Acta Polytechnica https://doi.org/10.14311/AP.2023.63.0356 Acta Polytechnica 63(5):356–363, 2023 © 2023 The Author(s). Licensed under a CC-BY 4.0 licence Published by the Czech Technical University in Prague APPLICATION OF THE SOURCE-JERK METHOD USING A NEUTRON GENERATOR IN A SUBCRITICAL REACTOR Jan Rataj∗, Jakub Mátl, Pavel Suk Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Department of Nuclear Reactors, Břehová 7, 115 19 Prague, Czech Republic ∗ corresponding author: jan.rataj@fjfi.cvut.cz Abstract. This paper describes the application of the Source-Jerk method using a neutron generator in the VR-1 reactor. The experiments were carried out on a shutdown reactor with subcriticality greater than -10 βeff. A D-D neutron generator located in the radial channel of the VR-1 reactor was used as an external neutron source for the Source-Jerk method. The obtained results were discussed and compared with a conventional Source-Jerk method used at the VR-1 reactor and with the values calculated by the Serpent 2 code. The presented experimental works and their results will allow to extend the methods of reactivity measurements on the VR-1 reactor. They will also help to optimise reactivity measurements on the new subcritical reactor VR-2, which is currently being commissioned at the Czech Technical University in Prague. Keywords: Source-Jerk method, reactivity measurement, experiment, neutron generator, subcritical reactor. 1. Introduction Reactivity is one of the key operating parameters of a nuclear reactor. It is therefore important to con- tinuously improve the various methods for measuring and determining reactivity. The ability to obtain in- formation on the reactivity of the system is essential for reactor control and maintenance of a fission chain reaction. Therefore, the work presented in this paper focuses on improvement of an experimental reactivity measurement method called the Source-Jerk method. All of the reactivity measurements described in this paper were performed at the VR-1 training re- actor operated at the Czech Technical University in Prague (CTU). The main experimental reactivity mea- surement methods used at the VR-1 reactor include Source-Jerk (SJ) and Rod-Drop (RD). Both methods are based on perturbation of the neutron population by dropping the control rod (RD) or sudden removal of an external neutron source (SJ). In the case of the VR-1 reactor, the removal of the AmBe radionuclide source, which is part of the reactor control system, has been the standard for the SJ method. Both the Source-Jerk method and the Rod-Drop method can vary in the way the methods are applied. Two main analysis techniques have been employed in the past: the prompt-drop approximation and the integral-flux method. The prompt-drop approxima- tion neglects the influence of delayed neutrons and depends only on the instantaneous change in neutron flux. This can lead to increased inaccuracy and high statistical error. On the contrary, the integral-flux method does take into account delayed neutrons and depends on the long-term decrease of the neutron population. Below, a brief description of the latter- mentioned technique is presented. The SJ and RD integral flux methods have been found to be highly accurate and can provide a direct measurement of the reactor reactivity [1]. In addition, a variety of technique modifications was proposed; see, e.g. [1, 2] The main objective of the presented work was the application of the Source-Jerk method using a neutron D-D generator and its comparison with the established reactivity measurement technique using a radionuclide source. The experiments performed and their results will allow one to extend the reactivity measurement methods on the VR-1 reactor. In addition, they will be used to optimise reactivity measurements on the new subcritical reactor VR-2, which is currently being commissioned at CTU [3]. 2. Source-Jerk Method The Source-Jerk method is an experimental reactivity measurement technique used in research reactors to assess subcriticality. The standard assumption of the SJ method is a subcritical core driven by an external static neutron source, while the reactor power remains constant. At time t = 0, the neutron source is removed and the neutron population begins to decrease. The reactivity in βeff is given by Equation (1) [1]: ρ(βeff) = n0∫ ∞ 0 n(t)dt [ 1 βeff 8∑ i=1 βeff,i λi + Λ βeff ] , (1) where: • n0 is the neutron density before source removal, • λi, βeff, and βeff,i are kinetic parameters of the delayed neutrons, • Λ is the prompt neutron generation time. 356 https://doi.org/10.14311/AP.2023.63.0356 https://creativecommons.org/licenses/by/4.0/ https://www.cvut.cz/en vol. 63 no. 5/2023 SJ method application using D-D generaor R E LA TI V E D E TE C TO R C O U N T R AT E [- ] TIME [s] ∫n(t)dt n0 Figure 1. Illustration of the Source-Jerk method [4]. The SJ method is illustrated in Figure 1. When applying the SJ method, it is necessary to modify Equation (1). In this work, the delayed neu- trons were described using an eight-group approxima- tion. For experimental applications, the equation can be modified as follows: ρ(βeff) = n0 − nb∫ 300s 0 (n(t) − nb)dt [ 1 βeff 8∑ i=1 βeff λi ] , (2) where nb is the background detector count rate. This modification helps reduce the measurement errors caused by background noise and captures the be- haviour of delayed neutrons. Since the mean gen- eration time depends on the criticality of the sys- tem, the term Λ βeff was neglected ( Λ βeff ≈ 10−2 <<∑8 i=1 βeff,i λi · βeff ≈ 10). Kinetic parameters λi and βeff,i were determined using the Serpent2 code; see Sec- tion 3. 2.1. Description of the experiment The main objective of the experiment was to study the advantages and/or disadvantages of the D-D neutron application for the Source-Jerk method. All experiments were carried out on the VR-1 re- actor. The VR-1 reactor (see Figure 2) is a training reactor operated by the Czech Technical University in Prague. It is a light-water reactor with uranium fuel. The fuel is a low-enriched (19.7 % of U-235) uranium fuel of the tube type [5]. The reactor core is housed in a pool-type reactor vessel. The core usually contains 17 to 21 fuel elements depending on the core configuration. The reactor is equipped with several dry vertical channels and one radial channel. The vertical channels are primarily used for the installation of neutron detectors. The radial channel is used mainly for beam experiments [5]. An Am-Be neutron source is used to start up the reactor. It ensures a sufficient level of signal at the output of the power measurement channels for any conditions and guarantees reliable core monitoring during the reactor start-up. The source is placed Figure 2. Cross section view of the VR-1 reactor showing location of the neutron generator in the radial channel of the reactor [6]. inside a shielded container below the reactor vessel and is moved pneumatically by pressurised air [5]. The VR-1 reactor is classified as a zero power reac- tor, as its maximum power is 500 W. Reactor power is measured by four fission chambers located around the reactor core in the vertical channels [5]. The VR-1 reactor was used in shutdown mode dur- ing the experiments, i.e. the reactivity ρ was less than -10 βeff. Boron-lined detectors SNM-10 and PMV1 detectors (fission chambers) were used to obtain the count rate (which is proportional to n(t)). The detec- tors were placed in the vertical channels located at different positions in the reactor core (see Figure 3). The boron detectors are portable and can be placed in any vertical channel; fission chambers, as part of the reactor I&C, are fixed in the core [5]. The D-D neutron generator P-385 was placed into the radial channel of the reactor (see Figure 2). The application of the Source-Jerk method pro- ceeded as follows. First, the average count rate n0 before the source removal was measured for 300 s. After the neutron source was removed, the integral∫ 300 0 n(t)dt was determined by numerical integration (trapezoidal rule), and finally, the mean value of nb was measured (also averaged for 300 s). The same procedure was followed for the AmBe source. The boron detectors were set at 2 different axial positions – at the centre of the core (position S) and at the upper edge of the core (position V); see Figure 4. The experimental work was divided into two parts: “Preliminary experiment” and “Main experiment”. 1The detectors are part of the reactor I&C used for opera- tional power measurement. 357 J. Rataj, J. Mátl, P. Suk Acta Polytechnica RADIAL CHANNEL B3B2B1 E1 E2 R2R1 PMV 4-trubkový PČ 6-trubkový PČ 8-trubkový PČ 8-trubkový PČ s vytěsnitelem maketa PČ regulační tyče vertikální kanály ⌀ 25, 32 mm vertikální kanál ⌀ 56 a 90 mm provozní měření výkonu reflektor koncovka potrubní pošty zařízení pro studium dynamiky reaktoru externí zdroj neutronů 4-tube fuel assembly 6-tube fuel assembly 8-tube fuel assembly 8-tube fuel assembly with flow displacer fuel dummy control rods experimental channels 25, 32 ⌀ mm vertical channels 56, 90 mm⌀ PMV detectors tube mail equipment for the study of reactor dynamics external source of neutrons boron detectors Figure 3. Scheme of the C18 active core configura- tion [4]. TOP OF THE CORE MIDDLE OF THE CORE BOTTOM OF THE CORE DETECTOR AXIAL POSITION V DETECTOR AXIAL POSITION S NEUTRON GENERATOR AMBE SOURCE Figure 4. Position of boron-lined detector. 2.2. Preliminary experiment The aim of the preliminary experiment was to opti- mise the vertical position of the detectors, compare the results using both neutron sources, and obtain general characteristics of the Source-Jerk method in 80 90 100 110 120 130 140 150 t (s) 0 500 1000 1500 2000 2500 3000 3500 n (1 /s ) Detector B5 count rate Detector F3 count rate Detector H4 count rate Figure 5. Boron detector count rate at position S with D-D generator [4]. 80 100 120 140 160 180 200 t (s) 0 10 20 30 40 50 60 n (1 /s ) Detector B5 count rate Detector F3 count rate Detector H4 count rate Figure 6. Boron detector count rate at position S with AmBe source [4]. the deep subcritical regime. It was observed that the detector count rate at position V was low with high relative fluctuations, leading to a significant observa- tional measurement error. This complication made the integral evaluation in Equation (2) difficult to de- termine and made it unacceptable for the application of the Source-Jerk method. Consequently, position S was established as the default. The use of the neutron D-D generator increased the count rate by about a factor of two, resulting in a lower observational er- ror. The count rate from boron detectors for different neutron sources and vertical positions is illustrated in Figures 5, 6 and 7. 2.3. Main experiment The main aim of the experiment was to obtain consis- tent reactivity values in order to compare both neutron sources and discuss their applicability. The time step was set to 1 s and 0.1 s. Both the D-D generator and the AmBe source were used as neutron sources. The results obtained were compared with the reactivity 358 vol. 63 no. 5/2023 SJ method application using D-D generaor 80 90 100 110 120 130 140 150 t (s) 0 5 10 15 20 25 30 n (1 /s ) Detector B5 count rate Detector F3 count rate Detector H4 count rate Figure 7. Boron detector count rate at position V with AmBe source [4]. 0 1 2 3 4 5 6 measurement 12 11 10 9 8 7 6 5 ( ef f) det B5 det F3 det H4 weighted average value: det B5 weighted average value: det F3 weighted average value: det H4 Figure 8. Reactivities obtained from boron detectors using the D-D generator – time step 1 s [4]. calculated using the Serpent 2 code. The calculated reactivity of the VR-1 reactor in the shutdown mode for the C18 core configuration was -10.84 βeff. Time step 1 s: The results revealed that time op- timisation of the neutron detection time step plays a crucial role in the Source-Jerk method and can significantly affect the results. As shown in Figures 8 and 9, a time step of 1 s resulted in random deviations in reactivity. This error was caused by an insufficient determination of the neutron source removal time. More specificallly, it takes several microseconds for the neutron generator to turn off and roughly 0.7 seconds for the AmBe source to be removed. Since the measurement time step of the detectors is 1 s, the source removal could occur at any point within this one-second interval. Consequently, the integral in Equation (2) varied sig- nificantly for each measurement. Furthermore, the exponential drop in the count rate was significant 0 1 2 3 4 5 6 7 measurement 10 9 8 7 6 5 ( eff ) det B5 det F3 det H4 weighted average value: det B5 weighted average value: det F3 weighted average value: det H4 Figure 9. Reactivities obtained from boron detectors using the AmBe source – time step 1 s [4]. ρ(βeff) – time step 1 s Neutron generator AmBe source det B5 -8.09 ± 0.06 -7.35 ± 0.12 det F3 -9.28 ± 0.10 -8.33 ± 0.17 det H4 -9.44 ± 0.07 -7.87 ± 0.09 Serpent -10.84 ± 10−2 Table 1. Weighted average values of reactivity from boron detectors. right from the beginning, resulting in differences of more than 1.5 βeff. The weighted average values of reactivity are listed in Table 1. To address this issue, the measurement time step was reduced to 0.1 s. Although the observational error slightly increased, the reactivity values became significantly more consistent. In the case of the 1 s time step, both boron detectors and fission chambers (PMV detectors) showed similar results. However, the count rate was lower for the PMV detectors. Time step 100 ms: By reducing the measurement time step, it was possible to determine the time of re- moval much more precisely, leading to stable reactivity values. However, as expected, the observational error increased. With the count rate being roughly 10 times lower, the data obtained from the PMV detectors were unusable. The reactivity values measured with two different neutron sources using boron detectors are illustrated in Figures 10, 11, 12, and 13, weighted values of reactivity from the boron detectors are in- cluded in Table 2 and the calculated subcriticality is described in Table 3. The comparison of both sources will be discussed in the following section. 359 J. Rataj, J. Mátl, P. Suk Acta Polytechnica 0 1 2 3 4 5 6 7 8 9 measurement 13 12 11 10 9 ( ef f) det B5 weighted average value: det B5 Figure 10. Reactivities obtained from boron detector B5 & D-D generator – time step 0.1 s [4]. 0 1 2 3 4 5 6 7 8 9 measurement 17 16 15 14 13 12 11 ( ef f) det F3 weighted average value: det F3 Figure 11. Reactivities obtained from boron detector F3 & D-D generator – time step 0.1 s [4]. ρ(βeff) – time step 100 ms Neutron generator AmBe source det B5 -10.60 ± 0.33 -8.25 ± 0.32 det F3 -12.92 ± 0.56 -8.55 ± 0.51 det H4 -10.56 ± 0.19 — Serpent -10.84 ± 10−2 Table 2. Weighted average values of reactivity from boron detectors. 3. Serpent model In order to compare the results of the experiment car- ried out on the VR-1 reactor, a complete 3D model of the reactor was created in the stochastic calculation code Serpent [7], version 2.1.32. The ENDF/B-VIII.0 nuclear data library was used to calculate the critical- ity of the core and the JEFF-3.3 library was used to calculate the kinetic parameters. The Serpent model of the VR-1 reactor is described in detail and vali- 0 1 2 3 4 5 6 7 8 9 measurement 11 10 9 8 7 ( eff ) det B5 weighted average value: det B5 Figure 12. Reactivities obtained from boron detector B5 & AmBe source – time step 0.1 s [4]. 0 1 2 3 4 5 6 7 8 9 measurement 12 11 10 9 8 7 ( ef f) det F3 weighted average value: det F3 Figure 13. Reactivities obtained from boron detector F3 & AmBe source – time step 0.1 s [4]. Radial channel Close Open keff [–] 0.9295 ± 1· 10−4 0.9228 ± 1· 10−4 ρ [pcm] -7585 ± 4 -8371 ± 4 ρ [βeff] -9.85 ± e−2 -10.84 ± e−2 Table 3. Subcriticality of the VR-1 reactor calculated using the Serpent code. dated in papers [8, 9]. This model was adjusted on the basis of the real geometry during the experiment with other neutron sources. The following models were created for both calcula- tions (criticality and core kinetics): • Model with closed radial channel (reference model). • Model with an open radial channel. • Model with an open radial channel, AmBe neutron source close to the core. • Model with an open radial channel filled by the 360 vol. 63 no. 5/2023 SJ method application using D-D generaor Figure 14. Visualisation of the external D-D neutron generator in the radial channel. D-D neutron generator. The open radial channel refers to a channel without inserted water plugs and shielding. In the provided simulation, the influence of neutron detectors within the vertical channels, including both the boron de- tectors and fission chamber detectors for operational power measurement, was not taken into account. De- spite this simplification, the impact on the obtained results remains negligible. In addition, the precise geometry of these detectors remains unknown. For a visual reference, Figure 14 displays the illustration of the VR-1 reactor with the external D-D neutron generator. The model with AmBe neutron source is visualised in the YZ direction in Figure 15. The X position is 0.5 cm to see the axial position of the neutron source, fuel assemblies, and radial channel. Serpent as a stochastic code requires the definition of the simulated particles. For the calculation of kinetic parameters without external neutron sources, the serpent pop card was used. The parameters of the pop card were 100 000 simulated neutrons, 2 000 active cycles, and 200 inactive cycles for source stabilisation. Criticality calculations were performed with 1 000 000 simulated neutrons, 1 500 active cycles, and 40 inactive cycles. In the case of the external neutron source calculation, the nps card was used with 109 simulated neutrons. In the absence of an external neutron source, the energy spectra within the core are mainly given by the fission reaction and the fuel/moderator fraction. When the D-D neutron generator is present in the radial channel, the energy spectra are primarily gov- erned by the neutrons coming from the generator, specifically at an energy of 2.4 MeV. The energy dis- Figure 15. Visualization of the external AmBe neu- tron source (the YZ direction, X position is 0.5 cm). 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0 2 4 6 8 10 R el at iv e ne ut ro n em is si on Energy (MeV) AmBe neutron spectra Figure 16. AmBe neutron spectra based on the ISO standard [10]. tribution of the AmBe neutron source is represented through histogram energy bins, according to the ISO standard [10]. Figure 16 shows the visualization of the AmBe energy spectra. The subcriticality of the reactor in the shutdown mode is given in Table 3 and the kinetic parameters are given in Table 4. The thermal neutron flux dis- tribution for the neutron generator and the AmBe source is shown in Figures 17 and 18. 4. Results The experiment revealed several interesting facts about the applicability of the Source-Jerk method using a neutron generator. Firstly, the D-D generator was capable of providing a much higher count rate compared to the radionuclide AmBe source. This can lead to a lower observational error. However, it is crucial to consider the detector dead time. 361 J. Rataj, J. Mátl, P. Suk Acta Polytechnica Group βeff λi 1 2.70183e−4± 1.89100e−6 1.24667e−2± 0.00000 2 1.18180e−3± 3.78200e−6 2.82917e−2± 0.00000 3 7.50609e−4± 3.00200e−6 4.25244e−2± 0.00000 4 1.56508e−3± 4.38200e−6 1.33042e−1± 0.00000 5 2.59736e−3± 5.71400e−6 2.92467e−1± 0.00000 6 7.36615e−4± 2.94600e−6 6.66488e−1± 0.00000 7 6.54765e−4± 2.75000e−6 1.63478 ± 00000 8 1.90750e−4± 1.54500e−6 3.55460 ± 00000 Λ 5.00163e−5± 3.00100e−8 βeff 7.94716e−3± 9.53700e−6∑8 i=1 βeff,i λi·βeff 1.2998e1± 3.15140e−2 Table 4. Kinetic parameters of the VR-1 reactor – open radial channel. -8,1158 -10,6029 -9,5956 -10,5030 -8,09 -10,60 -9,44 -10,56 -9,28 -12,92 -8,99 -20,55 -7,38 -7,40 -6,87 -6,84 7,97 -11,53 NG PMV2 B5 PMV1 PMV3 F3 H4 PMV4 Figure 17. Neutron flux distribution & reactivities – D-D generator. Another important aspect that has already been discussed in the previous section is the insufficient determination of the source removal time. This inabil- ity to determine the exact time of removal originated from the long measurement time step. In the case of the neutron generator, shortening the time step resulted in better and more consistent results, as the removal time was easily distinguishable. However, for the AmBe radionuclide source, it takes more than half a second for the source to be removed, making the improvement less significant due to the unclear decrease in the count rate. Furthermore, Figures 17 and 18 show the strong spatial dependence observed when using the neutron generator compared to the AmBe source. These fig- ures illustrate the spatial dependence by comparing the thermal neutron flux distribution in the core cal- culated via Serpent with the measured ρ(βeff). This uneven neutron flux distribution is primarily caused by the position of the neutron source. While the AmBe neutron source is centered under the reactor vessel, the neutron generator is placed in the radial -7,35 -8,25 -8,33 -8,55 -6,76 -8,02 -6,36 -6,62 -7,48 –8,50 -6,97 -7,68 -7,87 AmBe PMV2 B5 PMV1 PMV3 H4 F3 PMV4 Figure 18. Neutron flux distribution & reactivities – AmBe source. channel from the side of the reactor. This results in an uneven neutron flux distribution, which affects the measured reactivity depending on the position of the detector. Ultimately, the use of the AmBe radionuclide as a neutron source caused an overestimation of the inte- gral ∫ ∞ 0 n(t)dt, leading to higher measured reactivity values. This overestimation is, again, due to the source removal time. When the AmBe source is removed, it takes about 0.7 seconds for the source to return to the shielding box while it is still emitting neutrons. These emitted neutrons contribute to the integral eval- uation and cause an overestimation of the detector count after the source removal. In comparison, the average time for the neutron generator to turn off is a few microseconds. This highlights that the source removal time should be insignificant compared to the measurement time step. 5. Conclusions The set of spatially independent kinetic equations (see, e.g., [6]) may introduce variations in the obtained re- 362 vol. 63 no. 5/2023 SJ method application using D-D generaor activity values compared to the actual subcriticality. As a result, further investigations are needed to re- fine and modify the Source-Jerk method, taking into account the position of the detectors. In addition to the spatial dependence mentioned above, the concentration of the parent nuclei of the delayed neutrons, as well as the kinetic parameters λi and βeff,i, have spatial dependence. This may raise the question as to whether incorporating mathematical or computational methods into account for this de- pendence would make the determination of reactivity more precise. Moreover, the position of the neutron source relative to the active core and detector plays a significant role. Numerical calculations (see Figures 17 and 18) demon- strate that the placement of the external neutron source greatly affects the thermal flux distribution. This points out the critical importance of achieving a consistent neutron flux distribution in order to obtain accurate results from individual detectors. This study highlights several recommendations for further experimental work with the Source-Jerk method. Firstly, the neutrons emitted by the source should pass through the fuel and reach the detectors at a suitable distance, ensuring a sufficient detector count rate. Moreover, it is crucial to place the source in such a manner that it uniformly affects the entire core. Finally, great attention should be paid when selecting the appropriate time step for data collection and analysis. Addressing these recommendations and refining the methodology for reactivity measurements using the Source-Jerk method will contribute to enhancing the accuracy and reliability of reactor safety assessments and optimisation efforts in VR-1. This work will also provide a basis for more in-depth studies of the spatial dependence of the Source-Jerk method and for a development of pulsed reactivity measurement methods on the VR-2 reactor. Both of these studies will share the same experimental charateristics and some of the presented conclusions may be generalised. Acknowledgements The experimental work described in the paper was sup- ported by the project “Modernization of the Large Re- search Infrastructure VR-1 – Training Reactor for Research Activities” (reg. nr. CZ.02.1.01/0.0/0.0/ 18_046/0015833) supported by Operational Programme Research, Develop- ment and Education co-financed from European Structural and Investment Funds and from state budget of the Czech Republic. 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ISO/TC 85/SC 2 Radiological protection 1989. 363 https://digital.library.unt.edu/ark:/67531/metadc1056620/m2/1/high_res_d/5147458.pdf https://digital.library.unt.edu/ark:/67531/metadc1056620/m2/1/high_res_d/5147458.pdf https://doi.org/10.3929/ethz-a-000087577 https://doi.org/10.1016/j.nucengdes.2021.111578 https://enygf.org/new/ENYGF2023%20Book%20of%20Proceedings.pdf?_t=1690963680 https://enygf.org/new/ENYGF2023%20Book%20of%20Proceedings.pdf?_t=1690963680 https://doi.org/10.1109/EPE51172.2020.9269254 https://doi.org/10.1016/j.anucene.2018.09.007 http://montecarlo.vtt.fi/download/Serpent_manual.pdf http://montecarlo.vtt.fi/download/Serpent_manual.pdf https://doi.org/10.1016/j.anucene.2021.108757 https://doi.org/10.1051/epjconf/202124708008 Acta Polytechnica 63(5):356–363, 2023 1 Introduction 2 Source-Jerk Method 2.1 Description of the experiment 2.2 Preliminary experiment 2.3 Main experiment 3 Serpent model 4 Results 5 Conclusions Acknowledgements References