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Energetic consistency and momentum conservation in the gyrokinetic description of tokamak plasmas

机译：托卡马克等离子体回旋动力学描述中的能量一致性和动量守恒

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摘要

Gyrokinetic field theory is addressed in the context of a general Hamiltonian. The background magnetic geometry is static and axisymmetric and all dependence of the Lagrangian on dynamical variables is in the Hamiltonian or in free field terms. Equations for the fields are given by functional derivatives. The symmetry through the Hamiltonian with time and toroidal angle invariance of the geometry lead to energy and toroidal momentum conservation. In various levels of ordering against fluctuation amplitude, energetic consistency is exact. The role of this in the underpinning of conservation laws is emphasized. Local transport equations for the vorticity, toroidal momentum, and energy are derived. In particular, the momentum equation is shown for any form of Hamiltonian to be well behaved and to relax to its magnetohydrodynamic form when long wavelength approximations are taken in the Hamiltonian. Several currently used forms, those which form the basis of most global simulations, are shown to be well defined within the gyrokinetic field theory and energetic consistency.
机译：动力学场理论是在一般汉密尔顿主义的背景下提出的。背景磁几何是静态的并且是轴对称的，并且拉格朗日对动力学变量的所有依赖性都是哈密顿量或自由场术语。场的方程由函数导数给出。通过哈密顿量的对称性以及几何形状的时间和环面角不变性导致能量和环面动量守恒。在针对波动幅度的各种级别的排序中，能量一致性是精确的。强调了这一点在保护法的基础上的作用。推导出了涡度，环形动量和能量的局部输运方程。特别地，示出了当在哈密顿量中采用长波长近似时，任何形式的哈密顿量的动量方程都表现良好并且松弛为其磁流体动力学形式。几种当前使用的形式，构成了大多数全球模拟的基础，已被证明在陀螺运动场理论和高能一致性中得到了很好的定义。

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