Numerical Bifurcation Analysis of Heat Transfer by the Edge Plasma of a Tokamak

托卡马克边缘等离子体传热的数值分岔分析

• 批准号: 2580871
• 金额: --
• 依托单位: University of Oxford
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2580871
• 关键词: Numerical; Bifurcation; Analysis; Heat; Transfer

Nuclear fusion provides one of the most encouraging possibilities for the generation of clean and plentiful energy. The effort to harness this immense power is an active and vital area of research worldwide, while tokamaks-toroidal magnetic confinement fusion reactors-pose one of the promising techniques for doing so.The design and construction of such reactors require a detailed and analytical understanding of how the plasma behaves inside the chamber. Requiring temperatures on the order of 100 million Kelvin to sustain the fusion reaction, this plasma is inconceivably hot, fast, and turbulent. Failure to understand and correctly manage its stability can lead to reduced performance, loss of control and damage to components. The problem of ensuring effective stability under the phenomenal temperature gradients therefore is not just complex, but crucial.The project will work heavily with deflation-a numerical technique for exploring multiple solutions of nonlinear differential equations-with particular application to models of fluid heat transfer. This technique will be extended to periodic orbits and applied to problems in ordinary and partial nonlinear differential equations.The aim is to produce techniques deployable in the Excalibur project NEPTUNE, exploring the different possible mechanisms by which heat might be transferred by the edge plasma-or plasma scrape-off layer-within a tokamak. This project will combine hydrodynamics, numerical analysis, and nonlinear dynamics in application to exascale-class computations.Bifurcation analysis within fluid dynamics-numerical or otherwise-is a tremendously well-developed and active topic, offering many potential avenues of research.By way of example, one paper that provides an excellent springboard for some of the ideas that could be used in tackling this project is Fryderyk Wilczynski's 2019 PhD thesis "Convective Motions in the Scrape-Off Layer of Magnetically Confined Plasmas". Many of the results and methodology in this work are notably relevant to our problem.Wilczynski's paper focuses on the analysis of turbulence in the edge plasma, characterised by intermittent fluctuations known as filaments or blobs. Applying certain technical assumptions, the Braginskii equations of plasma dynamics are used to develop a 2-dimensional model of the scrape-off layer, on which Wilczynski performs extensive stability and bifurcation analysis. The resulting model bears resemblance to Rayleigh-Bénard convection in classical fluid dynamics, one of the most comprehensively studied examples of a nonlinear system.

核聚变为产生清洁和充足的能源提供了最令人鼓舞的可能性之一，利用这种巨大能量的努力是世界范围内一个活跃且重要的研究领域，而托卡马克（环形磁约束聚变反应堆）则是其中之一。这种反应堆的设计和建造需要对等离子体在室内的行为进行详细的分析，需要 1 亿开尔文的温度来维持聚变反应，这种等离子体是。难以想象的高温、快速和湍流，如果不了解并正确管理其稳定性，可能会导致性能下降、失控和组件损坏，因此，在巨大的温度梯度下确保有效的稳定性问题不仅复杂，而且至关重要。该项目将重点研究紧缩——一种探索非线性微分方程多重解的数值技术——特别适用于流体传热模型，该技术将扩展到周期轨道并应用于普通和偏非线性微分方程中的问题。目的是生产可在 Excalibur 项目 NEPTUNE 中部署的等离子体技术，探索托卡马克内边缘等离子体刮除层可能传递热量的不同可能机制。该项目将结合流体动力学、数值分析和非线性动力学。百亿亿级计算。流体动力学中的分岔分析（数值或其他）是一个非常成熟和活跃的主题，提供了许多潜在的研究途径。例如，一篇论文Fryderyk Wilczynski 2019 年的博士论文“磁约束等离子体刮掉层中的对流运动”为可用于该项目谈判的一些想法提供了一个极好的跳板，这项工作中的许多结果和方法都非常相关。 Wilczynski 的论文重点分析了边缘等离子体中的湍流，其特征是间歇性波动，称为细丝或应用某些技术假设，等离子体动力学的 Braginskii 方程用于开发刮掉层的二维模型，Wilczynski 在该模型上进行了广泛的稳定性和分岔分析，所得模型与瑞利-贝纳德对流相似。经典流体动力学，非线性系统研究最全面的例子之一。