The critical catastrophe revisited

Abstract

The neutron population in a prototype model of nuclear reactor can be described in terms of a collection of particles confined in a box and undergoing three key random mechanisms: diffusion, reproduction due to fissions, and death due to absorption events. When the reactor is operated at the critical point, and fissions are exactly compensated by absorptions, the whole neutron population might in principle go to extinction because of the wild fluctuations induced by births and deaths. This phenomenon, which has been named critical catastrophe, is nonetheless never observed in practice: feedback mechanisms acting on the total population, such as human intervention, have a stabilizing effect. In this work, we revisit the critical catastrophe by investigating the spatial behaviour of the fluctuations in a confined geometry. When the system is free to evolve, the neutrons may display a wild patchiness (clustering). On the contrary, imposing a population control on the total population acts also against the local fluctuations, and may thus inhibit the spatial clustering. The effectiveness of population control in quenching spatial fluctuations will be shown to depend on the competition between the mixing time of the neutrons (i.e., the average time taken for a particle to explore the finite viable space) and the extinction time. PACS numbers: 05.40.-a, 05.40.Fb, 02.50.-r

A simple implicit coupling scheme for Monte Carlo neutronics and isotopic depletion

“…Recently the phenomenon of neutron clustering has been shown to strongly affect Monte Carlo burn-up simulations (Dumonteil et al, 2014;Zoia et al, 2014;de Mulatier et al, 2015;Nowak et al, 2016;Sutton and Mittal, 2017;Cosgrove et al, 2019). Minimising its effects entails simulating large numbers of neutrons per cycle for fewer cycles (Dumonteil et al, 2014;Sutton and Mittal, 2017).…”

Patchy snapshots of nuclear chain reactions

“…A dedicated experimental program to quantify the scaling of spatial correlations with the reactor power and the reactor dominance ratio could offer perspectives to understand long-standing issues related to reactor power tilts (quadrant asymmetries of the power of unknown origin). For instance, radial power tilts in large reactor seem to closely follow the behavior of spatial correlations as they appear to be positively correlated to the reactor size (or decoupling) and to decrease with the reactor power [40]: this phenomenology could be compatible with a clustering triggered by local reactivity perturbations and enhanced by neutron population control using control rods [19,41]. Finally, both spatial and temporal correlations should be quenched by the presence of neutron leakage.…”

“…The main assumption is that no feedback mechanisms prevent these fluctuations from occurring. Indeed, these feedback mechanisms, such as the temperature effect at high power or operator-induced control rod movements at low power, supposedly quench the critical catastrophe (see for instance [17,35,36]). The 2017 RCF experiments featured a dedicated run targeting the detection of this "critical catastrophe".…”

“…Whenever spontaneous fissions cannot be neglected, a careful inspection of Eq. (19) indicates that ρ needs to be strictly negative, so as to ensure that the power of the nuclear reactor will stay constant (an exactly critical process could not prevent the power to linearly diverge in time under the linear additive production of neutrons coming from intrinsic sources). The full time-dependent dynamic of the neutron population can be therefore be recast under this form…”

“…The persistence of stochastic effects at operating conditions might instead screen this state of the reactor and shall therefore be avoided. In this respect, the appearance of fission-induced correlations in nuclear systems has been extensively investigated [15,16,17,18]; furthermore, neutron clustering has drawn much attention in recent years, with a special emphasis on numerical (Monte Carlo) simulations [13,14,19,20,21,22,23]. Quantifying and characterizing fluctuations and spatial correlations in a low-power reactor has a theoretical and practical interest: the experimental validation of theoretical fluctuations and correlations models at low power would allow to scale them at higher powers, numericaly far from reach.…”