Plasma turbulence in 3D magnetic fields

磁化等离子体中的小尺度不稳定性(微不稳定性)是由等离子体密度和温度的大尺度不均匀引起的。粒子和能量的相关湍流传输限制了托卡马克等离子体的限制，即沉浸在轴对称磁场中的等离子体，从而限制了二维磁场。因此，人们对托卡马克中的湍流和湍流输运的性质进行了大量的研究。然而，理想的限制磁场的轴对称会受到各种现象的影响。这些包括设计约束(例如，环形磁场线圈的离散放置导致环形磁场中的波纹)、大规模等离子体不稳定性以及应用于抑制局限于等离子体边缘的不期望的不稳定性的共振磁微扰(称为边缘局域模式或ELM)。尽管这样的3D修改很普遍，但关于三维磁场中的湍流方面的工作还很少。该项目的主要目的是了解破碎轴对称如何影响等离子体的微稳定性和湍流输运。这将涉及代码和算法开发、分析理论和数学建模的组合。特别是，学生的目标是：扩展3D通量管回转动力学程序STELA，以模拟磁通量表面周围的环形区域(使其成为“全通量表面”程序)，这是准确捕捉跨越通量表面内多个磁场线的“带状”模所必需的；开发一种新的伴随方法，用于有效地优化限制磁场的设计，以提高微观稳定性；扩展非轴对称扰动如何改变微观稳定性和输运的早期分析计算；并使用分析模型和数值构造的3D平衡的组合来模拟与磁柱相关的托卡马克等离子体。至少，我们的目标是对微观稳定性和输运如何在三维场中被改变有一个定性的了解：理想情况下，我们也能够利用这种理解并将其应用于诸如被共振磁微扰和/或存在长寿命磁流体(MHD)模式的输运所抑制的ELMS现象。最后，我们期望我们从这个项目中所学到的将为星光器中的输运和微观稳定性的研究提供信息，这些研究利用与禁闭场的3D性质相关的额外自由度来优化宏观稳定性和限制。这项研究有可能改变星光器设计的方向(以及托卡马克中的等离子体成形)，并为设计和使用共振磁微扰来稳定托卡马克中的ELM提供信息。这些成果中的每一个都将对设计磁约束聚变反应堆的途径产生重大影响。该项目属于EPSRC等离子体与激光和数值分析研究领域。这项研究将与库勒姆聚变能源中心的研究人员合作进行，特别是与将担任乔治亚·阿克顿联合主管的莎拉·牛顿博士合作进行。

Small scale instabilities (microinstabilities) are excited in magnetized plasma by large scale inhomogeneities in the plasma density and temperature. The associated turbulent transport of particles and energy limits the confinement of tokamak plasmas, i.e., plasmas immersed in axisymmetric-and thus two-dimensional-magnetic fields. Consequently, much effort has gone into understanding the properties of turbulence and turbulent transport in tokamaks. However, perfect axisymmetry of the confining magnetic field is marred by various phenomena. These include design constraints (e.g., the discrete placement of toroidal field coils leads to ripple in the toroidal magnetic field), large-scale plasma instabilities, and resonant magnetic perturbations that are applied to suppress undesirable instabilities localised to the edge of the plasma (called edge localised modes or ELMs). Despite the prevalence of such 3D modifications, there has been little work done on turbulence in three-dimensional magnetic fields. The main aim of this project is to understand how breaking axisymmetry affects plasma microstability and turbulent transport. This would involve a combination of code and algorithmic development, analytic theory, and mathematical modelling. In particular, the student would aim to: extend the 3D, flux tube gyrokinetic code stella to simulate an annular region surrounding a magnetic flux surface (making it a `full flux surface' code), which is needed to accurately capture 'zonal' modes that span multiple magnetic field lines within a flux surface; develop a novel adjoint method for efficiently optimising the design of the confining magnetic field to improve microstability; extend earlier analytic calculations of how nonaxisymmetric perturbations modify microstability and transport; and use a combination of analytical models and numerically-constructed 3D equilibria to model MAST-relevant tokamak plasmas. At the least we aim to develop a qualitative understanding of how microstability and transport are modified in 3D fields: Ideally, we would also be able to take this understanding and apply it to phenomena such as ELMs suppressed by resonant magnetic perturbations and/or transport in the presence of long-lived magnetohydrodynamic (MHD) modes. Finally, we expect that what we learn from this project will inform studies of transport and microstability in stellarators, which use the additional freedom associated with the 3D nature of the confining field to optimize macroscopic stability and confinement.This research has the potential to change the direction of stellarator design (as well as plasma shaping in tokamaks) and to inform the design and use of resonant magnetic perturbations to stabilise ELMs in tokamaks. Each of these outcomes would have a significant impact on the pathway to designing magnetic confinement fusion reactors.This project falls within the EPSRC research areas of Plasma and Lasers and Numerical Analysis. It is to be carried out in collaboration with researchers at the Culham Centre for Fusion Energy, in particular with Dr. Sarah Newton who will serve as a co-supervisor for Georgia Acton.