keV has shown that it is also suitable for the determination of absolute power density, if the share of fission origin 97Zr in the peak is quantified [11].
be identified with these peaks are 92Sr, 142La, 134I, 91Sr, and 138Cs, respectively. The analysis of the throughput of the detector shielding has been performed and correction algorithm was implemented to get more precise measurement results.
4. Conclusion
[1] V. Rypar, J. Kyncl, E., Novak, VVER Physics Experiments: Hexagonal Lattices (1.22 cm Pitch) of Low Enriched U(3.6, 4.4 wt% U235)O2 Fuel Assemblies in Light Water with Variable Fuel Assemblies Pitch, Report UJV Rez, Z2030, 2007, ICSBEP Handbook—LEU-COMP-THERM-087, 2007. [2] J..J. Peir, T.-K. Wang, C.-C. Liu, Appl. Radiat. Isot. 50 (1999) 1085. [3] F. Jatuffa, P. Grimma, R. van Geemerta, et al., Ann. Nucl. Energy 30 (2003) 911. [4] U.C. Bergmann, R. Chawla, F. Jatuff, M.F. Murphy, Nucl. Instrum. Methods Phys. Res., Sect. A 556 (2006) 331. [5] H. Krőhnert, G. Perret, M.F. Murphy, R. Chawla, Nucl. Instrum. Methods Phys. Res., Sect. A 624 (2010) 101. [6] F. Hudec, V. Rypar, E. Novák, Experimental Verification of Fission Density Distribution Around VVER-440 Control Assembly Model in LR-0 Reactor, Report 12203, NRI Rez, 2005. [7] Genie TM 2000 Spectroscopy Software, v. 3.2.2, Canberra Industries, Inc., 2009. [8] D.B. Pellowitz, MCNPX User0 s Manual, Version 2.6.0, Los Alamos Report No. LA CP 02 408, 2007. [9] ISOCS Model S573 Calibration Software, Canberra Industries, Inc., 2009. GenieTM2000 Spectroscopy software, v. 3.2.2, Canberra Industries, Inc., 2009. [10] M. Kostal, M. Svadlenkova, J. Milcak, Appl. Radiat. Isot. 78 (2013) 38. [11] M. Kostal, M. Svadlenkova, J. Milcak, Application of 97Zr on Absolute Determination of Power Density and Cladding Activation Contribution in the VVER-1000 Mock-Up on the LR-0 Research Reactor, Nucl. Instrum. Methods Phys. Res. Sect. A 738 (2014) 87–92.
A suitable method for power distribution determination in reactor core based on measurement and analysis of the short living fission products in lightly irradiated fuel pins has been developed on the experimental facility for gamma scanning at the LR-0 experimental reactor. The method includes the energy peak area correction to the radioactive decay. It has been done both by monitoring pin measurement and by computation method based on half-life of the radionuclide that is correctly assigned to the energy peak. The first (experimental) method is used for the determination of relative power distribution; the second one is useful also for absolute power density determination. As for the second method, selection of energy peaks suitable for the evaluation of power distribution in the experimental zeropower reactor LR-0 was made. The energies 1384, 641, 884, 847, 1024, and 1436 keV are the optimal ones. Radionuclides that can
Acknowledgments The experiments and calculations were funded by the Research Centre Rez Ltd. within Ministry of Education, Youth and Sport Czech Republic project MSM2672244501, and by the SUSEN Project CZ.1.05/ 2.1.00/03.0108 realized in the framework of the European Regional Development Fund (ERDF). References