On the determination of neutron multiplication by the Rossi-alpha method

Introduction. This work contains the results of determining the prompt neutron multiplication factor in the subcritical state of a one-core BFS facility, obtained by the neutron coincidence method, for which the influence of the error in the βeff in determining the multiplication factor turned out to be insignificant. The core of the facility consisted of rods filled with pellets of metallic depleted uranium, 37% enriched uranium dioxide and 95% enriched plutonium, sodium, stainless steel and Al2O3. Stainless steel served as a reflector. Methods. In contrast to the inverse kinetics equation solving (IKES) method, which is convenient for determining reactor subcritical states, the neutron coincidence method practically does not depend on the error in the value of the effective fraction of delayed neutrons βeff. If in the IKES method the reactivity value is obtained in fractions of βeff, i.e., from the measurement of delayed neutrons, the neutron coincidence method is based on the direct measurement of the value (1 – kσp)2, where is the effective multiplication factor by prompt neutrons. The total multiplication factor is defined as keff = kσp + βeff. If, for example, keff ≈ 0.9 (which is typical for determining the fuel burnup campaign), then it is the error in determining kσp that is the main one in comparison with the error in βeff. Thus, a 10% error in βeff of 0.003–0.004 (typical for plutonium breeders) will make a contribution to the error 1 – keff equal to 1 – kσp + βeff ≈ 0.00035, i.e., approximately 0.35%, but not 10%, as in the IKES method. Rossi-alpha measurements were carried out using two 3He counters and a time analyzer. The measurement channel width Δt was 1.0 μs. From these measurements, the value of the prompt neutron multiplication factor was obtained. In this case, the space-isotope correlation factor for the medium with a source was calculated using the following values: Φ(x) – solutions of the inhomogeneous equation for the neutron flux and Φ+(x) – solutions of the ajoint inhomogeneous equation. Results. The authors also present a comparison of the results of the Rossi-alpha experiment and measurements of the BFS-73 subcritical facility by the standard IKES method in determining the multiplication factor value. The data of the IKES method differ insignificantly from the results of the Rossi-alpha method over the entire range of changes in the subcriticality with an increase in the subcriticality of the BFS-73 one-core facility. Conclusion. It was impossible to apply the neutron coincidence method to fast reactors; however, the method turned out to be quite workable on their models created at the BFS facility, which was successfully demonstrated in this study.

Approach to Criticality

Source neutrons are essential for reactor restart after a long shutdown. The term “source neutrons” applied to a particular time interval refers to a steady supply of neutrons, constant over the time interval of interest. This supply must be independent of the current or very recent fission rate, which can vary over the time interval. Thus, source neutrons exclude prompt neutrons and even delayed neutrons which originate in the fuel (i.e., those born in the fuel itself). This exclusion does not apply to delayed photoneutrons, which come from fissions that have occurred a long time before, and whose numbers are quite constant over the current time interval (further discussion of this point below).

Measuring the delayed neutrons multiplicity and kinetic parameters for the thermal induced fission of 235U, 239Pu and 233U

In the normal operation of nuclear reactors, the kinetic behavior of the neutron population in the core is driven by the so-called delayed neutrons (DN). The DN yield per fission, their average lifetime and their groups’ abundances are the main physical parameters used to predict the kinetic behavior of the reactor and its reactivity. The overall uncertainty associated to reactivity predictions, which is linked directly to the nuclear reactor safety margins, is thus closely dependent on a few parameters associated with DN. Depending on the nuclear data library, DN kinetic parameters present significant discrepancies, even for major fissile isotopes such as 235U or 239Pu. In this context, CEA has long been working for improving DN nuclear data. In 2018, CEA launched the ALDEN project (Average Lifetime of DElayed Neutrons) in the framework of a collaboration between CEA/DES, CEA/DRF, CNRS/IN2P3 (LPSC, CENBG, LPC), ENSICAEN and Caen University. This program aims at measuring the kinetics of the delayed neutrons to derive the DN yield, their average lifetime and abundances. Two experimental campaigns focusing on the thermal fission of 235U were conducted in 2018 and 2019. They demonstrated the concept feasibility and gave high quality estimations of the DN multiplicity (1.631 ± 0.014 %) and average lifetime (8.82 ± 0.6 s) for 235U. More recently in March 2021, a more ambitious irradiation campaign was conducted on 239Pu and 233U. This paper details the new experimental setup, which was upgraded to meet ILL safety requirements for handling plutonium. The data analysis process is presented, with a focus on the problem of dead time correction. Finally, some preliminary delayed neutron decay curves are showed and discussed.

APPLICATION OF RESPONSE MATRIX METHOD TO TRANSIENT SIMULATIONS OF NUCLEAR SYSTEMS

Until recently, reactor transient problems were exclusively solved by approximate deterministic methods. The increase in available computing power made it feasible to approach the transient analyses with time-dependent Monte Carlo methods. These methods offer the first-principle solution to the space-time evolution of reactor power by explicitly tracking prompt neutrons, precursors of delayed neutrons and delayed neutrons in time and space. Nevertheless, a very significant computing cost is associated with such methods. The general benefits of the Monte Carlo approach may be retained at a reduced computing cost by applying a hybrid stochastic-deterministic computing scheme. Among such schemes are those based on the fission matrix and the response matrix formalisms. These schemes aim at estimating a variant of the Greens function during a Monte Carlo transport calculation, which is later used to formulate a deterministic approach to solving a space-time dependent problem. In this contribution, we provide an overview of the time-dependent response matrix method, which describes a system by a set of response functions. We have recently suggested an approach where the functions are determined during a Monte Carlo criticality calculation and are then used to deterministically solve the space-time behaviour of the system. Here, we compare the time-dependent response matrix solution with the transient fission matrix and the time-dependent Monte Carlo solutions for a control rod movement problem in a mini-core reactor geometry. The response matrix formalism results in a set of loosely connected equations which offers favourable scaling properties compared to the methods based on the fission matrix formalism.

On a significant slowing-down of the kinetics of fast transient processes in a fast reactor

The kinetics of nuclear reactors is determined by the average neutron lifetime. When the inserted reactivity is more than the effective delayed neutron fraction, the reactor kinetics becomes very rapid. It is possible to slow down the fast reactor kinetics by increasing the neutron lifetime. The authors consider the possibility of using the lead isotope, 208Pb, as a neutron reflector with specific properties in a lead-cooled fast reactor. To analyze the emerging effects in a reactor of this type, a point kinetics model was selected, which takes into account neutrons returning from the 208Pb reflector to the reactor core. Such specific properties of 208Pb as the high atomic weight and weak neutron absorption allow neutrons from the reactor core to penetrate deeply into the 208Pb reflector, slow down in it, and have a noticeable probability to return to the reactor core and affect the chain fission reaction. The neutrons coming back from the 208Pb reflector have a long ‘dead-time’, i.e., the sum of times when neutrons leave the reactor core, entering the 208Pb reflector, and then diffuse back into the reactor core. During the ‘dead-time’, these neutrons cannot affect the chain fission reaction. In terms of the delay time, the neutrons returning from the deep layers of the 208Pb reflector are close to the delayed neutrons. Moreover, the number of the neutrons coming back from the 208Pb reflector considerably exceeds the number of the delayed neutrons. As a result, the neutron lifetime formed by the prompt neutron lifetime and the ‘dead-time’ of the neutrons from the 208Pb reflector can be substantially increased. This will lead to a longer reactor acceleration period, which will mitigate the effects of prompt supercriticality. Thus, the use of 208Pb as a neutron reflector can significantly improve the fast reactor nuclear safety.

Detection of Neutrons Emitted From Reactor Primary Circuit Water by Discontinuing Flow Method

On-line activity measurement of fission products in a primary circuit water is often used for a fuel failure detection in research and power nuclear reactors. When gamma spectrometry is used for the activity measurement, high signal from 16N radionuclide and other activation products make the detection of fission products difficult. The detection of delayed neutrons emitted from several fission products is also used; however, if the detector is placed near the outlet coolant pipe, the signal from the delayed neutrons cannot be distinguished from the neutrons emitted due to 17N decay and deuterium photofission, with exception of a reactor scram condition. In this paper, a method of discontinuing the flow of primary circuit water is described. This method is based on the water flowing through a bypass on the outlet pipe to the sampling container and the flow is periodically temporarily interrupted, e.g., using 200 s + 200 s cycles. Neutrons located in the vicinity of the sampling container are continuously detected with a measuring sampling time of less than 2 s. The signal part, corresponding to the delayed neutrons, is evaluated by the signal decay analyzing during the flow interruption. The main sources of delayed neutrons suitable for this method are 137I, 87Br, and 88Br radionuclides with half-lives of 24.5 s, 55.7 s, and 16.5 s, respectively. The method was theoretically analyzed and experimentally verified in the LVR-15 research reactor.