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Gyro-water-bag approach in nonlinear gyrokinetic turbulence

机译：陀螺-水袋方法在非线性动力学动荡中的应用

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摘要

Turbulent transport is a key issue for controlled thermonuclear fusion based on magnetic confinement. The thermal confinement of a magnetized fusion plasma is essentially determined by the turbulent heat conduction across the equilibrium magnetic field. It has long been acknowledged, that the prediction of turbulent transport requires to solve Vlasov-type gyrokinetic equations. Although the kinetic description is more accurate than fluid models (MHD, gyro-fluid), because among other things it takes into account nonlinear resonant wave-particle interaction, kinetic modeling has the drawback of a huge computer resource request. An unifying approach consists in considering water-bag-like weak solutions of kinetic collisionless equations, which allow to reduce the full kinetic Vlasov equation into a set of hydrodynamic equations, while keeping its kinetic behaviour. As a result this exact reduction induces a multi-fluid numerical resolution cost. Therefore finding water-bag-like weak solutions of the gyrokinetic equations leads to the birth of the gyro-water-bag model. This model is suitable for studying linear and nonlinear low-frequency micro-instabilities and the associated anomalous transport in magnetically-confined plasmas. The present paper addresses the derivation of the nonlinear gyro-water-bag model, its quasilinear approximation and their numerical approximations by Runge-Kutta semi-Lagrangian methods and Runge-Kutta discontinuous Galerkin schemes respectively.
机译：湍流传输是基于磁约束的受控热核聚变的关键问题。磁化聚变等离子体的热限制主要由横跨平衡磁场的湍流热传导确定。长期以来，人们一直认为，湍流输运的预测需要解决弗拉索夫式的动力学方程。尽管动力学描述比流体模型（MHD，陀螺流体）更准确，但由于它尤其考虑了非线性共振波-粒子相互作用，因此动力学模型的缺点是需要大量的计算机资源。一种统一的方法是考虑动力学无碰撞方程式的类似于水袋的弱解，这可以将完整的动力学Vlasov方程式简化为一组流体动力学方程式，同时保持其动力学行为。结果，这种精确的减小引起了多流体数值分辨率的成本。因此，找到类似水袋的陀螺动力学方程的弱解导致了陀螺-水袋模型的诞生。该模型适用于研究线性和非线性低频微不稳定性以及磁约束等离子体中的相关异常传输。本文分别用Runge-Kutta半拉格朗日方法和Runge-Kutta间断Galerkin格式分别研究了非线性陀螺-水袋模型的推导，拟线性近似及其数值近似。

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