Symmetries of a reduced fluid-gyrokinetic system

Symmetries of a fluid-gyrokinetic model are investigated using Lie group techniques. Specifically the nonlinear system constructed by Zocco and Schekochihin (Zocco & Schekochihin 2011), which combines nonlinear fluid equations with a drift-kinetic description of parallel electron dynamics, is studied. Significantly, this model is fully gyrokinetic, allowing for arbitrary $k_{\bot \rho I}$ where $k_\bot$ is the perpendicular wave vector of the fluctuations and $\rho I}$ is the ion gyroradius. The model includes integral operators corresponding to gyroaveraging as well as the moment equations relating fluid variables to the kinetic distribution function. A large variety of exact symmetries is uncovered, some of which have unexpected form. Using these results, new nonlinear solutions are constructed, including a helical generalization of the Chapman-Kendall solution for a collapsing current sheet.本研究采用李群方法（Lie group techniques）对流体回旋动理学模型（fluid-gyrokinetic model）的对称性展开探究。具体而言，本文聚焦佐科与谢科钦（Zocco & Schekochihin 2011）构建的非线性系统——该系统将非线性流体方程与平行电子动力学的漂移动理学描述（drift-kinetic description）相结合。尤为关键的是，该模型属于完全回旋动理学模型，可适用于任意$k_{ot ho I}$，其中$k_ot$为涨落的垂直波矢，$ ho I$为离子回旋半径（ion gyroradius）。该模型包含对应回旋平均（gyroaveraging）的积分算子（integral operators），以及将流体变量与动理学分布函数（kinetic distribution function）相关联的矩方程（moment equations）。研究揭示了诸多精确对称性（exact symmetries），其中部分对称性具有出人意料的形式。基于上述研究成果，我们构建了全新的非线性解，其中包括针对坍缩电流片的查普曼-肯德尔解（Chapman-Kendall solution）的螺旋推广形式。