Plasma turbulence response to topology changes in the tokamak edge

核聚变实验的性能敏感地取决于装置壁附近的电离气体（=等离子体）。这个区域的特征是磁力线拓扑结构的变化。在发生核聚变反应的热等离子体区域（称为核心），磁力线沿遍历覆盖表面，从不与壁接触，而在靠近壁的区域（称为刮脱层（SOL）），磁力线在跨越有限长度后与壁接触。磁力线拓扑结构的这种变化对等离子体对扰动的响应有重要影响，因此对从热等离子体区域传输能量的湍流也有重要影响。作为第一步，学生将建立一个动力学模型来描述壁面附近的等离子体。等离子体的密度和温度将被视为归一化变量，它们将独立于分布函数的其余部分随时间演化。由于密度、温度和分布函数的其余部分之间的这种分离，该模型将顺利地与用于SOL的流体处理和用于核心的动力学处理相连接，其中湍流是对大多数静止等离子体的小扰动。一旦模型建立，学生将推导出热离子的流体方程。尽管离子通常比电子热，但许多SOL的流体模型都假设离子非常冷以简化方程。新的流体方程将适用于岩心和岩浆液，并将与现有的岩浆液模型进行比较。这些方程将在数值上实现，以研究等离子体从核心流向壁时等离子体量的演变。学生将关注电场，因为它在SOL和core中的确定方式非常不同。在溶胶中，电场主要由壁面的电势决定，而在核心中，电场由湍流动量输运决定。

The performance of nuclear fusion experiments depends sensitively on the ionized gas (=plasma) next to the wall of the device. This region is characterised by a change in the topology of the magnetic field lines. In the hot plasma region where fusion reactions happen, known as core, magnetic-field lines cover surfaces ergodically and never come into contact with the wall, whereas in the region near the wall, known as Scrape-Off-Layer (SOL), magnetic-field lines encounter the wall after spanning a finite length. This change in the topology of the magnetic-field lines has important effects on the response of the plasma to perturbations and hence on the turbulence that transports energy away from the hot plasma region. As a first step, the student will develop a kinetic model to describe the plasma near the wall. The density and the temperature of the plasma will be treated as normalization variables, and they will be evolved in time independently from the rest of the distribution function. Thanks to this separation between density, temperature and the rest of the distribution function, the model will connect smoothly with the fluid treatments used for the SOL and with kinetic treatments used for the core, where turbulence is a small perturbation to a mostly quiescent plasma.Once the model is developed, the student will derive fluid equations with hot ions. Even though ions are usually hotter than electrons, many fluid models for the SOL assume that ions are very cold to simplify the equations. The new fluid equations will be appropriate for both core and SOL, and they will be compared to existing SOL models. These equations will be implemented numerically to study the evolution of plasma quantities as the plasma flows from the core to the wall. The student will focus on the electric field because it is determined very differently in the SOL and in the core. In the SOL, the electric field is mostly determined by the potential at the wall, whereas in the core the electric field is determined by turbulent momentum transport.