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

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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.