The investigation of neutron noise is key to several applications in nuclear reactor physics, such as the detection of control rod or assembly vibrations and the diagnostic of coolant speed and void fraction. In this paper we will elucidate some aspects of the noise equations in the Fourier domain, for the case of periodic fuel rod vibrations with frequency ${\omega }_0$ in a small symmetrical system in which the perturbation is centrally located. We will in particular focus on the double frequency effect, i.e., the emergence of a noise component at $2{\omega }_0$ (possibly stronger than the one at the fundamental frequency ${\omega }_0$). Our analysis will be carried out without truncating the noise source at the first order and in the context of a non-perturbative approach (i.e., without resorting to linearization). For this purpose, we will select a simple benchmark configuration that is amenable to accurate reference solutions obtained by solving the exact time-dependent transport equations. The analysis carried out in this work suggests that the non-perturbative noise equations are mandatory in order to properly discriminate the possible emergence of double frequency effects in neutron noise, especially in view of comparing simulation results to experimental data.

中子噪声的研究对于核反应堆物理中的多种应用至关重要，例如控制杆或组件振动的检测以及冷却剂速度和空隙率的诊断。在本文中，我们将阐明在频率周期性变化的燃料棒振动情况下，傅立叶域中的噪声方程的某些方面。${\omega }_0$在一个小的对称系统中，扰动位于中心。我们将特别关注双频效应，即在$2{\omega }_0$ （可能比基本频率上的频率要强 ${\omega }_0$）。我们的分析将在不扰动噪声源的情况下进行，并且在非扰动方法的情况下（即，不求线性化）。为此，我们将选择一个简单的基准配置，该配置适用于通过求解与时间有关的精确运输方程式而获得的准确参考解决方案。这项工作进行的分析表明，非扰动噪声方程是强制性的，以便正确地区分中子噪声中双频效应的可能出现，特别是将模拟结果与实验数据进行比较时。