Toroidal component of velocity for geodesic acoustic modes in the edge plasmas of the J-TEXT tokamak

The toroidal component of the velocity for geodesic acoustic modes(GAMs)is first demonstrated.Multiple Langmuir probe arrays set up near the top tokamak of the J-TEXT were utilized for this study.A significant peak at the GAM frequency is observed in Mach number fluctuations.The toroidal velocity for the GAMs is estimated as 10–100 ms-1 and increases with the poloidal velocity.The ratio of toroidal component to the poloidal one of the velocity is mainly located in the interval between 0.3 and 1.0.With higher safety factors q,the ratio almost does not change with decreasing the safety factor,whereas it goes up sharply at low q.The coherencies between poloidal electric fields and Mach number fluctuations in turbulence frequency bands are also evaluated,and are higher than those between radial electric fields and Mach number fluctuations.

Nonlinear excitation of a geodesic acoustic mode by reversed shear Alfvén eignemodes

The parametric decay process of a reversed shear Alfvén eigenmeode(RSAE)into a geodesic acoustic mode and a kinetic RSAE is investigated using nonlinear gyrokinetic theory.The excitation conditions mainly require the pump RSAE amplitude to exceed a certain threshold,which could be readily satisfied in burning plasmas operated in steady-state advanced scenario.This decay process can contribute to thermal plasma heating and confinement improvement.

Damping of Geodesic Acoustic Mode by Trapped Electrons

We study the Landau resonance between geodesic acoustic mode（GAM） and trapped electrons as a GAM’s collisionless damping. The assumption of ˉωde 〈〈ωbeis adopted.The damping rate induced by trapped electrons is found to be an increasing function of q. In low q range, circulating-ion-induced damping rate is larger than that induced by trapped electrons.As q increases, the latter becomes larger than the former. The reason is that trapped electrons’ resonant velocity is close to vtefrom the lower side, whiles circulating ions’ resonant velocity gets bigger further from vti. So the number of resonant trapped electrons increases, whiles the number of resonant circulating ions decreases. The amplitude of damping rate induced by trapped electrons in the edge plasma can be comparable to that induced by circulating ions in the low q range.Another phenomenon we found is that in the chosen range of, the damping caused by trapped electrons has a maximum value at point εq for different q. The reason is that as is close to q,trapped electorns’ resonant velocity is close to vte.

Kinetic Theories of Geodesic Acoustic Modes：Radial Structure,Linear Excitation by Energetic Particles and Nonlinear Saturation＇

Geodesic acoustic modes（GAMs）are oscillating zonal mode structures unique to toroidal plasmas and are capable of regulating microscopic turbulence and associated transports.Inthispaper,three important aspects of GAM dynamics are investigated,namely（1） GAM continuous spectrum and its mode conversion to kinetic GAM （KGAM）;（2） 1inear excitation of energetic particle induced GAM （EGAM） and its coupling to the GAM continuum, and （3） nonlinear saturationofEGAMviawaveparticletrapping.TheanalogybetweentheGAM

Analytical Theory of the Geodesic Acoustic Mode in the Small and Large Orbit Drift Width Limits and its Application in a Study of Plasma Shaping Effect

Analytical theories of the geodesic acoustic mode （GAM） are reviewed in the small- and large-orbit drift width limits, respectively. Different physics pictures in these two limits are displayed. As an example, these two analytical methods are employed to investigate the plasma shaping effect on the frequency and collisionless damping rate of the GAM.

Kinetic theory of geodesic acoustic modes in toroidal plasmas:a brief review

Geodesic acoustic modes（GAM） are oscillating zonal structures unique to toroidal plasmas,and have been extensively studied in the past decades due to their potential capabilities of regulating microscopic turbulences and associated anomalous transport.This article reviews linear and nonlinear theories of GAM;with emphases on kinetic treatment,system nonuniformity and realistic magnetic geometry,in order to reflect the realistic experimental conditions.Specifically,in the linear physics,the resonant wave-particle interactions are discussed,with the application to resonant excitation by energetic particles（EPs）.The theory of EP-induced GAM（EGAM） is applied to realistic devices for the interpretation of experimental observations,and global effects due to coupling to GAM continuum are also discussed.Meanwhile,in the nonlinear physics,the spontaneous GAM excitation by microscale turbulences is reviewed,including the effects of various system nonuniformities.A unified theoretical framework of GAM/EGAM is then constructed based on our present understandings.The first-principle-based GAM/EGAM theories reviewed here,thus,provide the tools needed for the understanding and interpretation of experimental/numerical results.

Properties of Density Fluctuations Induced by Geodesic Acoustic Mode in the Edge of HT-7 Tokamak

Properties of the geodesic acoustic mode （GAM） density fluctuations are studied using two toroidally separated Langnmir triple-probe arrays on the top of HT-7 tokamak. The GAM scenario is identified in the potential fluctuations with the toroidally symmetric structure （n =0） and satisfying the temperature scaling of GAM mode frequency. Some theoretical predictions about the mode features of GAM density fluctuations are verified in our experiments： the toroidal mode number of GAM density fluctuations is n = 0; its amplitude is consistent with the theoretical prediction in a factor of 2; the density and potential fluctuations of GAM is in anti-phase at the top of plasma cross-section. Strong nonlinear interactions are found between GAM density fluctuations and ambient turbulence （AT）. The results support the conclusions that the envelope modulation of potential fluctuations is dominantly caused by the direct regulation of GAM in the generation processing, and the envelope modulation of density fluctuation is due to the GAM shear effect.

Geodesic acoustic modes in tokamak plasmas with anisotropic distribution and a radial equilibrium electric field

The dispersion relation of standard geodesic acoustic modes in tokamak plasmas with anisotropic distribution and a radial equilibrium electric field is derived and analyzed. Both frequencies and damping rates increase with respect to the poloidal Mach number which indicates the strength of the radial electric field. The strength of anisotropy is denoted by the ratio of the parallel temperature（T_‖） to the perpendicular temperature（T_⊥）. It is shown that, when the parallel temperature is lower than the perpendicular temperature, the enhanced anisotropy tends to enlarge the real frequency but reduces the damping rate, and when the parallel temperature is higher than the perpendicular temperature, the effect is opposite. The radial equilibrium electric field has stronger effect on the frequency and damping rate for the case with higher parallel temperature than the case with higher perpendicular temperature.

Magnetic Components of Geodesic Acoustic Modes in Plasmas with Anisotropic Ion Distribution

The existence of magnetic components in geodesic acoustic modes is investigated for a weakly anisotropic tokamak plasma with dual-temperature Maxwellian distributions for ions. An m = 1 perpendicular magnetic perturbation is discovered to be proportional to the relative difference between the two temperatures in addition to an m = 2 perpendicular magnetic perturbation which always exists due to the m = 2 parallel return current, with m the poloidal mode number. The dispersion relation and the mode frequency are also modified by the anisotropic distribution.

Geodesic acoustic mode in a reduced two-fluid model

A reduced two-fluid model is constructed to investigate the geodesic acoustic mode（GAM）. The ion dynamics is sufficiently considered by including an anisotropic pressure tensor and inhibited heat flux vector, whose evolutions are determined by equations derived from the 16-momentum model. Electrons are supposed to obey the Boltzmann distribution responding to the electrostatic oscillation with near ion acoustic velocity. In the large safety factor limit, the GAM frequency is identical with the kinetic one to the order of 1 q2 when zeroing the anisotropy. For general anisotropy, the reduced two-fluid model generates the frequency agreeing well with the kinetic result with arbitrary electron temperature. The present simplified fluid model will be of great use and interest for young researchers and students devoted to plasma physics.

Geodesic Acoustic Mode in Toroidally Axisymmetric Plasmas with Non-Circular Cross Sections

The geodesic acoustic mode （GAM）, first predicted by Winsor, Johnson and Dawson in an attempt to explain some experimentally observed low frequency oscillations in stellarators, is a special electrostatic fluid mode with low mode number and coupled with the so-called geodesic curvature of a toroidally confined plasma. The recent on this mode are due to the close relevance of the stabi- lization of drift turbulence by both the zonal flow and the GAM. Previously, the GAM was illustrated in very simple geometries,

Contribution of the Large Helical Device Plasmas to Alfvén Eigenmode Physics in Toroidal Plasmas

In the large helical device （LHD） having three dimensional configuration, Alfven eigenmodes （AEs） destabilized by energetic ions are widely investigated using neutral beam heated plasmas with monotonic and non-monotonic rotational transform （l/2π） profiles. In a plasma with monotonic l/2π-profile, core-localized toroidicity-induced Alfven eigenmode （TAE） as well as global one are often observed. With the increase in the averaged toroidal beta value, defined as the ratio of total plasma pressure to toroidal magnetic pressure, core-localized TAE with low toroidal mode number becomes global. In a relatively high beta plasma with monotonic l/2π-profile, two TAEs with different toroidal mode number often interact nonlinearly and generate another modes through three wave coupling. In a plasma with non-monotonic l/2π-profile generated by intense counter neutral beam current drive, reversed shear Alfven eigenmode （RSAE） and geodesic acoustic mode （CAM） excited by energetic ions were observed for the first time in a helical plasma. Nonlinear coupling was also observed between RSAE and GAM.

Contribution of joint experiments on small tokamaks in the framework of IAEA coordinated research projects to mainstream fusion research

Joint experiments(JEs)on small tokamaks have been regularly performed between 2005 and 2015 under the framework of the International Atomic Energy Agency(IAEA)coordinated research projects(CRPs).This paper describes the background and the rationale for these experiments,how they were organized and executed,main areas of research covered during these experiments,main results,contributions to mainstream fusion research,and discusses lessons learned and outcomes from these activities.We underline several of the most important scientific outputs and also specific outputs in the education of young scientists and scientists from developing countries and their importance.

Linear Gyro-Kinetic Response Function for Zonal Flows

A linear response function for zonal flows is obtained by solving the gyro-kinetic equation. This is an extension of a previous work which adopted the method of ＂integrating along particle orbit＂ to solve the drift kinetic equation. The formula derived in this paper is used to calculate the dispersion relation of geodesic acoustic mode, which is then compared with that of the gyro-kinetic analytic formula.

Gyrofluid Simulation of Ion-Scale Turbulence in Tokamak Plasmas

An improved three-field gyrofluid model is proposed to numerically simulate ion-scale turbulence in tokamak plasmas,which includes the nonlinear evolution of perturbed electrostatic potential,parallel ion velocity and ion pressure with adiabatic electron response.It is benchmarked through advancing a gyrofluid toroidal global(GFT G)code as well as the local version(GFT L),with the emphasis of the collisionless damping of zonal flows.The nonlinear equations are solved by using Fourier decomposition in poloidal and toroidal directions and semi-implicit finite difference method along radial direction.The numerical implementation is briefly explained,especially on the periodic boundary condition in GFT L version.As a numerical test and also practical application,the nonlinear excitation of geodesic acoustic mode(GAM),as well as its radial structure,is investigated in tokamak plasma turbulence.