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Localisation of a neutron source using measurements and calculation of the neutron flux and its gradient
Nuclear Instruments and Methods in Physics Research A 438 (1999) 345}355
Localisation of a neutron source using measurements and calculation of the neutron #ux and its gradient P. LindeH n, J.K.-H. Karlsson, B. Dahl, I. PaH zsit*, G. Por1 Department of Reactor Physics, Chalmers University of Technology, SE-412 96 Go( teborg, Sweden Received 20 July 1999
Abstract We have performed laboratory measurements of the neutron #ux and its gradient in a static model experiment, similar to a model problem proposed in PaH zsit (Ann. Nucl. Energy 24 (1997) 1257). The experimental system consists of a radioactive neutron source located in a water tank. The measurements are performed using a recently developed very small optical "bre detector. The measured values of the #ux and its gradient are then used to test the possibility of localising the source. The results show that it is possible to measure the #ux on the circumference of a circle and from this calculate the #ux gradient vector. Then, by comparison of the measured quantities with corresponding MCNP calculations, both the direction and the distance to the source are found and thus the position of the source can be determined. ( 1999 Elsevier Science B.V. All rights reserved. PACS: 28.20.Gd; 29.40.Mc; 28.41.Rc Keywords: Localisation; Flux gradient; Optical "bre; Scintillation detector
1. Introduction It was suggested in Ref. [1] that the use of the neutron current could be advantageous for the diagnostics of various space-dependent anomalies, such as the localisation of a static source or a control rod tip. In reactor noise diagnostics, the timedependent current may be even more useful than the time-dependent #ux for localisation of vibrating
* Corresponding author. Tel.: 0031-772-1000; fax: 0031-7723079. 1 On leave of absence from Technical University, Budapest, Hungary E-mail address: [email protected] (I. PaH zsit)
components. In this paper, we will demonstrate experimentally the feasibility of using the current for localising a radioactive neutron source in a homogeneous medium. Since there is no current detector presently available, we have to utilise the #ux gradient as a measure of the current. In neutron di!usion theory, the current is directly proportional to the #ux gradient and thus we assume that di!usion theory is adequate in this study. The #ux gradient in two dimensions can be obtained either from a number of scalar #ux measurements performed on the circumference of a circle or on lines in each main direction. Thus, to realise a gradient detector and be able to "t it into standard instrumentation guide tubes in a pressurized water reactor (PWR), we
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need to use very small #ux detectors. The detector should also have a good spatial resolution, which inherently comes with the small physical size, and reasonable e$ciency, radiation hardness and cost. Until recently, no such detectors were readily available. However, a very small radiation detector, consisting of an optical "bre, whose tip is covered with a mixture of converter material, scintillation material and adhesive paste, was developed recently at Nagoya University, Japan [2]. The detector has been used previously in measurements of the fast and thermal axial #ux pro"les in a research reactor [3] and for measurements of the 14.1 MeV neutrons from a D-T neutron generator [4]. Due to its small size and simplicity, this #ux detector also appears to be a good candidate for the elementary #ux measurements in a future current detector. In this paper, we report on measurements of the #ux and the gradient, performed by using the "ber detector in a static system composed of a radioactive neutron source located in a tank "lled with water. The purpose of these measurements is to investigate the behaviour of the #ux and its gradient in a model system. Another aim is to test the possibility of localising the source from the measured values of the #ux and gradient at a single spatial position, as was proposed in Ref. [1].
2. Experimental The detector consists of LiF converter and ZnS(Ag) powder mixed together and pasted with epoxy glue on the tip of a glass optical "bre of diameter 2 mm. Because of the poor optical properties of ZnS, the detector mixture is made thin (&0.3 mm). A layer of opaque paint is also applied on the "bre tip for protection against light and mechanical damage (Fig. 1). The neutrons are captured by the 6Li nucleus in the reaction 6 Li#1 nP3 H#4 He (1) 2 1 0 3 where 4.78 MeV of kinetic energy is also released and shared between the product particles. The cross section for this reaction behaves as 1/v and hence it is large for thermal neutrons and it de-
Fig. 1. The measurement system.
creases with increasing neutron energy. For fast neutrons the detector can be considered as completely transparent. When a neutron is absorbed, the resulting ionised reaction products excite the electrons in the ZnS crystals and the excited electron states deexcite by emitting scintillation light photons. The light pulses produced in the detector are guided by the optical "bre to a photo-multiplier tube (Hamamatsu R5600U Head-on PMT). The PM-tube is connected via an ampli"er chain (ORTEC 113 and 575A) to a multi-channel analyser (MCA). The MCA used is an ORTEC 926 ADCAM MCB, which is controlled by the companion MAESTROTM program (A65-BI ver. 3.0). A schematic view of the measurement system is shown in Fig. 1. The experimental arrangement is shown in Fig. 2. The measurements were performed in a cylindrical water tank of 92 cm diameter. The radioactive neutron source (3 Ci Am}Be) was attached to the top of a support beam and placed in the centre of the tank. The optical "bre with its neutron-sensitive tip was inserted into an aluminium guide tube, which was sealed to protect the "bre from light and direct contact with the water. The tube was put vertically down into the water from a bridge across the water tank. The active part of the neutron detector was positioned on the same
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3. Measurement results and analysis
Fig. 2. (a) A schematic "gure of the experimental setup. (b) A photo taken from above down into the water tank. This picture shows the actual measurement con"guration.
horizontal plane as the centre of the source. To place the detector in an exact radial position in relation to the source, a thin guiding needle at the tip of the guide tube was put into a speci"c hole out of several small holes drilled in a plastic support plate. The holes in the support plate form a number of circles, which are denoted by the letters A}F, with di!erent radii and di!erent distances from the centre of the circles to the centre of the source. The measurement con"guration and the pattern of holes are both shown in Fig. 2b. Four of the circles have the same radius 1.0 cm, while circle E is smaller with a radius of 0.5 cm and F is larger with a radius of 2.0 cm. The radius of the circle a!ects the number of detector positions (i.e., holes) that can be placed along the circumference of the circle. There are 12 angular points with 303 intervals for the circles with 1.0 cm and 2.0 cm radii, respectively, and six points at 603 intervals for the small circle with 0.5 cm radius.
Some characteristics of our small "bre detector can be seen in the amplitude spectrum in Fig. 3. A large value of the channel number on the x-axis corresponds to a large signal amplitude from the detector. To exclude some of the low-energy background noise, we have set a discrimination level (see Fig. 3) on the analog to digital converter and thus the amplitude spectrum shows only signals with an amplitude larger than this discrimination level. Due to the small active size of the detector, there is a very high probability that a large part of the energy is lost from the detector. This means that the detection probability of events with a small amplitude is high and the probability decreases with increasing amplitudes. The lost energy is carried away by either the product particles or the light photons which are leaving the detector volume. The photons can also be lost at the entrance of the optical "bre, in the "bre itself or be absorbed by detector materials. In Fig. 4 the detector count rate as a function of distance from the source centre is shown. In fact, these values were actually measured on the circle contours mentioned previously, but here we have put them in a cylindrical coordinate system with its pivot at the source centre. The position and extension of the measurement circles are also indicated by arrows in the "gure. Close to the source, the count rate increases with increasing distance from the source and it exhibits a maximum at about 3 cm from the source centre. At larger distances, the count rate decreases exponentially with increasing distance from the source. The reason for the presence of the maximum lies with the energy dependence of the neutron #ux around the source. The neutrons are all emitted as fast neutrons by the source and they are then slowed down and thermalised in the water moderator. Hence, at the position of the source the thermal #ux is small. With increasing distance from the source, the thermal #ux "rst increases, due to the slowing down of fast neutrons, and then it reaches a maximum followed by a thermal #ux decrease, due to the absorption of thermal neutrons. Since the detector is only sensitive to thermal neutrons, the measured count rate in Fig. 4 corresponds to the thermal #ux.
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Fig. 3. A typical amplitude spectrum obtained from the "bre detector.
The measured count rates I(u) as functions of the angle u in each circle are shown in Fig. 5. For each circle, the value of zero degrees corresponds to the direction towards the position of the source. The angle is counted in the clockwise direction. In general, the count rate in Fig. 5 has a maximum where the distance to the source is the smallest, i.e., at zero degrees, and the count rate has a minimum at 1803, i.e., at the largest distance from the source. Circle A, however, has a double-humped shape of the count rate as a function of angle with maxima at $903 and minima at 0 and 1803. The reason for this shape is that circle A extends across the maximum of the count rate in Fig. 4. Thus, the point on circle A that is closest to the source, lies on the l.h.s. of the maximum, while the points at $903 lie at the maximum and the point at 1803. lies at r.h.s. of the maximum value. The error bars in Figs. 4 and 5 re#ect only the statistical uncertainty in the measurements. In addition to the statistical error there is also a possible
signi"cant error due to non-perfect positioning of the aluminium guide tube. The reason is that in our experimental set-up it is di$cult to support the guide tube, such that it stands exactly perpendicular to the support plate (see Fig. 2). Thus, there is a possibility for the guide tube to lean either away or towards the source and therefore give a contribution to the error, which is not taken into account in the error bars shown. For example, in circle E the count rate measured at 603 deviates strongly from the expected value, most probably because of nonperfect positioning of the guide tube. The #ux gradient with respect to the distance from the source can be simply calculated from the #uxes in Fig. 4. This method gives only the gradient in a single direction, while the gradient has two components, one in the radial and one in the azimuthal direction. The system is of course cylindrically symmetric and hence the azimuthal direction is unimportant in our particular case. However, we would like to develop a general method and hence
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Fig. 4. The measurement results for the count rate plotted as a function of distance from the source centre. The position and extension of the measurement circles are indicated by arrows.
determine a possible symmetry from the measurement itself. The amount of deviation from perfect cylindrical symmetry of the measurements can also give a useful indication of the error in the method employed. An e$cient method to determine both components of the #ux gradient in a single spatial point is found by using the de"nition of a gradient in the form { / dr +/"lim C S S?0
(2)
where the integral is taken over the circle C which bounds the surface area S. By taking a number of measurements of the count rate I, which is proportional to the #ux, on the contour of a circle with radius R, the two components of the gradient can
be calculated as
P
(3)
P
(4)
LI 1 2p J " " I(u) cosu du x Lx pR 0 and 1 2p LI I(u) sinu du. J " " y Ly pR 0
Eqs. (3) and (4) are given in the coordinate system used for each circle in the measurement. In this system the x-direction points towards the position of the source, i.e., the same as the negative radial direction in the cylindrical coordinate system of the source. The y-direction at the measured circle thus corresponds to the azimuthal direction in the source coordinate system. The average detector count rate at the centre of the measured circle is
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Fig. 5. The count rate for each circle as a function of angle. The zero degree angle corresponds to the direction towards the position of the source centre.
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obtained as
P
1 2p I(u) du (5) IM " 2p 0 where the integrals in Eqs. (3)}(5) are carried out numerically by using a simple summation. The results obtained for the gradient and average count rate for each circle, as well as the distance from the source and radius of the circle used, are given in Table 1. The gradient is given in the form of an absolute value and an angle of direction as D+ID"JJ2#J2 y x L+I"atan[J /J ]. (6) y x In the results, a zero direction angle indicates the direction towards the source centre. It is seen in the table that the angle is indeed close to zero for all circles, except A, for which the gradient points approximately in the opposite direction, i.e., away from the source. This is due to the previously mentioned fact that the slope of the count rate curve in Fig. 4 changes sign across the maximum and circle A lies on the upward slope, while all the other circles lie on the downward slope of the curve. Thus, circle A will have a gradient with $1803 angle, i.e., the gradient points in the direction away from the source. The deviation of the angle from the exact results, i.e., zero or $1803, gives a good indication of the total measurement error in the experimental determination of the direction to the source. In general, relatively accurate values for the angle are obtained for the circles B}D and F, while the values for
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circles A and E are less accurate. For circle E, the deviation is &123 and in this case the abovementioned outlying measurement at 603 is the one responsible for this particularly large deviation. Similarly for circle A, the count rate curve in Fig. 5 is not as symmetric around 1803 as it should be. Most probably this is due to the non-perfect alignment of the guide tube. The statistical uncertainty in the measured count rates is propagated into the values calculated for the gradient and its angle of direction. The calculated statistical errors in the gradient and its angle of direction are also shown in Table 1. Regarding the angle of direction, the estimated statistical errors cannot explain the deviation of the calculated angles from the expected results of zero or $1803. This shows that the statistical error is only a small fraction of the total measurement error. In any case, the calculated statistical errors in the table show that the magnitude of the count rate di!erence across the circle, i.e., *I"I(03)!I(1803) in Fig. 5, a!ects the accuracy. The smaller the change in *I (i.e., the smaller the gradient) the larger the statistical error in the resulting value for the gradient. By comparing the error estimates of D+ID for circles B, E and F, it is clear that the smaller the circle (i.e., the smaller the change in *I) the larger the statistical error. Thus, to accurately determine gradients with small absolute values, large circles are required. Another problem of the gradient estimation appears if the physical gradient changes signi"cantly within the area of the circle. In this case, we obtain an average value of the gradient across the circle rather than a precise estimate of
Table 1 Results Circle
A B C D E F
Distance from source to circle (cm)
2.6 4.6 6.6 8.6 4.6 4.6
Radius of circle (cm)
1.0 1.0 1.0 1.0 0.5 2.0
IM (s~1)
20.47$0.21 18.25$0.18 14.20$0.14 10.22$0.10 18.67$0.19 18.06$0.20
+I D+ID (cm1 s~1)
L+I (3)
0.0737$0.3555 1.903$0.237 2.237$0.180 1.711$0.130 1.842$0.580 1.728$0.134
!144.25$4.83 2.52$0.12 !1.732$0.081 !0.949$0.075 12.489$0.287 3.985$0.079
D+ID IM (cm~1)
0.0036$0.0174 0.104$0.014 0.157$0.014 0.167$0.012 0.099$0.032 0.0957$0.008
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the gradient at the circle centre. The value of the gradient for Circle F is somewhat lower than that for circle B and this is because circle F is so large that the gradient changes signi"cantly within the circle. The gradient determined from circle A also su!ers from the same problem as circle F. We can conclude that for a successful and accurate determination of the gradient, using the method of measuring the #ux on the circumference of a circle (or sphere in a 3-D system), two qualitative conditions need to be ful"lled. First, the gradient should vary very little within the measurement circle. If this is not ful"lled, one will obtain an estimate of the gradient of the #ux surface that is de"ned by the measurement circle, instead of the #ux gradient at the position of the centre of the circle. In our case, this was satis"ed by circles B}E, but not for A and F. Second, the amount of change experienced by the count rate across the circle should be relatively large, i.e., *I should be large. The reason is that the presence of statistical errors in the measurement points leads to large errors in the estimated values for the gradient when *I is very small. In our measurements, both circles A and E have small *I. According to these criteria, the estimated values obtained from circles B}D have small errors, while the results obtained from circles A, E and F have somewhat larger errors. The above discussion indicates some of the problems in constructing a gradient detector using the present principle. The circle needs to be small enough to give a localised measurement such that the gradient does not change signi"cantly within the area of the circle. On the other hand, the circle also needs to be large to yield an accurate estimate of the gradient, especially for small gradients. Thus, some compromise is necessary to optimize the performance of the method. For the detector to be useful in practice, we need also to be able to "t it into a standard instrumentation tube of a PWR. In a Westinghouse PWR the instrument tube has an inner diameter of 1.146 cm. Thus, the maximum diameter of a measurement circle in a future gradient detector should be about 1 cm, which is the same size as our circle E. The measurement of the #ux gradient estimates the direction pointing towards the source. By using two such measurements, we can "nd the position of
Fig. 6. Dependence of the gradient to #ux ratio on the distance from the source.
the source by triangulation. It is also possible to "nd the source position with the use of only a single measurement position. In this case the quantity D+ID/I is used together with a calculated curve of the ratio of the gradient and the #ux as a function of distance from the source. The method was "rst described in Ref. [1] using one-group theory and it is illustrated in Fig. 6. A value of D+ID/I is determined from an experiment and by using the curve in Fig. 6 or inverting the corresponding equation, we obtain an estimate of the distance from the source. Already in Ref. [1] it was made clear that the uncertainty in the estimation of the distance by using this method increases with increasing distance from the source. The reason is that the quantity D+ID/I tends towards a saturation value with increasing distance from the source. The one-group theory example in Fig. 6 can only be used for illustration of the method of determining the distance to the source. In a realistic case, like our experimental determination of the distance to the source, we have to take the energy dependence into account. This was "rst done by calculating the neutron #ux using two-group di!usion theory assuming a point source in an in"nite homogenous medium. This solution decreases monotonically as the distance from the source increases (Fig. 7a) and it cannot describe the maximum, which is found in the measurements (Fig. 4). To reconstruct this e!ect, we have used a spherical volume source instead of a point source. In this case, we obtain a solution with a similar shape as the measured count rates (Fig. 7a). However, there is still some deviation between the
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Fig. 7. (a) The detector count rate as a function of distance from the source. (b) The values of D+ID/I as obtained from MCNP and two-group theory calculations as well as from the measurements.
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calculated curve and the measurements, especially close to the source surface, such that this solution is also inadequate for estimation of the distance from the source. To obtain a more accurate solution, transport theory calculations are necessary. We have used the Monte Carlo code MCNP, version 4.2, to calculate the multigroup neutron #ux in the water tank. The neutron source used in the experiment consists of a steel cylinder "lled with a mixture of 241Am and Be. The cylindrical source geometry was simulated by modelling an ellipsoidal volume source in the centre of the tank. The steel container was an ellipsoidal shell with the same volume and materials as the real container. The outer short axes of the ellipsoid was 1.12 cm and the long axes was 2.1 cm. The volume inside the steel shell was "lled with an amount of Am and Be that would give the same source strength as the real source. The production of the neutrons was however not described by the radioactive decay within the source. The above materials were only used to account for the scattering and absorption reactions of the neutrons within the source itself. The production of the neutrons was assumed to take place on the surface of the source with an energy spectrum corresponding to that of an Am}Be source as given in Ref. [5]. This distribution was placed on the outer surface of the steel container and was considered to be equal in all directions. In this way we get the same source strength and energy dependence as from the real source. For detection we used congruent tally spheres with their centres located at the source
centre. The radii of the tally spheres were varied from 2.12 to 31.12 cm. This corresponds to detection at distances of 1}30 cm from the short axis of the source steel container. The results of the Monte Carlo calculations were convoluted with the JEF 2.2 capture cross-sections for the Li reaction to obtain an estimate of the count rate in the detector. The results in comparison with the measurements and the two-group theory calculations are shown in Fig. 7a. The results have been normalised to the measurements. The "gure shows that the MCNP calculations agree well with the results of the measurements. In Fig. 7b we show the values of D+ID/I as obtained from the MCNP and the two-group theory calculations and from the integration over the measurement circles as given in Table 1, respectively. The measurement results are indicated by circles and denoted by letters corresponding to the measurement circle used to obtain that particular point. Each measurement point is plotted at the ordinate value of D+ID/I obtained from Table 1 and at the abscissa value of the distance from the source to the centre of the measurement circle. The curve obtained from the MCNP calculations can now be used to calculate the values of the distances corresponding to the measured values of D+ID/I and then we can compare the estimated and exact values of the distance to the source. The results are summarized in Table 2. Table 2 shows that the deviations in the determination of the position of the source are rather small. All individual relative deviations are less
Table 2 Estimation of the distance to the source Circle
Distance from source to circle (cm)
Estimation of the distance to the source from the D+ID/I values and the MCNP curve in Fig. 7b (cm)
Deviation between the estimated and the true distance (cm)
Relative deviation (%)
A B C D E F
2.6 4.6 6.6 8.6 4.6 4.6
2.84 4.34 6.80 7.36 4.12 4.12
0.24 !0.26 0.20 !1.24 !0.48 !0.48
9.2 5.7 3.0 14 10 10
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than 15% and most deviations are 10% (&5 mm) or smaller. Circle D has the largest deviation of 14% or 12 mm. The discussion previously indicated that circles B}D are expected to be the most accurate. In light of the deviations shown in Table 2, this is true for B and C, but not for D. The reason is that circle D is close to the saturation level in Fig. 7b and then the uncertainty in the estimation of the distance is the greatest. At very small distances from the source, the situation is just the opposite. Even large statistical errors in D+ID/I yield relatively small errors in the estimate of the distance. The sensitivity to statistical errors is thus small to the left (circle A) and large to the right (circle D) in Fig. 7b. The circles E and F has a medium error and the reason is that their values of D+ID/I are a bit too small. This is due to the relatively large statistical uncertainty for the small circle E and for circle F the reason is that the gradient changes within the circle as compared to that for circle B. Based on the results shown in Table 2, we conclude that it is feasible to use D+ID/I for determination of the distance to the source with a relative accuracy of about 10% for distances shorter than about 10 cm. 4. Conclusions Measurements were performed using a very small scintillation detector attached to an optical "bre. The small size of this detector makes it suitable for performing measurements which require good spatial resolution. This detector was utilized in measurements of the #ux induced by a neutron source in a homogeneous medium (water). One purpose of these measurements has been to test the detector and related equipment. Another purpose has been to test a scheme of measuring the #ux gradient by measuring a number of points on the circumference of circles. The result is a measurement of the average #ux and the gradient at the centre of the circle. The results indicate that the circle should have a small radius, such that the
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gradient does not vary signi"cantly inside the circle. The circle should also be large enough to yield a signi"cant #ux di!erence across the circle diameter, in order to avoid errors due to statistical uncertainties in the measurements. Thus, some compromise is necessary to optimise the performance of the method. The results for the #ux and gradient agree well with those obtained from Monte Carlo calculations using MCNP and from qualitative considerations regarding the measurement symmetry. The gradient yields an accurate estimate of the direction to the source. Further, for small distances to the source ((&10 cm) the quantity D+ID/I can be used to estimate the distance from the measured circle to the source along the direction given by the gradient. This estimation of the distances agrees well with the true distances. Finally, we conclude that the method proposed in Ref. [1] can be successfully utilised for the localisation of a radioactive neutron source using the #ux and its gradient.
Acknowledgements We would like to thank Ryszard Rydz, Lasse Urholm and Lennart Norberg for the design and construction of the experimental set-up. This project was supported by the Swedish Nuclear Power Inspectorate, contract No. 14.5980942-98242.
References [1] I. PaH zsit, Ann. Nucl. Energy 24 (1997) 1257. [2] C. Mori, T. Osada, K. Yanagida, T. Aoyama, A. Uritani, H. Miyahara, Y. Yamane, K. Kobayashi, C. Ichihara, S. Shiroya, J. Nucl. Sci. Technol. 31 (1994) 248. [3] Y. Yamane, A. Uritani, T. Misawa, J.K.-H. Karlsson, I. PaH zsit, Nucl. Instr. and Meth. A 432 (1999) 403. [4] Y. Yamane, P. LindeH n, J. Karlsson, I. PaH zsit, Nucl. Instr. and Meth. A 416 (1998) 371. [5] K.W. Geiger, L. van der Zwan, Nucl. Instr. and Meth. 131 (1975) 315.
Localisation of a neutron source using measurements and calculation of the neutron #ux and its gradient P. LindeH n, J.K.-H. Karlsson, B. Dahl, I. PaH zsit*, G. Por1 Department of Reactor Physics, Chalmers University of Technology, SE-412 96 Go( teborg, Sweden Received 20 July 1999
Abstract We have performed laboratory measurements of the neutron #ux and its gradient in a static model experiment, similar to a model problem proposed in PaH zsit (Ann. Nucl. Energy 24 (1997) 1257). The experimental system consists of a radioactive neutron source located in a water tank. The measurements are performed using a recently developed very small optical "bre detector. The measured values of the #ux and its gradient are then used to test the possibility of localising the source. The results show that it is possible to measure the #ux on the circumference of a circle and from this calculate the #ux gradient vector. Then, by comparison of the measured quantities with corresponding MCNP calculations, both the direction and the distance to the source are found and thus the position of the source can be determined. ( 1999 Elsevier Science B.V. All rights reserved. PACS: 28.20.Gd; 29.40.Mc; 28.41.Rc Keywords: Localisation; Flux gradient; Optical "bre; Scintillation detector
1. Introduction It was suggested in Ref. [1] that the use of the neutron current could be advantageous for the diagnostics of various space-dependent anomalies, such as the localisation of a static source or a control rod tip. In reactor noise diagnostics, the timedependent current may be even more useful than the time-dependent #ux for localisation of vibrating
* Corresponding author. Tel.: 0031-772-1000; fax: 0031-7723079. 1 On leave of absence from Technical University, Budapest, Hungary E-mail address: [email protected] (I. PaH zsit)
components. In this paper, we will demonstrate experimentally the feasibility of using the current for localising a radioactive neutron source in a homogeneous medium. Since there is no current detector presently available, we have to utilise the #ux gradient as a measure of the current. In neutron di!usion theory, the current is directly proportional to the #ux gradient and thus we assume that di!usion theory is adequate in this study. The #ux gradient in two dimensions can be obtained either from a number of scalar #ux measurements performed on the circumference of a circle or on lines in each main direction. Thus, to realise a gradient detector and be able to "t it into standard instrumentation guide tubes in a pressurized water reactor (PWR), we
0168-9002/99/$ - see front matter ( 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 9 ) 0 0 8 3 0 - X
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need to use very small #ux detectors. The detector should also have a good spatial resolution, which inherently comes with the small physical size, and reasonable e$ciency, radiation hardness and cost. Until recently, no such detectors were readily available. However, a very small radiation detector, consisting of an optical "bre, whose tip is covered with a mixture of converter material, scintillation material and adhesive paste, was developed recently at Nagoya University, Japan [2]. The detector has been used previously in measurements of the fast and thermal axial #ux pro"les in a research reactor [3] and for measurements of the 14.1 MeV neutrons from a D-T neutron generator [4]. Due to its small size and simplicity, this #ux detector also appears to be a good candidate for the elementary #ux measurements in a future current detector. In this paper, we report on measurements of the #ux and the gradient, performed by using the "ber detector in a static system composed of a radioactive neutron source located in a tank "lled with water. The purpose of these measurements is to investigate the behaviour of the #ux and its gradient in a model system. Another aim is to test the possibility of localising the source from the measured values of the #ux and gradient at a single spatial position, as was proposed in Ref. [1].
2. Experimental The detector consists of LiF converter and ZnS(Ag) powder mixed together and pasted with epoxy glue on the tip of a glass optical "bre of diameter 2 mm. Because of the poor optical properties of ZnS, the detector mixture is made thin (&0.3 mm). A layer of opaque paint is also applied on the "bre tip for protection against light and mechanical damage (Fig. 1). The neutrons are captured by the 6Li nucleus in the reaction 6 Li#1 nP3 H#4 He (1) 2 1 0 3 where 4.78 MeV of kinetic energy is also released and shared between the product particles. The cross section for this reaction behaves as 1/v and hence it is large for thermal neutrons and it de-
Fig. 1. The measurement system.
creases with increasing neutron energy. For fast neutrons the detector can be considered as completely transparent. When a neutron is absorbed, the resulting ionised reaction products excite the electrons in the ZnS crystals and the excited electron states deexcite by emitting scintillation light photons. The light pulses produced in the detector are guided by the optical "bre to a photo-multiplier tube (Hamamatsu R5600U Head-on PMT). The PM-tube is connected via an ampli"er chain (ORTEC 113 and 575A) to a multi-channel analyser (MCA). The MCA used is an ORTEC 926 ADCAM MCB, which is controlled by the companion MAESTROTM program (A65-BI ver. 3.0). A schematic view of the measurement system is shown in Fig. 1. The experimental arrangement is shown in Fig. 2. The measurements were performed in a cylindrical water tank of 92 cm diameter. The radioactive neutron source (3 Ci Am}Be) was attached to the top of a support beam and placed in the centre of the tank. The optical "bre with its neutron-sensitive tip was inserted into an aluminium guide tube, which was sealed to protect the "bre from light and direct contact with the water. The tube was put vertically down into the water from a bridge across the water tank. The active part of the neutron detector was positioned on the same
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3. Measurement results and analysis
Fig. 2. (a) A schematic "gure of the experimental setup. (b) A photo taken from above down into the water tank. This picture shows the actual measurement con"guration.
horizontal plane as the centre of the source. To place the detector in an exact radial position in relation to the source, a thin guiding needle at the tip of the guide tube was put into a speci"c hole out of several small holes drilled in a plastic support plate. The holes in the support plate form a number of circles, which are denoted by the letters A}F, with di!erent radii and di!erent distances from the centre of the circles to the centre of the source. The measurement con"guration and the pattern of holes are both shown in Fig. 2b. Four of the circles have the same radius 1.0 cm, while circle E is smaller with a radius of 0.5 cm and F is larger with a radius of 2.0 cm. The radius of the circle a!ects the number of detector positions (i.e., holes) that can be placed along the circumference of the circle. There are 12 angular points with 303 intervals for the circles with 1.0 cm and 2.0 cm radii, respectively, and six points at 603 intervals for the small circle with 0.5 cm radius.
Some characteristics of our small "bre detector can be seen in the amplitude spectrum in Fig. 3. A large value of the channel number on the x-axis corresponds to a large signal amplitude from the detector. To exclude some of the low-energy background noise, we have set a discrimination level (see Fig. 3) on the analog to digital converter and thus the amplitude spectrum shows only signals with an amplitude larger than this discrimination level. Due to the small active size of the detector, there is a very high probability that a large part of the energy is lost from the detector. This means that the detection probability of events with a small amplitude is high and the probability decreases with increasing amplitudes. The lost energy is carried away by either the product particles or the light photons which are leaving the detector volume. The photons can also be lost at the entrance of the optical "bre, in the "bre itself or be absorbed by detector materials. In Fig. 4 the detector count rate as a function of distance from the source centre is shown. In fact, these values were actually measured on the circle contours mentioned previously, but here we have put them in a cylindrical coordinate system with its pivot at the source centre. The position and extension of the measurement circles are also indicated by arrows in the "gure. Close to the source, the count rate increases with increasing distance from the source and it exhibits a maximum at about 3 cm from the source centre. At larger distances, the count rate decreases exponentially with increasing distance from the source. The reason for the presence of the maximum lies with the energy dependence of the neutron #ux around the source. The neutrons are all emitted as fast neutrons by the source and they are then slowed down and thermalised in the water moderator. Hence, at the position of the source the thermal #ux is small. With increasing distance from the source, the thermal #ux "rst increases, due to the slowing down of fast neutrons, and then it reaches a maximum followed by a thermal #ux decrease, due to the absorption of thermal neutrons. Since the detector is only sensitive to thermal neutrons, the measured count rate in Fig. 4 corresponds to the thermal #ux.
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Fig. 3. A typical amplitude spectrum obtained from the "bre detector.
The measured count rates I(u) as functions of the angle u in each circle are shown in Fig. 5. For each circle, the value of zero degrees corresponds to the direction towards the position of the source. The angle is counted in the clockwise direction. In general, the count rate in Fig. 5 has a maximum where the distance to the source is the smallest, i.e., at zero degrees, and the count rate has a minimum at 1803, i.e., at the largest distance from the source. Circle A, however, has a double-humped shape of the count rate as a function of angle with maxima at $903 and minima at 0 and 1803. The reason for this shape is that circle A extends across the maximum of the count rate in Fig. 4. Thus, the point on circle A that is closest to the source, lies on the l.h.s. of the maximum, while the points at $903 lie at the maximum and the point at 1803. lies at r.h.s. of the maximum value. The error bars in Figs. 4 and 5 re#ect only the statistical uncertainty in the measurements. In addition to the statistical error there is also a possible
signi"cant error due to non-perfect positioning of the aluminium guide tube. The reason is that in our experimental set-up it is di$cult to support the guide tube, such that it stands exactly perpendicular to the support plate (see Fig. 2). Thus, there is a possibility for the guide tube to lean either away or towards the source and therefore give a contribution to the error, which is not taken into account in the error bars shown. For example, in circle E the count rate measured at 603 deviates strongly from the expected value, most probably because of nonperfect positioning of the guide tube. The #ux gradient with respect to the distance from the source can be simply calculated from the #uxes in Fig. 4. This method gives only the gradient in a single direction, while the gradient has two components, one in the radial and one in the azimuthal direction. The system is of course cylindrically symmetric and hence the azimuthal direction is unimportant in our particular case. However, we would like to develop a general method and hence
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Fig. 4. The measurement results for the count rate plotted as a function of distance from the source centre. The position and extension of the measurement circles are indicated by arrows.
determine a possible symmetry from the measurement itself. The amount of deviation from perfect cylindrical symmetry of the measurements can also give a useful indication of the error in the method employed. An e$cient method to determine both components of the #ux gradient in a single spatial point is found by using the de"nition of a gradient in the form { / dr +/"lim C S S?0
(2)
where the integral is taken over the circle C which bounds the surface area S. By taking a number of measurements of the count rate I, which is proportional to the #ux, on the contour of a circle with radius R, the two components of the gradient can
be calculated as
P
(3)
P
(4)
LI 1 2p J " " I(u) cosu du x Lx pR 0 and 1 2p LI I(u) sinu du. J " " y Ly pR 0
Eqs. (3) and (4) are given in the coordinate system used for each circle in the measurement. In this system the x-direction points towards the position of the source, i.e., the same as the negative radial direction in the cylindrical coordinate system of the source. The y-direction at the measured circle thus corresponds to the azimuthal direction in the source coordinate system. The average detector count rate at the centre of the measured circle is
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Fig. 5. The count rate for each circle as a function of angle. The zero degree angle corresponds to the direction towards the position of the source centre.
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obtained as
P
1 2p I(u) du (5) IM " 2p 0 where the integrals in Eqs. (3)}(5) are carried out numerically by using a simple summation. The results obtained for the gradient and average count rate for each circle, as well as the distance from the source and radius of the circle used, are given in Table 1. The gradient is given in the form of an absolute value and an angle of direction as D+ID"JJ2#J2 y x L+I"atan[J /J ]. (6) y x In the results, a zero direction angle indicates the direction towards the source centre. It is seen in the table that the angle is indeed close to zero for all circles, except A, for which the gradient points approximately in the opposite direction, i.e., away from the source. This is due to the previously mentioned fact that the slope of the count rate curve in Fig. 4 changes sign across the maximum and circle A lies on the upward slope, while all the other circles lie on the downward slope of the curve. Thus, circle A will have a gradient with $1803 angle, i.e., the gradient points in the direction away from the source. The deviation of the angle from the exact results, i.e., zero or $1803, gives a good indication of the total measurement error in the experimental determination of the direction to the source. In general, relatively accurate values for the angle are obtained for the circles B}D and F, while the values for
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circles A and E are less accurate. For circle E, the deviation is &123 and in this case the abovementioned outlying measurement at 603 is the one responsible for this particularly large deviation. Similarly for circle A, the count rate curve in Fig. 5 is not as symmetric around 1803 as it should be. Most probably this is due to the non-perfect alignment of the guide tube. The statistical uncertainty in the measured count rates is propagated into the values calculated for the gradient and its angle of direction. The calculated statistical errors in the gradient and its angle of direction are also shown in Table 1. Regarding the angle of direction, the estimated statistical errors cannot explain the deviation of the calculated angles from the expected results of zero or $1803. This shows that the statistical error is only a small fraction of the total measurement error. In any case, the calculated statistical errors in the table show that the magnitude of the count rate di!erence across the circle, i.e., *I"I(03)!I(1803) in Fig. 5, a!ects the accuracy. The smaller the change in *I (i.e., the smaller the gradient) the larger the statistical error in the resulting value for the gradient. By comparing the error estimates of D+ID for circles B, E and F, it is clear that the smaller the circle (i.e., the smaller the change in *I) the larger the statistical error. Thus, to accurately determine gradients with small absolute values, large circles are required. Another problem of the gradient estimation appears if the physical gradient changes signi"cantly within the area of the circle. In this case, we obtain an average value of the gradient across the circle rather than a precise estimate of
Table 1 Results Circle
A B C D E F
Distance from source to circle (cm)
2.6 4.6 6.6 8.6 4.6 4.6
Radius of circle (cm)
1.0 1.0 1.0 1.0 0.5 2.0
IM (s~1)
20.47$0.21 18.25$0.18 14.20$0.14 10.22$0.10 18.67$0.19 18.06$0.20
+I D+ID (cm1 s~1)
L+I (3)
0.0737$0.3555 1.903$0.237 2.237$0.180 1.711$0.130 1.842$0.580 1.728$0.134
!144.25$4.83 2.52$0.12 !1.732$0.081 !0.949$0.075 12.489$0.287 3.985$0.079
D+ID IM (cm~1)
0.0036$0.0174 0.104$0.014 0.157$0.014 0.167$0.012 0.099$0.032 0.0957$0.008
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the gradient at the circle centre. The value of the gradient for Circle F is somewhat lower than that for circle B and this is because circle F is so large that the gradient changes signi"cantly within the circle. The gradient determined from circle A also su!ers from the same problem as circle F. We can conclude that for a successful and accurate determination of the gradient, using the method of measuring the #ux on the circumference of a circle (or sphere in a 3-D system), two qualitative conditions need to be ful"lled. First, the gradient should vary very little within the measurement circle. If this is not ful"lled, one will obtain an estimate of the gradient of the #ux surface that is de"ned by the measurement circle, instead of the #ux gradient at the position of the centre of the circle. In our case, this was satis"ed by circles B}E, but not for A and F. Second, the amount of change experienced by the count rate across the circle should be relatively large, i.e., *I should be large. The reason is that the presence of statistical errors in the measurement points leads to large errors in the estimated values for the gradient when *I is very small. In our measurements, both circles A and E have small *I. According to these criteria, the estimated values obtained from circles B}D have small errors, while the results obtained from circles A, E and F have somewhat larger errors. The above discussion indicates some of the problems in constructing a gradient detector using the present principle. The circle needs to be small enough to give a localised measurement such that the gradient does not change signi"cantly within the area of the circle. On the other hand, the circle also needs to be large to yield an accurate estimate of the gradient, especially for small gradients. Thus, some compromise is necessary to optimize the performance of the method. For the detector to be useful in practice, we need also to be able to "t it into a standard instrumentation tube of a PWR. In a Westinghouse PWR the instrument tube has an inner diameter of 1.146 cm. Thus, the maximum diameter of a measurement circle in a future gradient detector should be about 1 cm, which is the same size as our circle E. The measurement of the #ux gradient estimates the direction pointing towards the source. By using two such measurements, we can "nd the position of
Fig. 6. Dependence of the gradient to #ux ratio on the distance from the source.
the source by triangulation. It is also possible to "nd the source position with the use of only a single measurement position. In this case the quantity D+ID/I is used together with a calculated curve of the ratio of the gradient and the #ux as a function of distance from the source. The method was "rst described in Ref. [1] using one-group theory and it is illustrated in Fig. 6. A value of D+ID/I is determined from an experiment and by using the curve in Fig. 6 or inverting the corresponding equation, we obtain an estimate of the distance from the source. Already in Ref. [1] it was made clear that the uncertainty in the estimation of the distance by using this method increases with increasing distance from the source. The reason is that the quantity D+ID/I tends towards a saturation value with increasing distance from the source. The one-group theory example in Fig. 6 can only be used for illustration of the method of determining the distance to the source. In a realistic case, like our experimental determination of the distance to the source, we have to take the energy dependence into account. This was "rst done by calculating the neutron #ux using two-group di!usion theory assuming a point source in an in"nite homogenous medium. This solution decreases monotonically as the distance from the source increases (Fig. 7a) and it cannot describe the maximum, which is found in the measurements (Fig. 4). To reconstruct this e!ect, we have used a spherical volume source instead of a point source. In this case, we obtain a solution with a similar shape as the measured count rates (Fig. 7a). However, there is still some deviation between the
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Fig. 7. (a) The detector count rate as a function of distance from the source. (b) The values of D+ID/I as obtained from MCNP and two-group theory calculations as well as from the measurements.
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calculated curve and the measurements, especially close to the source surface, such that this solution is also inadequate for estimation of the distance from the source. To obtain a more accurate solution, transport theory calculations are necessary. We have used the Monte Carlo code MCNP, version 4.2, to calculate the multigroup neutron #ux in the water tank. The neutron source used in the experiment consists of a steel cylinder "lled with a mixture of 241Am and Be. The cylindrical source geometry was simulated by modelling an ellipsoidal volume source in the centre of the tank. The steel container was an ellipsoidal shell with the same volume and materials as the real container. The outer short axes of the ellipsoid was 1.12 cm and the long axes was 2.1 cm. The volume inside the steel shell was "lled with an amount of Am and Be that would give the same source strength as the real source. The production of the neutrons was however not described by the radioactive decay within the source. The above materials were only used to account for the scattering and absorption reactions of the neutrons within the source itself. The production of the neutrons was assumed to take place on the surface of the source with an energy spectrum corresponding to that of an Am}Be source as given in Ref. [5]. This distribution was placed on the outer surface of the steel container and was considered to be equal in all directions. In this way we get the same source strength and energy dependence as from the real source. For detection we used congruent tally spheres with their centres located at the source
centre. The radii of the tally spheres were varied from 2.12 to 31.12 cm. This corresponds to detection at distances of 1}30 cm from the short axis of the source steel container. The results of the Monte Carlo calculations were convoluted with the JEF 2.2 capture cross-sections for the Li reaction to obtain an estimate of the count rate in the detector. The results in comparison with the measurements and the two-group theory calculations are shown in Fig. 7a. The results have been normalised to the measurements. The "gure shows that the MCNP calculations agree well with the results of the measurements. In Fig. 7b we show the values of D+ID/I as obtained from the MCNP and the two-group theory calculations and from the integration over the measurement circles as given in Table 1, respectively. The measurement results are indicated by circles and denoted by letters corresponding to the measurement circle used to obtain that particular point. Each measurement point is plotted at the ordinate value of D+ID/I obtained from Table 1 and at the abscissa value of the distance from the source to the centre of the measurement circle. The curve obtained from the MCNP calculations can now be used to calculate the values of the distances corresponding to the measured values of D+ID/I and then we can compare the estimated and exact values of the distance to the source. The results are summarized in Table 2. Table 2 shows that the deviations in the determination of the position of the source are rather small. All individual relative deviations are less
Table 2 Estimation of the distance to the source Circle
Distance from source to circle (cm)
Estimation of the distance to the source from the D+ID/I values and the MCNP curve in Fig. 7b (cm)
Deviation between the estimated and the true distance (cm)
Relative deviation (%)
A B C D E F
2.6 4.6 6.6 8.6 4.6 4.6
2.84 4.34 6.80 7.36 4.12 4.12
0.24 !0.26 0.20 !1.24 !0.48 !0.48
9.2 5.7 3.0 14 10 10
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than 15% and most deviations are 10% (&5 mm) or smaller. Circle D has the largest deviation of 14% or 12 mm. The discussion previously indicated that circles B}D are expected to be the most accurate. In light of the deviations shown in Table 2, this is true for B and C, but not for D. The reason is that circle D is close to the saturation level in Fig. 7b and then the uncertainty in the estimation of the distance is the greatest. At very small distances from the source, the situation is just the opposite. Even large statistical errors in D+ID/I yield relatively small errors in the estimate of the distance. The sensitivity to statistical errors is thus small to the left (circle A) and large to the right (circle D) in Fig. 7b. The circles E and F has a medium error and the reason is that their values of D+ID/I are a bit too small. This is due to the relatively large statistical uncertainty for the small circle E and for circle F the reason is that the gradient changes within the circle as compared to that for circle B. Based on the results shown in Table 2, we conclude that it is feasible to use D+ID/I for determination of the distance to the source with a relative accuracy of about 10% for distances shorter than about 10 cm. 4. Conclusions Measurements were performed using a very small scintillation detector attached to an optical "bre. The small size of this detector makes it suitable for performing measurements which require good spatial resolution. This detector was utilized in measurements of the #ux induced by a neutron source in a homogeneous medium (water). One purpose of these measurements has been to test the detector and related equipment. Another purpose has been to test a scheme of measuring the #ux gradient by measuring a number of points on the circumference of circles. The result is a measurement of the average #ux and the gradient at the centre of the circle. The results indicate that the circle should have a small radius, such that the
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gradient does not vary signi"cantly inside the circle. The circle should also be large enough to yield a signi"cant #ux di!erence across the circle diameter, in order to avoid errors due to statistical uncertainties in the measurements. Thus, some compromise is necessary to optimise the performance of the method. The results for the #ux and gradient agree well with those obtained from Monte Carlo calculations using MCNP and from qualitative considerations regarding the measurement symmetry. The gradient yields an accurate estimate of the direction to the source. Further, for small distances to the source ((&10 cm) the quantity D+ID/I can be used to estimate the distance from the measured circle to the source along the direction given by the gradient. This estimation of the distances agrees well with the true distances. Finally, we conclude that the method proposed in Ref. [1] can be successfully utilised for the localisation of a radioactive neutron source using the #ux and its gradient.
Acknowledgements We would like to thank Ryszard Rydz, Lasse Urholm and Lennart Norberg for the design and construction of the experimental set-up. This project was supported by the Swedish Nuclear Power Inspectorate, contract No. 14.5980942-98242.
References [1] I. PaH zsit, Ann. Nucl. Energy 24 (1997) 1257. [2] C. Mori, T. Osada, K. Yanagida, T. Aoyama, A. Uritani, H. Miyahara, Y. Yamane, K. Kobayashi, C. Ichihara, S. Shiroya, J. Nucl. Sci. Technol. 31 (1994) 248. [3] Y. Yamane, A. Uritani, T. Misawa, J.K.-H. Karlsson, I. PaH zsit, Nucl. Instr. and Meth. A 432 (1999) 403. [4] Y. Yamane, P. LindeH n, J. Karlsson, I. PaH zsit, Nucl. Instr. and Meth. A 416 (1998) 371. [5] K.W. Geiger, L. van der Zwan, Nucl. Instr. and Meth. 131 (1975) 315.