Introduction
Noise measurements offer a powerful non-invasive technique to observe a given fissile system’s kinetic parameters. The kinetic parameters encompass the coefficients of the differential equations describing the temporal behavior of a neutron population in a neutron multiplying medium. Previous work [1] has provided estimates of kinetic parameters for the CROCUS zero-power reactor using multiple detector types to observe the neutrons and gamma rays that arise from fission. Our work seeks to improve the detector toolkit by using a dual-particle-sensitive organic scintillator setup. This approach will detect both neutrons and gamma rays simultaneously and conduct dual-particle noise with a single detector type, reducing the complexity of the measurement system and potentially improving measurement capabilities.
The neutron noise equations are derived using the point kinetics assumptions, leading to a set of equations that can be solved cost-efficiently and, if the system indeed allows for the used assumptions, offer a precise predictor for time-dependent phenomena of neutron populations [2]. Noise measurements refer to a method to estimate the prompt decay constant,
Beyond this, point kinetic parameters remain constant during steady-state operations, providing a potential verification metric for reactor operations. Past and current safeguarding of nuclear research reactors does not prescribe online monitoring by default [12], [13]. The frequent estimate of
In the past, estimates of the prompt neutron decay constant from neutron noise measurements of the CROCUS zero-power reactor at critical (
Previous estimates of the prompt neutron decay constant (
In the previous works, neutron and gamma-ray noise were measured with neutron-only and gamma-only sensitive detectors. Notably, the detectors were set either into the control rod tubes in the core center, or very close to the fuel. In both cases, the detectors influenced the neutron economy of the reactor (and therefore also the reactor’s prompt decay constant). This work uses organic scintillator measurements in the CROCUS zero-power reactor to leverage and investigate the potential benefits of, dual-particle sensitivity in a single detector volume for combined gamma-ray and neutron noise analysis. The organic scintillators in this work detect gamma-rays via Compton scattering and neutrons mainly via elastic scattering on hydrogen nuclei. Future work would benefit from the inclusion of organic scintillators with neutron capture capabilities, such as lithium or boron-loaded organic scintillators [18], [19], [20].
We set three trans-stilbene [21], [22] detectors and one organic glass (OGS) [23], [24], [25] detector deep in the CROCUS water reflector and outside the reactor vessel. Our work shows the successful application of organic scintillators for noise measurements in a light-water, zero-power research reactor for the first time. The detectors were well outside regions where they could measurably influence the neutron population in the reactor, thereby offering a potentially less biased estimate of
This article is structured as follows. In Section II, we describe the CROCUS reactor in Section II-A, the experimental setup in Section II-B, organic scintillators and the pulse-shape discrimination technique in Section II-C, and the PSD techniques in Section II-D. We present and discuss estimates of the prompt neutron decay constant,
Methods
A. CROCUS Research Reactor
The CROCUS zero-power research reactor is a two-region, water-moderated uranium core operated by the Laboratory for Reactor Physics and Systems Behaviour (LRS) at the Swiss Federal Institute of Technology Lausanne (EPFL). It is housed in a concrete shielding of about 1.3-m thickness, see Fig. 2. It is a zero-power reactor, with a maximum power of up to 100 W. The reactor core is an approximately cylindrical configuration with a diameter of about 58 cm and a height of 100 cm, consisting of two fuel zones (see Fig. 3). The central zone is loaded with 336 UO2 fuel rods (1.806 wt.%-enriched), set in a square lattice with a pitch of 1.837 cm. The peripheral zone is loaded with up to 176 thicker,
Top-down view of the CROCUS reactor from above the concrete shield. The top wall may be opened when the reactor is shut down.
Schematic view of the CROCUS reactor, showing the vessel, fuel grids, fuel elements, and water level when in operation.
B. Neutron-Gamma Noise Experimental Setup
We placed two 5.08-cm-diameter by 5.08-cm-length trans-stilbene [21], [22] detectors in the water moderator offset 20 cm from the edge of the Umet zone and on the north (S2N) and east (S2E) sides of the reactor, as detailed in Fig. 4(a), with the active volume of each detector centered about the mid-height of the active fuel volume. A sealed, clear plastic tube fastened to the grid held the detector in position and protected the assembly from water. The detectors were connected to a CAEN DT5730S, 500-MHz, 14-bit digitizer, and a CAEN DT1470ET high-voltage unit [22] in the reactor control room through diagnostic channels connecting the control room and containment while maximizing shielding. After a gradual search for the critical water level (959.3 mm), we measured the reactor for 120 min at 3 mW critical.
Diagrammatic representations of axial cuts through the center height of the CROCUS reactor vessel highlighting the fuel grid, detector positions, and vessel boundary for each measurement. (a) First measurement, the 2-in (5.08 cm) trans-stilbene detectors are placed 20 cm from the edge of the Umet zones on the north (S2N) and east (S2E) sides of the reactor core in the CROCUS moderator. (b) Second measurement, the 2-in (5.08 cm) trans-stilbene detectors are placed outside the CROCUS vessel (S2NW and S2NE), one 6-mm trans-stilbene detector is placed at the east edge of the core (S6E), and one 6-mm organic glass detector is placed at the north edge of the core (O6N).
In a follow-up measurement, we moved these two detectors to positions outside the vessel on the north side (S2NW and S2NE) as shown in Fig. 4(b). The centers of the two detectors were 80 cm from the reactor core. Concurrently, we placed two 6-mm cubic detectors, one composed of trans-stilbene (S6E) and one composed of organic glass (O6N) [25], [27] as close as possible to the reactor core. We include the organic glass detector in our measurements due to the rising popularity and availability of organic glass and because trans-stilbene crystal detectors are currently unavailable to purchase from a vendor. After a gradual search for the critical water level (960.0 mm), we measured the reactor for 120 min at 20 mW critical.
Both detector configurations pose essentially no effect on the reactor kinetic state with positions in the water moderator and outside the vessel. Previous measurements introduced detectors in control rod positions and more fissile material (fission chambers) adjacent to the reactor core, posing direct effects on the neutron economy. The largest impact on the kinetic state of our experiment may be caused by the absence of water where the S6E and O6N detector tubes are located.
C. Organic Scintillators and Pulse-Shape Discrimination
Organic scintillators are dual-particle sensitive detectors. The hydrocarbon volume is sensitive to gamma rays mainly through Compton scattering on atomic electrons and sensitive to neutrons mainly through elastic scattering on hydrogen nuclei. Gamma-ray Compton scattering interactions cause free electron travel in the scintillator volume that deposits energy along a track length proportional to the energy of the Compton scatter. Neutron elastic scatter on hydrogen atoms causes proton tracks of much shorter length than energy equivalent electrons. Due to the higher stopping power of protons compared to electrons, a higher density of triplet excitation states occurs, resulting in a higher ratio of delayed fluorescence to prompt fluorescence. For this reason, the light output of neutron elastic scattering is delayed relative to energy-equivalent gamma-ray Compton scattering [28], [29], [30].
The difference in track length also warrants consideration of the detector geometry. A small detector of the same shape as a larger detector will have a higher surface area to volume ratio. The higher this ratio, the more likely scattered particles are to escape the detector volume. Because the electrons have a longer track length than protons, the leakage likelihood of electrons in a small volume is compounded, especially if the maximum dimension of the detector approaches the mean free path of the electrons. The same logic applies to the escape of scattered gamma rays and neutrons. This difference in leakage will cause gamma-ray interactions to have a decreased absolute light output and a higher relative decrease than equivalent neutron interaction light output [31], [32], [33].
We calibrate the light output of an organic scintillator using the Compton edge produced by a measured, mono-energetic (662-keV) 137Cs source [22]. The detectors are calibrated by fitting the measured pulse-integral distribution for the Compton edge location (478 keV). When both collisions have equivalent energy deposition, the neutron light output from elastic scattering on hydrogen is less than the gamma-ray light output from Compton scattering [34]. For this reason, the detectors are only sensitive to fast neutrons. With a detection threshold of about 700 keV electron equivalent (keVee), this would equate to a 3-MeV neutron detection threshold [25], [29].
The incident neutron and gamma-ray radiation may be discriminated on the fly with charge-integration-based pulse-shape discrimination. By quantifying the delayed light output of neutrons in comparison to gamma rays, we discriminate between the two types of radiation. We quantify delayed light output with the tail over total ratio (
D. PSD Technique
The time-dependent behavior of the neutron flux \begin{equation*} \frac {d n\left ({{t}}\right )}{dt} = \frac {\rho \left ({{t}}\right ) -\beta _{\text {eff}}}{\Lambda } n\left ({{t}}\right ) + \sum _{i} \lambda _{i} c_{i} + S \tag {1}\end{equation*}
\begin{equation*} \alpha = \frac {\beta _{\text {eff}}-\rho }{\Lambda }. \tag {2}\end{equation*}
\begin{equation*} P_{ii} \left ({{\tau }}\right )= \frac {1}{2} Y \alpha e^{-\alpha |\tau |} \tag {3}\end{equation*}
\begin{equation*} Y= \frac {\epsilon D_{\nu }}{\left ({{\beta _{\text {eff}}-\rho }}\right )^{2} } \tag {4}\end{equation*}
\begin{equation*} P_{ii} \left ({{\tau }}\right )= \epsilon F_{0} \cdot \left ({{\frac {1}{2} Y_{1} \alpha e^{-\alpha |\tau | }+ \delta \left ({{\tau }}\right )}}\right ). \tag {5}\end{equation*}
The auto PSD (APSD) method is an arguably more robust method to estimate \begin{align*} G_{ii}\left ({{\omega }}\right ) & = \int _{-\infty }^{\infty } dt \cdot e^{-i\omega t} P_{ii}\left ({{t}}\right ) \\ & =\epsilon _{i} F_{0} + \frac {\epsilon _{i}^{2} F_{0} D_{\nu }}{\left ({{\beta _{\text {eff}}-\rho }}\right )^{2}}\frac {1}{1 + \omega ^{2} / \alpha ^{2} }. \tag {6}\end{align*}
The cross PSD CPSD similarly develops from the cross-correlation of two detectors, which theoretically removes the white noise [38], [39]\begin{equation*} G_{ij}\left ({{\omega }}\right ) \!= \!\int _{-\infty }^{\infty } dt \cdot e^{-i\omega t} P_{ij}\left ({{t}}\right )\! =\! \frac {\epsilon _{i} \epsilon _{j} F_{0} D_{\nu }}{\left ({{\beta _{\text {eff}}-\rho }}\right )^{2}}\frac {1}{1 + \omega ^{2} / \alpha ^{2} }. \tag {7}\end{equation*}
Both APSD and CPSD are fit with the same function \begin{equation*} G_{ij}\left ({{\omega }}\right ) = \text {A} + \frac {\text {B}}{1 + f^{2} / f_{c}^{2} }. \tag {8}\end{equation*}
Results and Discussion
The pulse-shape discrimination heatmaps in Fig. 5 contrast the discrimination quality of our three types of detectors. S2E shows two distinct neutron and gamma-ray bands at high (
Pulse-shape discrimination heat maps of tail over total ratios against the total light output in keV-electron-equivalent for (a) S2E, (b) S6E, and (c) O6N detectors. The color values are in counts per heatmap cell. The ratio values above 0.2, 0.25, and 0.28 are taken to be neutrons and below are taken to be gamma-rays for the S2E, S6E, and O6N detectors respectively.
The resultant APSD distribution from the east detector yields a precise estimate of
APSD distributions of S2E for (a) all pulses and (b) neutron classified pulses alongside the CPSD distributions of S2E/S2N for (c) all pulses and (d) neutron classified pulses. All distributions are generated from a 120-min measurement at 3 mW critical.
Correspondingly, we summarize APSD
The CPSD estimate using the S2E and S2N detectors is
The gamma-only estimates with the S2E/S2N and S2NW/S2NE pairs are compared to previous estimates with CeBr3 and simulated Serpent 2 IFP in Fig. 7(a). The S2E/S2N pair gamma-only estimates are in excellent agreement with the previously calculated values and the precision is similar to the CeBr3 measurements in-core in the control rod tube positions. The S2NW/S2NE pair gamma-only estimate agrees with the previous APSD estimates, but the CPSD estimate is just outside of one standard deviation agreement. Nevertheless, we have provided promising and comparable estimates for gamma noise without the need to place detectors in the reactor core. These results are less invasive and simpler to implement.
The neutron-only estimates are compared for the S2E/S2N to previous work in Fig. 6(d). The APSD estimates for the pair do not agree, but confine 235U fission chamber values. The S2E/S2N neutron-only CPSD estimate agrees with the 235U fission chamber value, but the S2E/S2N has quite high uncertainty in comparison.
Conclusion and Future Work
Our results provide new estimates of the prompt neutron decay constant,
In an attempt to prove dual-particle noise in a moderated reactor spectrum, the fast neutron signal collected by our detectors was insufficient to conduct PSD analysis reliably on the neutron noise. Nonetheless, the neutron-only CPSD estimate of
The gamma-ray noise measurements compare well to previous measurements and simulations [1], [5], [16], [40]. The precise estimates from the gamma-ray noise motivate the future calculation of
Our estimates of
ACKNOWLEDGMENT
The authors would like to thank J.-P. Abegg for the logistical support in getting the sensitive detection equipment from EPFL to Geneva Airport (GVA).