Small-scale turbulence to large-scale flows and magnetic fields: a gyrokinetic investigation

等离子体代表了物质的最丰富的状态，包括几乎所有的可见宇宙。大多数天体物理等离子体都处于湍流运动状态。湍流表征了等离子体和流体中无数物理过程的行为，例如，大气流、太阳耀斑或吸积盘。湍流是经典物理学中尚未解决的重要问题之一，尽管它的丰富性和实用性，但它仍然是经典物理学中尚未解决的问题之一。本研究计划的重点是小尺度湍流在大尺度结构形成中的作用。这种现象的突出例子是1）发电机机制的长期问题（即，天体磁场的起源和永久化），以及2）流体或等离子体中大规模流动的形成，例如，木星大气中的条纹一个统一的主题，我们的方法来解决这个问题是应用先进的模型，超越了常用的MHD模型。 首先，我们将考虑一个被称为霍尔MHD的流体模型，它构成了一个统一框架的基础，用于理解运动学和磁大尺度结构的出现，而这些结构是由小尺度湍流混合而成的。拟议的项目提供了肥沃的土壤，分析和数值的进步。所谓的双/多贝尔特拉米国家在这些过程中发挥着关键作用，初步工作将寻求阐明这些国家的作用，以制定简化的分析模型，指导随后的调查。此外，我们将扩大我们的研究范围，包括基于（陀螺仪）动力学模型的数值研究，旨在测试流体理论的预测和识别动力学系统固有的新效应。特别是，使用的动力学理论将促进一种新的热发电机机制的研究，其中小尺度的热湍流的波动可能会饲料的形成大规模的结构，这个项目的结果将大大推进我们的理解，有序的大规模结构发生在天体物理系统和实验室（在托卡马克带状流）。此外，它们还将揭示等离子体中湍流能量转换的不同路径。深入了解这些问题将有助于我们开发简化模型，提供定量正确的预测这些基本的和普遍存在的等离子体现象。

Plasma represents the most abundant state of matter comprising almost all of the visible Universe. Most astrophysical plasmas are in a state of turbulent motion. Turbulence characterizes the behaviour of a myriad of physical processes in both plasmas and fluids, e.g., atmospheric streams, solar flares or accretion disks. Despite its abundance and practical importance, turbulence remains one of the outstanding unsolved problems in classical physics.The research program outlined in this proposal focuses on the role of small-scale turbulence in the formation of large-scale structures. Prominent examples of such phenomena are 1) the long-standing problem of the dynamo mechanism (i.e., the origin and perpetuation of the magnetic fields of celestial objects), and 2) the formation of large-scale flows in fluids or plasmas, e.g., the stripes in Jupiter's atmosphere. A unifying theme for our approach to this problem is the application of advanced models that go beyond the commonly used MHD model. First, we shall consider a fluid model known as Hall MHD, which forms the basis of a unified framework for understanding the emergence of both kinematic and magnetic large-scale structures out of a mixture of small-scale turbulence. The proposed project provides fertile ground for both analytical and numerical advances. The so-called Double/Multi Beltrami States play a pivotal role in these processes and initial efforts will seek to elucidate the role of such states in order to formulate reduced analytical models that will guide subsequent investigations. Further, we shall expand the scope of our research to include numerical studies based on (gyro)kinetic models aimed at testing the predictions of the fluid theories and identifying novel effects intrinsic to kinetic systems. In particular, the use of a kinetic theory will facilitate studies of a novel thermal dynamo mechanism wherein small-scale thermal turbulent fluctuations may feed the formation of large-scale structures.The results of this project will substantially advance our understanding of the ordered large-scale structures occurring in astrophysical systems and in the laboratory (zonal flows in tokamaks). In addition, they will also shed light on the different paths of turbulent energy conversion in plasmas. Deeper insights into those issues will help us develop reduced models which provide quantitatively correct predictions of these fundamental and ubiquitous plasma phenomena.