托卡马克无碰撞捕获电子模在时空表象中的群速度

Group velocity in spatiotemporal representation of collisionless trapped electron mode in tokamak

按照章等[Zhang Y Z, Liu Z Y, Mahajan S M, Xie T, Liu J 2017 Phys. Plasmas 24 122304]发展的漂移波-带状流理论,将多重尺度导数展开法应用到电子漂移动理学方程,零级为描述微观尺度捕获电子模的线性本征模方程,一级为介观尺度受带状流调制的捕获电子模的包络方程.其中线性本征模方程已经在谢等[Xie T, Zhang Y Z, Mahajan S M, Wu F, He Hongda, Liu Z Y 2019 Phys. Plasmas 26 022503]的研究中被求解,利用该文得到的捕获电子模的本征值和二维模式结构计算包络方程中的群速度.径向群速度由托卡马克磁场的测地曲率贡献,极向群速度来自逆磁漂移速度和法向曲率,它们仅是极向角的函数,后者给出极向角到时间的映射.径向群速度作为时间的函数,其周期在毫秒量级,具有快速过零的特征.这为研究捕获电子模驱动带状流提供了充实的理论基础.

The multiple scale derivative expansion method is used to manipulate the electron drift kinetic equation,following the theoretical framework of drift wave–zonal flow system developed by Zhang et al.[Zhang Y Z,Liu Z Y,Mahajan S M,Xie T,Liu J 2017 Phys.Plasmas 24122304].At the zeroth order it is the linear eigenmode equation describing the trapped electron mode on a mirco-scale.At the first order it is the envelop equation for trapped electron mode modulated by the zonal flow on a meso-scale.The eigenmode equation has been solved by Xie et al.[Xie T,Zhang Y Z,Mahajan S M,Wu F,He Hongda,Liu Z Y 2019 Phys.Plasmas 26022503]to obtain the eigenvalue and two-dimensional mode structure of trapped electron mode.These are essential components in calculating group velocities contained in the envelop equation.The radial group velocity arises from the geodesic curvature of magnetic field in tokamak.The poloidal group velocity stems from the normal curvature and diamagnetic drift velocity,which yields the mapping between the poloidal angle and time.Since the radial group velocity is also a function of poloidal angle,it is mapped to a periodic function of time with a period of milliseconds.The numerical results indicate the rapid zero-crossing,which is significant in the drift wave–zonal flow system and provides a sound foundation for studying zonal flow driven by trapped electron mode.