Statistical Formulation of Intermittency in Magnetized Plasmas

相干结构，如大尺度剪切流，是许多物理系统的共同特征。这些结构在化学杂质、动量等量的混合和输运中起着至关重要的作用，特别是它们可能会减少局部输运，形成所谓的输运屏障。小尺度湍流也影响大尺度结构，这种反馈导致了自我调节的可能性。此外，相干结构可以通过相干平流和间歇性(均匀随机、高斯背景上方的相干波动)导致快速(超扩散)传输。由于由此产生的动力学的复杂性，关于这些相干结构的形成及其对运输的影响的理论还远未完成。特别是，相干结构引起的阵发现象使基于单个(平均)湍流系数的传统平均场理论失效，而对湍流输运的正确描述需要统计公式。该研究计划的目的是促进对相干结构对湍流输运影响的理论理解，具体目的是利用非微扰方法(超越平均场理论)来发展阵发现象的统计公式。虽然主要侧重于实验室等离子体的应用，但鉴于其跨学科性质，拟议研究的结果无疑将对许多其他领域(如天体物理、地球物理和空间等离子体、地球大气、气象学、海洋学和工程问题)产生重大影响，从而促进这些学科的研究。

Coherent structures, such as large-scale shear flows, are common features in many physical systems. These structures play a crucial role in the mixing and transport of quantities like chemical impurities, momentum, etc. In particular, they may reduce the transport locally, forming a so-called transport barrier. The small-scale turbulence also affects the large scale structures, with this feedback leading to the possibility of self-regulation. Furthermore, coherent structures can cause fast (super-diffusive) transport by coherent advection as well as intermittency (coherent fluctuations above a uniformly random, Gaussian background). Due to the complexity of the resulting dynamics, a theory of the formation of these coherent structures and their impact on transport is far from complete. In particular, intermittency caused by coherent structures invalidates a traditional mean-field theory based on single (average) turbulent coefficients, and a proper description of turbulent transport demands statistical formulation.The aim of the proposed research programme is to advance the theoretical understanding of the effects of coherent structures on turbulent transport, with the specific objective of developing the statistical formulation of intermittency by using non-perturbative methods (beyond mean field theory). While the main focus is on the applications to laboratory plasmas, in view of its interdisciplinary nature, the outcome of the proposed research will no doubt have significant implications for many other fields (e.g. astrophysical, geophysical and space plasmas, Earth's atmosphere, meteorology, oceanography, and engineering problems), stimulating researches in those disciplines.