Abstract:

Based on Vlasov equation, a set of two dimensional gyrokinetic integral eigenmode equations for drift instabilities in tokamak plasmas is derived. All kinetic effects of ions, including transience parallel to magnetic field, drifts induced by curvature and gradient of magnetic field, and effect of finite Larmor radius are included. Not only the radial structure but also the coupling of neighboring poloidal modes induced by toroidicity of the magnetic field and poloidal structure of the modes may be obtained from these equations, in contrast to ballooning mode representation treatment which can give mode structure along magnetic field lines only. The equations provide theoretical bases for relevant numerical simulation investigation.

Key words: Drift instability, Ion temperature gradient, Toroidal magnetic field configuration, Rational surface, Integral eigenmode equation

摘要：

从弗拉索夫方程出发，导出了托卡马克等离子体中漂移不稳定性的回旋动理学二维本征模积分方程组。该方程组保留了离子的动理学效应，包括沿磁场的运动、磁场梯度和曲率漂移以及有限拉莫半径效应。与传统的采用气球模表象得到的一维回旋动理学方程(其只能给出不稳定模沿磁场线的结构)不同，该方程组不仅能给出托卡马克等离子体中漂移不稳定模的径向结构，同时还考虑了由离子的环形性漂移引起的相邻极向模之间的线性耦合，进而得到模的极向结构。该结果为相应的数值模拟研究提供了理论基础。

关键词: 漂移不稳定性, 离子温度梯度, 环状位形, 有理面, 积分本征模方程