A gyrokinetic model is presented that can properly describe large and small amplitude electromagnetic fluctuations occurring on scale lengths ranging from the electron Larmor radius to the equilibrium perpendicular pressure gradient scale length, and the arbitrarily large deviations from thermal equilibrium that are present in the plasma periphery of tokamak devices. The formulation of the gyrokinetic model is based on a second-order accurate description of the single charged particle dynamics, derived from Lie perturbation theory, where the fast particle gyromotion is decoupled from the slow drifts assuming that the ratio of the ion sound Larmor radius to the perpendicular equilibrium pressure scale length is small. The collective behaviour of the plasma is obtained by a gyrokinetic Boltzmann equation that describes the evolution of the gyroaveraged distribution function. The collisional effects are included by a nonlinear gyrokinetic Dougherty collision operator. The gyrokinetic model is then developed into a set of coupled fluid equations referred to as the gyrokinetic moment hierarchy. To obtain this hierarchy, the gyroaveraged distribution function is expanded onto a Hermite–Laguerre velocity-space polynomial basis. Then, the gyrokinetic equation is projected onto the same basis yielding the spatial and temporal evolution of the Hermite–Laguerre expansion coefficients. A closed set of fluid equations for the lowest-order coefficients is presented. The Hermite–Laguerre projection is performed accurately at arbitrary perpendicular wavenumber values. Finally, the self-consistent evolution of the electromagnetic fields is described by a set of gyrokinetic Maxwell equations derived from a variational principle where the velocity integrals are explicitly evaluated.

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托卡马克装置等离子体外围的回转动力学模型

提出了一个陀螺动力学模型，可以正确描述发生在从电子拉莫尔半径到平衡垂直压力梯度尺度长度的尺度长度上发生的大小振幅电磁波动，以及存在于等离子体外围的任意大的热平衡偏差。托卡马克装置。陀螺动力学模型的公式是基于对单个带电粒子动力学的二阶精确描述，该描述源自李微扰理论，其中假设离子声拉莫尔半径与垂直平衡压力标尺长度较小。等离子体的集体行为是通过描述陀螺平均分布函数演变的陀螺动力学玻尔兹曼方程获得的。碰撞效应包含在非线性陀螺动力学 Dougherty 碰撞算子中。然后将旋动模型发展为一组称为旋动力矩层次的耦合流体方程。为了获得这种层次结构，将陀螺平均分布函数扩展到 Hermite-Laguerre 速度空间多项式基础上。然后，将旋动方程投影到相同的基础上，从而产生 Hermite-Laguerre 膨胀系数的空间和时间演变。给出了一组用于最低阶系数的封闭流体方程。Hermite-Laguerre 投影在任意垂直波数值处精确执行。