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Modelling RF heating in toroidal geometry: on the discrete bounce spectrum and the continuous bounce average

机译:在环形几何中模拟RF加热:在离散的反弹频谱和连续的反弹平均值上

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摘要

Starting from a more general formalism due to Lamalle [Plasma Phys. Contr. Fusion 32, 1409 (1997)], the dielectric response of a tokamak plasma to a radiofrequency (RF) perturbation is evaluated using a simple decorrelation model, assuming the poloidal cross-section of the magnetic surfaces to be circular and retaining leading-order terms in the drift parameter. Toroidicity, poloidal magnetic field and particle trapping are included in the model. Constants of the motion are used as independent variables. A semi-analytical method is adopted to evaluate the bounce spectrum of the dielectric response (needed to solve the wave equation) and the associated RF diffusion operator (required for solving the Fokker-Planck equation). The accent is on a study of this bounce spectrum. In particular, the link between the discrete bounce spectrum and the continuous bounce integral is highlightted. The critical parameter for the global justification of the replacement of the sum on the bounce spectrum by a bounce average is the relative magnitude of the decorrelation and bounce times. That for the local justification is the second derivative of the periodic part of the relative wave-particle phase. Numerical examples are provided to give a qualitative feeling for the justification of this substitution. The relation between the results presented here and those based on Hamiltonian models or on a simplified geometry is discussed.
机译:从Lamalle [等离子物理学报,控制[Fusion 32,1409(1997)],使用简单的去相关模型评估了托卡马克等离子体对射频(RF)扰动的介电响应,假定磁性表面的倍数截面为圆形并保留了前导项在漂移参数中。该模型包括环形性,极向磁场和粒子捕获。运动常数用作自变量。采用半分析方法评估介电响应的弹跳光谱(需要求解波动方程)和相关的RF扩散算子(求解Fokker-Planck方程需要)。重点是研究此反弹频谱。特别地,突出了离散反弹光谱和连续反弹积分之间的联系。用弹跳平均值替换弹跳频谱上的总和的全局合理性的关键参数是去相关和弹跳时间的相对大小。用于局部调整的是相对波粒相位的周期部分的二阶导数。提供了数字示例,以给定这种替换的理由有质的感觉。讨论了此处介绍的结果与基于汉密尔顿模型或简化几何的结果之间的关系。

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