托卡马克理想磁流体不稳定性的统一描述(Ⅱ）

采用磁力线为直线的坐标系，进一步将托卡马克理想磁流体剪切阿尔芬运动方程展开，获得了描述低模数环形阿尔芬本征模（TAE和EAE）的方程。     

托卡马克等离子体中动力剪切阿尔芬波不稳定性的数值研究

用积分本征模方程研究了在托卡马克等离子体中包含全部动力学效应的动力剪切阿尔芬波模 (无论是否存在温度梯度). 引入了一个新的积分变量，将实平面的积分解析延拓到复平面. 这样可以同时研究增长模和阻尼模. 结果表明，在有离子温度梯度(ITG)的情况下，激发动 力剪切阿尔芬不稳定性所需的等离子体压强梯度比激发理想磁流体动力学气球模不稳定性的 阈值低得多，没有ITG时两者相同. 与动力无碰撞气球模结果不同，当有限ITG存在时，剪切 阿尔芬模存在第二稳定区. 关键词： 动力剪切阿尔芬模 磁流体气球模 阈值压强梯度     

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采用本征模式的数值打靶方法研究了离散阿尔芬本征模在DⅢ-D高性能运行条件下的物理特性,包括负磁剪切位形、高性能加热、正反中性束注入、内部输运垒以及高自举电流和甚高约束运行状态对这种阿尔芬模式的影响。在DⅢ-D托卡马克装置负磁剪切位形及先进运行状态实验参数下这些离散阿尔芬本征模存在于宽的径向区域,且具有广泛的本征频谱;高性能加热、同向中性束注入以及内部输运垒的存在有利于产生多个较深的气球模驱动势阱,由之得以很好地形成这种阿尔芬束缚态本征模;在高自举电流和甚高约束运行条件下这些离散阿尔芬本征模束缚态能够在更广的径向区域存在,且可具有较高的本征频率。另外,参照DⅢ-D装置放电实验数据的时间演变情况,这些离散阿尔芬本征模能在很宽的运行参数范围内出现,使之成为该类大型托卡马克实验中可能广泛存在的潜在不稳定性。     

弱相对论电子等离子体的宏观非寻常模稳定性

本文利用宏观冷流体模型及麦克斯韦方程研究了磁约束在圆柱形导体容器内的弱相对论电子等离子体的宏观非寻常模稳定性，寻出了槽纹扰动下（ｋｚ＝０）的普遍本征方程，分析中包含平衡自洽场。在低频扰动情况下，简化了本征方程，并仔细研究了电子等离子体在矩形分布下的稳定性质。     

四流体模型与托卡马克等离子体中的扰动粒子流

基于俘获粒子极向运动的约束条件，提出了一个简单而有效地描述俘获粒子运动及其对某些不稳定性的影响的四流体模型。作为该模型的应用，推导了各种扰动粒子流和扰动条件下的新经典电导率及包括了惯性效应的更普遍的自举电流表示式，并对役向局域的低极向模数的一类扰动，导出了包含俘获粒子效应的本征模方程。     

HL-2A装置反剪切阿尔芬本征模实验观测与模拟验证

利用 AMC 程序获取了不同最小安全因子( q_min )情况下反剪切阿尔芬本征模频率(RSAE)的变化特征： 当最小安全因子 q_min >1 时,RSAE 频率随着 q_min 增大而增大;当 q_min <1 时,RSAE 频率随着 q_min 减小而增大。这 与简化 RSAE 色散关系给出的频率相符。在 HL-2A 电流爬升期间和锯齿期间分别发现了 q_min >1 和 q_min <1 情况下 缓慢向上扫频的模。这些模的频率介于环向阿尔芬本征模和比压阿尔芬本征模之间,与 AMC 得到的 RSAE 模频 率一致,模的径向结构由单一极向谐波组成,并且高度局域在 q_min 附近,具有典型的 RSAE 特征。     

“A=2托卡马克堆芯等离子体基本特性研究”2006年进展

主要涉及两方面的研究内容：第一是托卡马克等离子体的磁流体气球模稳定性研究；第二是HL-2A装置电子回旋加热有关的基础理论问题。包括三方面研究成果：（1）简要报道了关于负剪切区电阻气球模不稳定性及本征函数特性，给出了增长率与等离子体参数的定标关系；（2）利用Solov’ev位形中严格的气球模方程，讨论了应用广泛的s，α平衡模型的正确性；（3）计算分析了由弱磁场侧垂直入射的电子回旋波寻常模在HL-2A等离子体中的功率沉积剖面。     

环形轴对称等离子体的理想磁流体简正模方程

本文在环形轴对称正文坐标系中对理想磁流体运动方程进行了严格自洽的讨论,通过对压缩量·ξ项的分析,发现在ω~2《K_1~2C_~2及ω~2》K_1~2C_5~2的两种极限情况下,可以仅用两个标函数来描述全域性模的运动。对于托卡马克等离子体,可引入剪切阿尔芬近似,得到由一个标函数描述的本征运动方程,它类似于文献中常用的简化托卡马克方程,但有一些重要不同点。该方程可用于分析计算各种频段的磁流体线性运动(包括扭曲模、阿尔芬波、间隙模等)。     

理想磁流体气球模本征方程的数值解法

一、基本方程 Tokamak等离子体高n气球模的不稳定性研究,归结为求解下述常微分方程的最大本征值Γ。     

等离子体形变对边界局域模的作用研究

在磁流体模拟代码BOUT++剥离气球模三场模块框架下研究了等离子体形变参数(拉长比和三角形变)对边界局域模的影响。研究表明,在线性阶段,拉长比主要作用于剥离气球模中气球模成分,抑制了环向模数较高的气球模不稳定性;而三角形变则对剥离气球模中剥离模成分和气球模成分均有抑制作用。在非线性阶段,拉长比导致边界E×B剪切率增加,迫使压强扰动的正值部分向等离子体芯部发展,导致边界局域模的能量损失增加;三角形变则导致边界E×B剪切率降低,使得压强扰动可以向等离子体边缘发展,台基向等离子体芯部的崩塌减弱,从而对边界局域模起到缓解作用。     

Double-gap Alfvén eigenmodes: revisiting eigenmode interaction with the alfvén continuum

A new type of global shear Alfvén eigenmode is found in tokamak plasmas where the mode localization is in the region intersecting the Alfvén continuum. The eigenmode is formed by the coupling of two solutions from two adjacent gaps (akin to potential wells) in the shear Alfvén continuum. For tokamak plasmas with reversed magnetic shear, it is shown that the toroidicity-induced solution tunnels through the continuum to match the ellipticity-induced Alfvén eigenmode so that the resulting solution is continuous at the point of resonance with the continuum. The existence of these double-gap Alfvén eigenmodes allows for potentially new ways of coupling edge fields to the plasma core in conditions where the core region is conventionally considered inaccessible. Implications include new approaches to heating and current drive in fusion plasmas as well as its possible use as a core diagnostic in burning plasmas.     

Three-wave interactions between fast-ion modes in the National Spherical Torus Experiment

Simultaneous bursts of energetic particle mode (EPM) and toroidicity-induced Alfvén eigenmode (TAE) activity that correlate with significant fast-ion loss are observed in beam heated plasmas. Three-wave interactions between these modes are conclusively identified, indicating fixed phase relationships. This nonlinear coupling concentrates the energy of the TAEs into a toroidally localized perturbation frozen in the frame of a rigid, toroidally rotating structure formed by the EPMs. This redistribution of energy is significant because it will modify the effect of the TAEs on fast-ion loss.     

Nonlinear Coupling of Reversed Shear Alfvén Eigenmode and Toroidal Alfvén Eigenmode during Current Ramp

Two novel nonlinear mode coupling processes for reversed shear Alfvén eigenmode(RSAE) nonlinear saturation are proposed and investigated. In the first process, the RSAE nonlinearly couples to a co-propagating toroidal Alfvén eigenmode(TAE) with the same toroidal and poloidal mode numbers, and generates a geodesic acoustic mode. In the second process, the RSAE couples to a counter-propagating TAE and generates an ion acoustic wave quasi-mode. The condition for the two processes to occur is favored during current ramp. Both the processes contribute to effectively saturate the Alfvénic instabilities, as well as nonlinearly transfer of energy from energetic fusion alpha particles to fuel ions in burning plasmas.     

β-induced Alfvén eigenmodes destabilized by energetic electrons in a Tokamak plasma

The β-induced Alfvén eigenmode (BAE) excited by energetic electrons has been identified for the first time both in the Ohmic and electron cyclotron resonance heating plasma in HL-2A. The features of the instability, including its frequency, mode number, and propagation direction, can be observed by magnetic pickup probes. The mode frequency is comparable to that of the continuum accumulation point of the lowest frequency gap induced by the shear Alfvén continuous spectrum due to finite β effect, and it is proportional to Alfvén velocity at thermal ion β held constant. The experimental results show that the BAE is related not only with the population of the energetic electrons, but also their energy and pitch angles. The results indicate that the barely circulating and deeply trapped electrons play an important role in the mode excitation.     

Role of flow shear in the ballooning stability of tokamak transport barriers

A tokamak's confinement time is greatly increased by a transport barrier (TB), a region having a high pressure gradient and usually also a strongly sheared plasma flow. The pressure gradient in a TB can be limited by ideal magnetohydrodynamic instabilities with a high toroidal mode number n ("ballooning modes"). Previous studies in the limit n--> infinity showed that arbitrarily small (but nonzero) flow shears have a large stabilizing influence. In contrast, the more realistic finite n ballooning modes studied here are found to be insensitive to sub-Alfvénic flow shears, provided the magnetic shear s approximately 1 (typical for TBs near the plasma's edge). However, for the lower magnetic shears that are associated with internal transport barriers, significantly lower flow shears will influence ballooning mode stability, and flow shear should be retained in the analysis of their stability.     

Mechanism of stabilization of ballooning modes by toroidal rotation shear in tokamaks

A ballooning perturbation in a toroidally rotating tokamak is expanded by square-integrable eigenfunctions of an eigenvalue problem associated with ballooning modes in a static plasma. Especially a weight function is chosen such that the eigenvalue problem has only the discrete spectrum. The eigenvalues evolve in time owing to toroidal rotation shear, resulting in a countably infinite number of crossings among them. The crossings cause energy transfer from an unstable mode to the infinite number of stable modes; such transfer works as the stabilization mechanism of the ballooning mode.     

腔内倾斜扰动对正支共焦腔本征模式的影响

针对激光器出光过程中腔内像差扰动带来的光束质量下降问题,分析了正支共焦腔腔内不同位置倾斜扰动对本征模式的影响,采用数值迭代法计算了理想状态及腔内不同位置倾斜扰动状态下的本征模式、相位Zernike像差拟合系数.结果表明：对大小给定的扰动,相位相对敏感性从凸面镜到凹面镜逐渐增加,且腔模倾斜像差增大的同时还将导致离焦、像散等高阶像差的增大,因此作腔内补偿时,应使补偿平面尽可能靠近凹面镜.     

托卡马克中漂移不稳定性的回旋动理学二维本征模方程

从弗拉索夫方程出发,导出了托卡马克等离子体中漂移不稳定性的回旋动理学二维本征模积分方程组。该方程组保留了离子的动理学效应,包括沿磁场的运动、磁场梯度和曲率漂移以及有限拉莫半径效应。与传统的采用气球模表象得到的一维回旋动理学方程(其只能给出不稳定模沿磁场线的结构)不同,该方程组不仅能给出托卡马克等离子体中漂移不稳定模的径向结构,同时还考虑了由离子的环形性漂移引起的相邻极向模之间的线性耦合,进而得到模的极向结构。该结果为相应的数值模拟研究提供了理论基础。     

Stability of tokamak plasmas with internal transport barriers against high n ideal magnetohydrodynamic ballooning mode

A ballooning mode equation for tokamak plasma, with the toroidicity and the Shafranov shift effects included, is derived for a shift circular flux tokamak configuration. Using this equation, the stability of the plasma configuration with an internal transport barrier （ITB） against the high n （the toroidal mode number） ideal magnetohydrodynamic （MHD） ballooning mode is analysed. It is shown that both the toroidicity and the Shaftanov shift effects are stabilizing. In the ITB region, these effects give rise to a low shear stable channel between the first and the second stability regions. Out of the ITB region towards the plasma edge, the stabilizing effect of the Shaftanov shift causes the unstable zone to be significantly narrowed.     

Fast ion induced shearing of 2D Alfvén eigenmodes measured by electron cyclotron emission imaging

Two-dimensional images of electron temperature perturbations are obtained with electron cyclotron emission imaging (ECEI) on the DIII-D tokamak and compared to Alfvén eigenmode structures obtained by numerical modeling using both ideal MHD and hybrid MHD-gyrofluid codes. While many features of the observations are found to be in excellent agreement with simulations using an ideal MHD code (NOVA), other characteristics distinctly reveal the influence of fast ions on the mode structures. These features are found to be well described by the nonperturbative hybrid MHD-gyrofluid model TAEFL.