The Eulerian variational formulation of the gyrokinetic system in general spatial coordinates
The Eulerian variational formulation of the gyrokinetic system in general spatial coordinates
复制标题
DOI：
10.1063/5.0027905
复制
发表时间：
2020-09
影响因子：
2.2
通讯作者：
H. Sugama;S. Matsuoka;M. Nunami;Shinsuke Satake
中科院分区：
文献类型：
--
作者：
H. Sugama;S. Matsuoka;M. Nunami;Shinsuke Satake
本文推广了文[H. Sugama，{\it et al}.物理学\ Plasmas {\bf 25}，102506（2018）].利用系统拉格朗日量在任意空间坐标变换下的不变性，推导出陀螺中心分布函数和湍流势满足的局部动量平衡方程，并将其作为控制方程的解。这种推导与传统的空间平移方法不同，在空间平移中，非对称正则压力张量通常进入动量平衡方程。在本研究中，拉格朗日密度相对于度量张量的变化被用来直接获得对称压力张量，其中包括湍流对动量输运的影响。此外，它示出在这项工作中如何修改的动量平衡时，碰撞和/或外部源项被添加到gyrokinetic方程。这里得到的结果被认为是有用的全球gyrokinetic模拟调查新古典和湍流输运过程，即使在一般的非轴对称环形系统。
The Eulerian variational formulation of the gyrokinetic system with electrostatic turbulence is presented in general spatial coordinates by extending our previous work [H. Sugama, {\it et al}., Phys.\ Plasmas {\bf 25}, 102506 (2018)]. The invariance of the Lagrangian of the system under an arbitrary spatial coordinate transformation is used to derive the local momentum balance equation satisfied by the gyrocenter distribution functions and the turbulent potential which are given as solutions of the governing equations. This derivation is in contrast with the conventional method using the spatial translation in which the asymmetric canonical pressure tensor generally enters the momentum balance equation. In the present study, the variation of the Lagrangian density with respect to the metric tensor is taken to directly obtain the symmetric pressure tensor which includes the effect of turbulence on the momentum transport. In addition, it is shown in this work how the momentum balance is modified when the collision and/or external source terms are added to the gyrokinetic equation. The results obtained here are considered useful for global gyrokinetic simulations investigating both neoclassical and turbulent transport processes even in general non-axisymmetric toroidal systems.