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性激发的。相关的粒子和能量的湍流输运限制了托卡马克等离子体的限制，即等离子体浸入轴对称磁场，因此是二维磁场。因此，在理解托卡马克湍流和湍流输运的性质方面已经付出了很多努力。然而，约束磁场的完美轴对称受到各种现象的破坏。这些包括设计限制（例如，环面磁场线圈的离散放置导致环面磁场的纹波），大规模等离子体不稳定性，以及用于抑制等离子体边缘不期望的不稳定性（称为边缘局部化模式或elm）的共振磁扰动。尽管这种三维修正很流行，但在三维磁场中的湍流方面做的工作很少。本项目的主要目的是了解轴对称破缺如何影响等离子体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结合。特别是，学生的目标是：扩展3D磁通管回旋动力学代码stella，以模拟磁通表面周围的环形区域（使其成为“全磁通表面”代码），这需要准确捕获磁通表面内跨越多个磁场线的“区域”模式；开发一种新的伴随方法，有效地优化围磁场的设计，以提高微稳定性；扩展非轴对称微扰如何改变微稳定性和输运的早期分析计算；并结合分析模型和数值构建的三维平衡来模拟与mast相关的托卡马克等离子体。至少，我们的目标是对微稳定性和输运如何在3D场中被修改进行定性理解：理想情况下，我们也能够将这种理解应用于共振磁扰动和/或在长寿命磁流体动力学（MHD）模式存在下的输运抑制的elm等现象。最后，我们希望我们从这个项目中学到的东西将为仿星器的输运和微稳定性研究提供信息，这些研究利用与约束场的3D性质相关的额外自由来优化宏观稳定性和约束。这项研究有可能改变仿星器设计的方向（以及托卡马克中的等离子体成型），并为设计和使用共振磁扰动来稳定托卡马克中的elm提供信息。这些结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的等离子体和激光以及数值分析研究领域。它将与Culham聚变能中心的研究人员合作进行，特别是与Sarah Newton博士合作，她将担任Georgia Acton的联合主管。

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.