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Damping of geodesic acoustic mode by Trapped Electrons

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Plasma Science and Technology 2014年第7期16卷 650-656页

作者：张双喜高喆武文韬仇志勇张双喜高喆武文韬 Department of modern Physics University of Science and Technology of China Hefei 230026 China Key Laboratory of Pulsed Power Institute of Fluid Physics China Academy of Engineering Physics Mianyang 621900 China Department of Engineering Physics Tsinghua University Beijing 10008 China Institute for Fusion Theory and Simulation Zhejiang University Hangzhou 310027 China

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.

关键词： geodesic acoustic mode landau resonance trapped electrons bounce frequency

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

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Plasma Science and Technology 2011年第1期13卷 15-20页

作者：高喆 Department of Engineering Physics Tsinghua Univerisity

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.

关键词： geodesic acoustic mode plasma shaping orbit drift width analytical theory

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

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Plasma Science and Technology 2018年第8期20卷 16-21页

作者：明玥周登王文家 Institute of Plasma Physics Chinese Academy of Sciences Hefei 230031 People's Republic of China University of Science and Technology of China Hefei 230026 People's Republic of China Center for Magnetic Fusion Theory Chinese Academy of Sciences Hefei 230031 People's Republic of China

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.

关键词： geodesic acoustic mode anisotropy equilibrium flow

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

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Plasma Science and Technology 2021年第10期23卷 112-119页

作者：谢耀禹赵开君陈志鹏董家齐 Kimitaka ITOH 陈忠勇石跃江丁永华程钧严龙文刘海程芝峰杨州军王能超王璐许健强梁云峰 J-TEXT Team School of Nuclear Science and Engineering East China University of TechnologyNanchang 330013People’s Republic of China International Joint Research Laboratory of Magnetic Confinement Fusion and Plasma Physics State Key Laboratory of Advanced Electromagnetic Engineering and TechnologySchool of Electrical and Electronic EngineeringHuazhong University of Science and TechnologyWuhan 430074People's Republic of China Southwestern Institute of Physics Chengdu 610041People's Republic of China Institute of Science and Technology Research Chubu UniversityKasuga 816-8580Japan Research Center for Plasma Turbulence Kyushu UniversityKyushu UniversityChubu UniversityAichi 487-8501Japan National Institute for Fusion Science Toki 509-5292Japan ENN Science and Technology Development Co. Ltdand Hebei Key Laboratory of Compact FusionLangfang 065001People's Republic of China Institute of Fusion Science School of Physical Science and TechnologySouthwest Jiaotong UniversityChengdu 610031People's Republic of China

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.

关键词： zonal flow geodesic acoustic mode tokamak return flow Mach number

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

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Plasma Science and Technology 2020年第5期22卷 25-34页

作者： M GRYAZNEVICH J SToCKEL G VAN OOST E DEL BOSCO V SVOBODA A MELNIKOV R KAMENDJE A MALAQUIAS G MANK R MIKLASZEWSKI the IAEA CRP JEs Teams Tokamak Energy Ltd Milton ParkOxon OX144SDUnited Kingdom Faculty of Nuclear Phys.and Phys.Eng. Czech Technical University11519 Prague 1Czech Republic Dep.of Applied Physics Ghent University9000 GhentBelgium INPE São Josédos Campos 12227-010Brazil National Research Centre‘Kurchatov Institute’ 123182 MoscowRussia National Research Nuclear University(MEPhI) 115409 MoscowRussia EUROfusion 85748 GarchingGermany Dep.Physics Instituto Superior TécnicoUniv.de Lisboa1049-001 LisbonPortugal National Research University‘Moscow Power Eng.Institute'(MPEI) 111250 MoscowRussia JEN Jülicher Entsorgungsgesellschaft für Nuklearanlagen mbH 116052412 JülichGermany Institute of Plasma Physics and Laser Microfusion 01-497 WarsawPoland IAEA NAPS Physics Section VIC P.O.Box 100 A-1400 ViennaAustria

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.

关键词： small tokamaks joint experiments IAEA CRP education and training turbulence geodesic acoustic mode

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

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Plasma Science and Technology 2018年第9期20卷 24-49页

作者： Zhiyong QIU Liu CHEN Fulvio ZONCA Institute for Fusion Theory and Simulation and Department of Physics Zhejiang University Department of Physics and Astronomy University of California ENEA Fusion and Nuclear Safety Department

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.

关键词： geodesic acoustic mode kinetic theory nonlinear physics energetic particle physics

Kinetic Theories of geodesic acoustic modes：Radial Structure,Linear Excitation by Energetic Particles and Nonlinear Saturation＇

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Plasma Science and Technology 2011年第3期13卷 257-266页

作者： QIU Zhiyong(仇志勇) Fulvio ZONCA CHEN Liu(陈骝) Institute for Fusion Theory and Simulation Zhejiang UniversityHangzhou 310027China Associazione Euratom=ENEA sulla Fusione C. P. 65 -I-00044-Frascati. Italy Dept. of Physics and Astronomy Univ. of California Irvine CA 92697-4575 USA

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

关键词： geodesic acoustic mode continuum energetic particles wave particle trapping

Linear Gyro-Kinetic Response Function for Zonal Flows

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Plasma Science and Technology 2011年第2期13卷 157-161页

作者： T.WATARI Y.HAMADA National Institute for Fusion Science

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.

关键词： zonal flow geodesic acoustic mode integrating along particle orbits

Magnetic Components of geodesic acoustic modes in Plasmas with Anisotropic Ion Distribution

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Plasma Science and Technology 2010年第1期12卷 6-10页

作者：张淼周登 Institute of Plasma Physics Chinese Academy of Sciences Center for Magnetic Fusion Theory Chinese Academy of Sciences

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.

关键词： geodesic acoustic mode harmonic expansion