13年等离子体暑期学校--董家齐老师讲义

1、托卡马克输运研究简引,董家齐 核工业西南物理研究院 浙江大学聚变理论与模拟中心 中国等离子体物理暑期学校 华中科技大学 2013.7.15-7.19,目录,I. 引言 II. 单粒子运动 III. 输运方程 IV. 输运模型 V. 输运和约束研究现状 VI. 结束语,1. 引言,本届暑期学校的主题： 托卡马克等离子体微观不稳定性与（质量、动量和能量的）输运 本届暑期学校的主要内容 什么是微观不稳定性 为什么要研究微观不稳定性，微观不稳定性与输运的关系 输运与实现核聚变的关系 托卡马克等离子体中的主要的微观不稳定性 开展微观不稳定性研究的理论和实验的方法和手段 微观不稳定性研究的成果及其在输运和约束研究中的应用 微观不稳定性和输运研究的现状和面临的挑战 本届暑期学校的授课安排 1. EAST 实验进展: 2. HL-2A实验进展:,3. Status of transport study in tokamak plasmas Single charged particle motion in tokamak magnetic configuration of circular cross

2、 section; brief introduction of classical, neoclassical and turbulent transports (particle, momentum and energy): theory and experimental observations; 4. Review of methodology for experimental study of transport Main diagnostic tools, equipment setups, experimental designs and data analysis methods, influential examples; 5. Electrostatic/electromagnetic drift instabilities (ITG, ETG) in slab geometry Derivation of dispersion equations: fluid, drift kinetic and gyrokinetic; analytic solutions of

3、 the equations; physics explanation of the modes, experimental observations; 6. Linear electrostatic/electromagnetic drift instabilities (ITG, ETG, CTEM ) in tokamaks: fluid and kinetic theories and experimental observations ; Linear dispersion equations, typical results and applications, including related linear and quasi-linear theories of transport, limitations of the theories and experimental observations ;,7. Nonlinear electrostatic/electromagnetic drift instabilities (ITG, ETG, CTEM ) in t

4、okamaks: fluid and kinetic simulations Equations, methods, codes, applications, including related transport analysis, important results on particle, momentum and energy transport, and open issues, 8. Introduction of zonal flow and GAM: theory and experiment: concepts of zonal flow (ZF) and GAM, possible roles played by ZF and GAM, non-linear excitation of GAM, experimental observations of ZF and GAM on domestic tokamaks (HT-7 and HL-2A), open issues 9. Experimental evidences and observations of

5、electrostatic drift instabilities (ITG, ETG, CTEM ) and turbulent transport in tokamaks： Electrostatic potential fluctuations, density fluctuations, magnetic fluctuations; critical gradient of instability vs. transport dependence on gradient; transport reduction vs. fluctuation suppression; measured fluctuation vs. theoretical predictions, transport barrier and H-mode, open issues,最容易实现的核聚变,实现自持核聚变的条件,When W=const.,and to square of the minor radius,本届暑期学校的主题 本届暑期学校学习内容安排的总体思路 最容易实现的核聚变 实现自持核聚变的条

6、件 (1)理想点火条件 (2)近似点火条件 能量约束时间，其与输运系数和装置规模（大小）的关系,Equilibrium magnetic fields: toroidal field Poloidal field,Tokamak Magnetic configuration,II. 单粒子运动,Parallel (lognitudinal) motion: Rotation: Drifts of guiding center i) Electric field drift:,ii) magnetic gradient ( ) drift：,iii) magnetic curvature drift：,iv)trapping, bounce and toroidal drift,a) Particle trapping b) Bounce period of the trapped particles c) Toroidal drift of trapped particles,3, Diamagnetic drift of plasma fluids,It is in the vert

7、ical direction at the low field side (LFS) of the torus; It induces charge separation and then plasma outward motion.,III. 输运方程,IV. 输运模型 1. 经典输运,2. 新经典输运,碰撞区的扩散-粒子模型（1）,l,碰撞区的扩散-粒子模型（2）,碰撞区的扩散-粒子模型（3）,as,碰撞区的扩散-流体模型（1）,碰撞区的扩散-流体模型（2）,碰撞区的扩散-流体模型（3）,香蕉区的扩散-粒子模型（1）,香蕉区的扩散-粒子模型（2）,香蕉区的扩散-粒子模型（3）,by,香蕉区的扩散-粒子模型 （4）,坪区的扩散（1）,坪区的扩散（2）,坪区的扩散（3）,径向电场对扩散的影响,环向电场对扩散的影响,effect,局域输运 非局域输运,4.非局域输运,Non-local effect by carbon injection,Non-local effect by a fast current ramp,Repetitive SMBI prolong the non-loc

8、ality phenomena to 100ms. Intensity of the Ha decrease and the density increase. The stored energe increase during non-locality.,The non-locality experiments with SMBI,5. 动量输运,为什么要研究动量输运：涨落的增长率与极向速度的径向梯度（剪切）密切相关：,环向速度与储能和温度梯度相关：,环向速度和L-H转换功率阈值相关：,经典和新经典动量输运理论？,V. 输运和约束研究现状,TFTR,DIII-D,JT-60U,经典理论与实验的比较,ASDEX装置上的H-mode实验特征,1. L-H转换是一种分叉现象 (1) In an H-discharge the particle content of the plasma rises sharply without external gas feed; (2) The development of an H-discharge during the beam heating phase is determined by the setting of the plasma parameters for the preceding Ohmic phase and by the level of heating power.,内部输运垒(ITB)-JET,VI. 结束语,两体碰撞引起的输运不足以解释实验观测到的输运引起的损失 涨落（湍流）引起的输运占主导 物理机制的理解取得了很大的进展，但还没具备可以预言实验的能力，尤其是电子输运 什么类型的湍流？如何主导？如何研究？进展如何?有哪些没有解决的问题需要你们去研究？,思考题,这个聚变功率的表达式的适用条件是什么？ 讨论新经典输运有何意义？新经典输运系数为什么分成三个区，三个区各有何特点？ 得到输运系数的主要步骤是那几步？,谢谢！,

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