陀螺动力学的Laguerre-Hermite伪谱速度公式
Laguerre-Hermite Pseudo-Spectral Velocity Formulation of Gyrokinetics
摘要：
近几十年来，托卡马克湍流的第一性原理模拟已被证明具有重要价值。我们开发了一个伪谱速度制定的湍流方程，平滑插值之间的高效，但分辨率较低的3D gyrofluid表示和传统的，但更昂贵的5D gyrokinetic表示。我们的提法是一个投影的非线性gyrokinetic方程的Laguerre-Hermite速度空间的基础上。我们将讨论与碰撞、闭包和熵有关的问题。虽然任何碰撞算子都可以用于制定，我们强调一个模型算子，具有特别稀疏的拉盖尔-厄米特表示，同时满足守恒定律和H定理。自由流，磁漂移，和非线性相位混合每个引起的封闭问题，我们讨论的利益和自由能守恒的不稳定性。我们表明，该模型是能够再现线性不稳定性和纬向流动力学的陀螺动力学结果。因此，最终的模型是适当的不稳定性，湍流和运输的研究在广泛的几何形状，包括托卡马克和仿星器。
英文摘要：
First-principles simulations of tokamak turbulence have proven to be of great value in recent decades. We develop a pseudo-spectral velocity formulation of the turbulence equations that smoothly interpolates between the highly efficient but lower resolution 3D gyrofluid representation and the conventional but more expensive 5D gyrokinetic representation. Our formulation is a projection of the nonlinear gyrokinetic equation onto a Laguerre-Hermite velocity-space basis. We discuss issues related to collisions, closures, and entropy. While any collision operator can be used in the formulation, we highlight a model operator that has a particularly sparse Laguerre-Hermite representation, while satisfying conservation laws and the H theorem. Free streaming, magnetic drifts, and nonlinear phase mixing each give rise to closure problems, which we discuss in relation to the instabilities of interest and to free energy conservation. We show that the model is capable of reproducing gyrokinetic results for linear instabilities and zonal flow dynamics. Thus the final model is appropriate for the study of instabilities, turbulence, and transport in a wide range of geometries, including tokamaks and stellarators.
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