Field-theoretic approach to neutron noise in nuclear reactors

An operating nuclear reactor is designed to maintain a sustained fission chain reaction in its core, which results from a delicate balance between neutron creations (i.e., fissions) and total absorptions. This balance is associated with random fluctuations that can have two, very different, origins. A distinction must thus be made between low-power noise, whose origin lies in the inherently stochastic nature of neutron interactions with matter, and high-power noise, whose origin lies in the particular thermomechanical constraints associated with the environment in which neutrons propagate. Modeling the behavior of this noisy neutron population with the help of stochastic differential equations, we first show how the Martin-Siggia-Rose-Janssen-De Dominicis (MSRJD) formalism, providing a field theoretical representation of the problem, reveals a convenient and adapted tool for the calculation of observable consequences of neutron noise. In particular, we show how the MSRJD approach is capable of encompassing both types of neutron noises in the same formalism. Emphasizing then on power noise, it is shown how the self-sustained chain reaction developing in a reactor core might be sensitive to noise-induced transitions. Establishing an unprecedented connection between the neutron population evolving in a reactor core and the celebrated Kardar-Parisi-Zhang (KPZ) equation, we indeed find evidence that a noisy reactor core power distribution might be subject to a process analogous to the roughening transition, well-known to occur in systems described by the KPZ equation.

Figure 1

Comparison of the theoretical results obtained for both the mean number of neutrons and its variance with a numerical integration of Eq. (3). The calculations are performed with the following set of parameters: $N_0=1000,S=10,\rho =-4.{10}^{-5},\sigma =0.03$ (so $\theta =49.{10}^{-5}$), and $\gamma =0.02$.

Figure 2

Comparison of the theoretical mean numbers of neutron and precursor derived with the MSRJD approach with a direct numerical integration of Eq. (2) using the Milstein technique. The calculation is performed using the following set of parameters: $N_0=1000,S=10,\rho =-400.{10}^{-5},\beta =600.{10}^{-5},\sigma =0.03, \gamma =0.02$, and ${\lambda }_D=ln2$.