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A reflection on the fractional order nuclear reactor dynamics

机译：关于分数核反应堆动力学的反思

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Bifurcation and stability analysis in the coupled integer-fractional order dynamic equations of a nuclear reactor is carried out in this work. To this end, the dynamics of a Pressurized Water Reactor (PWR) is taken into account as a mainstay design in the water reactor technology. The effect of fractional derivative order on the stability threshold and the onset of bifurcation phenomena is inspected therein with the temperature feedback coefficient taken as the bifurcation parameter. Overall, the transport of neutrons inside the nuclear reactor core, especially in the high neutron absorbing spaces such as the fuel or control rod, resembles that of a sub-diffusion phenomenon. As such, the pertaining equations which comprise neutron diffusion terms are more carefully treated within a fractional order framework. In this work, a formal approach is examined to help readily compute system poles and the associated stable half plane. Results confirm a sensible tendency to-wards instability as the value of the fractional order is decreased and a more sub-diffusive regime is established. (C) 2019 Elsevier Inc. All rights reserved.
机译：在这项工作中进行了核反应堆的耦合整数阶动态方程中的分叉和稳定性分析。为此，将加压水反应器（PWR）的动态视为水反应堆技术中的主干设计。分数衍生顺序对稳定性阈值和分叉现象发作的影响，以与分叉参数所采用的温度反馈系数进行检查。总的来说，核反应堆芯内的中子输送，特别是在诸如燃料或控制杆的高中吸收空间中，类似于子扩散现象。这样，包括中子扩散项的有关的方程式更仔细地在分数阶框架内处理。在这项工作中，检查正式的方法，以帮助容易地计算系统极和相关的稳定半平面。结果证实了对病房不稳定的明智倾向，因为分数阶的值减少，并且建立了更多的子扩散制度。 （c）2019 Elsevier Inc.保留所有权利。

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