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...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.展开更多
Through a systematically developed theory,we demonstrate that the motion of Instanton identified in Zhang et al(2017 Phys.Plasmas 24122304)is highly correlated to the intermittent excitation and propagation of geodesi...Through a systematically developed theory,we demonstrate that the motion of Instanton identified in Zhang et al(2017 Phys.Plasmas 24122304)is highly correlated to the intermittent excitation and propagation of geodesic acoustic mode(GAM)that is observed in tokamaks.While many numerical simulations have observed the phenomena,it is the first theory that reveals the physical mechanism behind GAM intermittent excitation and propagation.The preceding work is based on the micro-turbulence associated with toroidal ion temperature gradient mode,and slab-based phenomenological model of zonal flow.When full toroidal effect is introduced into the system,two branches of zonal flow emerge:the torus-modified low frequency zonal flow(TLFZF),and GAM,necessitating a unified exploration of GAM and TLFZF.Indeed,we observe that the transition from the Caviton to Instanton is triggered by a rapid zero-crossing of radial group velocity of drift wave and is found to be strongly correlated with the GAM onset.Many features peculiar to intermittent GAMs,observed in real machines,are thus identified in the numerical experiment.The results will be displayed in figures and in a movie;first for single central rational surface,and then with coupled multiple central rational surfaces.The periodic bursting first shown disappears as being replaced by irregular one,more similar to the intermittent characteristics observed in GAM experiments.展开更多
There are two distinct phases in the evolution of drift wave envelope in the presence of zonal flow.A long-lived standing wave phase,which we call the Caviton,and a short-lived traveling wave phase(in radial direction...There are two distinct phases in the evolution of drift wave envelope in the presence of zonal flow.A long-lived standing wave phase,which we call the Caviton,and a short-lived traveling wave phase(in radial direction) we call the Instanton.Several abrupt phenomena observed in tokamaks,such as intermittent excitation of geodesic acoustic mode(GAM) shown in this paper,could be attributed to the sudden and fast radial motion of Instanton.The composite drift wave-zonal flow system evolves at the two well-separate scales:the micro-scale and the meso-scale.The eigenmode equation of the model defines the zero-order(micro-scale) variation;it is solved by making use of the two-dimensional(2 D) weakly asymmetric ballooning theory(WABT),a theory suitable for modes localized to rational surface like drift waves,and then refined by shifted inverse power method,an iterative finite difference method.The next order is the equation of electron drift wave(EDW) envelope(containing group velocity of EDW) which is modulated by the zonal flow generated by Reynolds stress of EDW.This equation is coupled to the zonal flow equation,and numerically solved in spatiotemporal representation;the results are displayed in self-explanatory graphs.One observes a strong correlation between the Caviton-Instanton transition and the zero-crossing of radial group velocity of EDW.The calculation brings out the defining characteristics of the Instanton:it begins as a linear traveling wave right after the transition.Then,it evolves to a nonlinear stage with increasing frequency all the way to 20 kHz.The modulation to Reynolds stress in zonal flow equation brought in by the nonlinear Instanton will cause resonant excitation to GAM.The intermittency is shown due to the random phase mixing between multiple central rational surfaces in the reaction region.展开更多
基金ITER-China Program(2010GB107000)National Natural Science Foundation of China(NSFC-11075162)National Magnetic Confinement Fusion Science Program(China)(2009GB101002)
文摘按照章等[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.
基金supported in part by the National MCF Energy R&D Program of China(Nos.2018YFE0311200 and 2017YFE0301204)National Natural Science Foundation of China(Nos.U1967206,11975231,11805203 and 11775222)+1 种基金Key Research Program of Frontier Science CAS(QYZDB-SSW-SYS004)the US Dept.of Energy(No.DE-FG02-04ER-54742)。
文摘Through a systematically developed theory,we demonstrate that the motion of Instanton identified in Zhang et al(2017 Phys.Plasmas 24122304)is highly correlated to the intermittent excitation and propagation of geodesic acoustic mode(GAM)that is observed in tokamaks.While many numerical simulations have observed the phenomena,it is the first theory that reveals the physical mechanism behind GAM intermittent excitation and propagation.The preceding work is based on the micro-turbulence associated with toroidal ion temperature gradient mode,and slab-based phenomenological model of zonal flow.When full toroidal effect is introduced into the system,two branches of zonal flow emerge:the torus-modified low frequency zonal flow(TLFZF),and GAM,necessitating a unified exploration of GAM and TLFZF.Indeed,we observe that the transition from the Caviton to Instanton is triggered by a rapid zero-crossing of radial group velocity of drift wave and is found to be strongly correlated with the GAM onset.Many features peculiar to intermittent GAMs,observed in real machines,are thus identified in the numerical experiment.The results will be displayed in figures and in a movie;first for single central rational surface,and then with coupled multiple central rational surfaces.The periodic bursting first shown disappears as being replaced by irregular one,more similar to the intermittent characteristics observed in GAM experiments.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.U1967206,11975231,11805203,and 11775222)the National MCF Energy Research and Development Program,China(Grant Nos.2018YFE0311200 and 2017YFE0301204)the Key Research Program of Frontier Sciences,Chinese Academy of Sciences(Grant No.QYZDB-SSW-SYS004)。
文摘There are two distinct phases in the evolution of drift wave envelope in the presence of zonal flow.A long-lived standing wave phase,which we call the Caviton,and a short-lived traveling wave phase(in radial direction) we call the Instanton.Several abrupt phenomena observed in tokamaks,such as intermittent excitation of geodesic acoustic mode(GAM) shown in this paper,could be attributed to the sudden and fast radial motion of Instanton.The composite drift wave-zonal flow system evolves at the two well-separate scales:the micro-scale and the meso-scale.The eigenmode equation of the model defines the zero-order(micro-scale) variation;it is solved by making use of the two-dimensional(2 D) weakly asymmetric ballooning theory(WABT),a theory suitable for modes localized to rational surface like drift waves,and then refined by shifted inverse power method,an iterative finite difference method.The next order is the equation of electron drift wave(EDW) envelope(containing group velocity of EDW) which is modulated by the zonal flow generated by Reynolds stress of EDW.This equation is coupled to the zonal flow equation,and numerically solved in spatiotemporal representation;the results are displayed in self-explanatory graphs.One observes a strong correlation between the Caviton-Instanton transition and the zero-crossing of radial group velocity of EDW.The calculation brings out the defining characteristics of the Instanton:it begins as a linear traveling wave right after the transition.Then,it evolves to a nonlinear stage with increasing frequency all the way to 20 kHz.The modulation to Reynolds stress in zonal flow equation brought in by the nonlinear Instanton will cause resonant excitation to GAM.The intermittency is shown due to the random phase mixing between multiple central rational surfaces in the reaction region.
