等离子体平衡逆问题的一种数值解法

本文借助离散化算子,把滤波方法推广到非圆截面,对具有非圆截面的等离子体平衡逆问题建立了一个稳定的显式逆推滤波算法;给出了部分非圆截面的计算结果;对圆截面情形的数值解与解析解作了比较。     

环形轴对称锐边界等离子体的扭曲模不稳定性

本文对任意环径比、任意β值、任意截面形状的轴对称锐边界等离子体,给出了正确的边界条件,导出了无导体壳和存在导体壳两种情况下扭曲模稳定性的能量矩阵,对环向波数n为1,2,3的能量矩阵,给出了可快速、精确积分的具体形式,对不同环径比和不同拉长度b/α的椭圆形、跑道形(包括圆形)截面的等离子体进行了数值计算。计算结果表明,跑道形截面等离子体的临界β值比相应的椭圆形截面的β值高,随着b/α的增大,跑道形截面的临界β值也增加。导体壳有一定的稳定作用。从系统稳定性边缘态的本征矢量来看,存在导体壳时极向扰动的最大分量是模数1的扰动。与J.P.Freidberg和W.Grossmann的工作比较,在环径比为2时,圆截面等离子体的临界β值相差23％,临界q值相差15％。     

非圆截面等离子体MHD不稳定性的研究

本文采用阶跃电流模型研究了非圆截面环电流器等离子体的MHD不稳定性,使札哈洛夫(Zakharov)的工作推广到非圆截面,得到了新的稳定性判据。它指出了椭圆形变,三角形变,电流梯度以及q值(所谓的安全因子)对等离子体的β值的影响。为了得到最大的β值,本文给出了最佳q值公式。对等离子体的不同参数计算了临界β值,并与由局部模判据和气球模的数值计算所得到的结果进行了比较。文中指出,电流梯度的存在是对等离子体β值影响的重要因素;非圆截面等离子体比圆截面等离子体可能得到更高的β值。     

导体壳对电阻磁流体不稳定性的影响

结合HL-1装置的条件,采用撕裂模的准线性理论,研究了托克马克中导体壁对m=2/n=1扰动模的稳定作用。着重研究了导体壁位置,等离子体电流分布,等离子体位形对这种稳定效应的影响。结果表明,共振面的位置与壁的稳定作用有密切关系,存q_a接近于2的位形中,m=2的撕裂模扰动可以被靠近等离子体的导体壁完全抑制。导体壁的稳定效应与等离子体电流分布相联系,在一些现实的电流分布中,只要适当地压低等离子体边界区的电流密度,壁的稳定效应会更加显现出来。     

托卡马克理想导体壁与磁流体不稳定性

为了探索等离子体磁流体力学(MHD)不稳定性的导体壁效应以及壁设计思想,研究了基于HL-2A托卡马克偏滤器位形的、自由边界和多种形式的理想导体壁条件下的等离子体MHD不稳定性与装置MHD运行β极限.在稳定性计算中,考虑的是n=1扭曲模,该模对托卡马克等离子体MHD不稳定性有决定性的影响.研究着眼于验证多种形状导体壁抑制内、外扭曲模的有效性,观察运行β极限的变化,并讨论分析相关物理.研究发现在离等离子体适当距离处放置一个理想导体壁,可有效抑制外扭曲模.在壁与等离子体表面的平均距离相同、且足够小的条件下,圆截面壁并不一定是最佳选择,设置一个经过优化的多边形导体壁能更有效地抑制MHD不稳定性,它使本装置的理想MHD运行β极限β_N提高到2.73,比自由边界条件下(即假设壁设置在无穷远处的)装置的运行β极限值(～2.56)提高了约6.5%.这暗示需要根据有拉长、有变形的等离子体的极向截面形状,优化制作一个离等离子体表面平均距离尽可能近的多边形导体壁,才能取得抑制外扭曲模、提高β极限的最佳效果.     

非圆截面托卡马克轴对称模的反馈稳定

通过直接解真空区扰动磁面的边值问题,本文解析地研究了非闭合导壳对托卡马克中轴对称MHD模的反馈稳定性。我们取等离子体截面为椭圆,反馈系统由导壳和主动反馈线圈构成。结果表明,两块放在等离子体上下的导体块有很强的稳定作用;电阻壳可用以抑制高频模式,主动反馈线圈可用以稳定低频模式。 关键词：     

非圆截面托卡马克等离子体边缘磁场结构的快速Mapping方法

介绍利用等离子体磁面的傅里叶及边缘泰勒展开的解析表达式,得到非圆截面托卡马克等离子体边缘磁面结构的快速mapping方法。最后作为例子给出在TEXT-U装置实验中上的mapping图。     

非圆截面托卡马克等离子边缘磁场结构的快速Mapping方法

介绍利用等离子体磁面的傅里叶及边缘泰勒展开的解析表达式，得到非圆截面托卡马克等离子体边缘磁面结构的快速ｍａｐｐｉｎ方法。最后作为例子给出在ＴＥＸＴ－Ｕ装置实验中上的ｍａｐｐｉｎｇ图。     

用正问题代码求逆问题的尝试

本文介绍了一种用正问题代码通过某种逆过程来求解逆问题的数值目的。我们使用这种目的在平衡代码SWEQU^[1]的基础上开发了一个名为SWSTAB的计算非圆截面托卡马克等离子体竖直不稳定性的程序。利用该程序我们计算了成型线圈条件下,上下不对称等离子体的竖直不稳定性,研究了等离子体形状因子(椭圆半轴比,三角形变)及等离子体与成型线圈之间距离对稳定性的影响,方便地得到了用其它目的不易得到的物理结果。     

非圆截面托卡马克等离子体边缘磁场的解析解及重构方法

本文用傅里叶及边缘泰勒展开的方法，导出了非圆截面托卡马克等离子体边缘磁面的解析解及其重构的方法。最后作为例子，给出了在ＴＥＸＴ－Ｕ装置中按实际参数重构的等离子体边缘磁面结构及重构的误差。     

The effect of sawtooth oscillations on the alpha particle distribution and energy balance in the ITER plasma

The mixing of toroidal plasma under the conditions of sawtooth oscillations is considered using the Kadomtsev model. A new mixing formula for the averaged distribution function of fast transit and trapped particles is proposed in the methodology of a kinetic equation averaged over drift trajectories. The proposed formula generalizes the known results for the case of non-circular magnetic surfaces, an arbitrary aspect ratio, and charged particle drift trajectories significantly deviating from the magnetic surfaces. The formula is applicable for a sufficiently wide class of instabilities. The 3D kinetic equation is numerically solved using the FPP- 3D computation code for parameters close to the ITER inductive scenario. The alpha particle distribution function and the power introduced by alpha particles in plasma when sawtooth oscillations occur are calculated. It is shown that such oscillations may change the energy input of a thermonuclear reaction in certain areas by several times.     

Plasma Response to Resonant Perturbations at Tokamak Edge

In certain circumstances, plasma response suppresses magnetic islands expected at perturbed resonant magnetic surfaces. We investigate the plasma response to the resonant magnetic perturbations in a large aspect ratio tokamak perturbed by external resonant helical windings, considering polar toroidal coordinates for which analytical toroidal equilibrium solutions and perturbing fields are available. We apply an empirical approach to mimic the plasma screening effects by introducing presumed plasma current sheets on the resonance surfaces to cancel the RMP effects. Numerical examples show the effect of plasma response reducing magnetic islands at the plasma edge and also regularizing field lines around the resonant surface. The distribution of connection lengths along the plasma cross section indicates that the plasma response increases the connection lengths since more toroidal turns are performed until a field line reaches the tokamak wall.     

Numerical study of physical properties of resistive wall modes in tokamaks

The effect of plasma with toroidal rotation on the resistive wall modes in tokamaks is studied numerically. An eigenvalue method is adopted to calculate the growth rate of the modes for changing plasma resistivity and plasma density distribution, as well as the diffusion time of magnetic field through the resistive wall. It is found that the resistive wall mode can be suppressed by the toroidal rotation of the plasma. Also, the growth rate of the resistive wall mode decreases when the edge plasma density is the same as the core plasma density, but it only changes slightly with the plasma resistivity.     

圆环面电流磁场的近轴近似

本文在局部极坐标系中。求出分布在圆环面上的电流分量的近轴近似展开式。所得结果,可用于环形等离子体内扰动电流的定量测量问题。     

Observation of plasma toroidal-momentum dissipation by neoclassical toroidal viscosity

Dissipation of plasma toroidal angular momentum is observed in the National Spherical Torus Experiment due to applied nonaxisymmetric magnetic fields and their plasma-induced increase by resonant field amplification and resistive wall mode destabilization. The measured decrease of the plasma toroidal angular momentum profile is compared to calculations of nonresonant drag torque based on the theory of neoclassical toroidal viscosity. Quantitative agreement between experiment and theory is found when the effect of toroidally trapped particles is included.     

Analytic description of tokamak equilibrium sustained by high fraction bootstrap current

By using an expansion technique based on the tokamak ordering, the Grad－Shafranov equation is analytically solved for tokamak equilibrium sustained by a full bootstrap current. This approximate approach is suitable for equilibria with non-circular cross-sections of modest ellipse and triangular deformations. As an input parameter set, the plasma pressure profile and the electron and the ion temperature profiles can be selected as arbitrary functions of the averaged minor radius. Equilibrium properties of this plasma are discussed.     

Eigenmodes for electromagnetic waves propagating in a toroidalcavity

A solution has been attempted by means of the Helmholtz equation for an electromagnetic wave propagating in an empty torus in a system of toroidal coordinates. The electromagnetic fields are expressed in terms of the Hertz vector to obtain a scalar Helmholtz equation. The latter has been solved by making use of an inverse aspect ratio expansion of the solution. Unlike most previous workers, the authors have obtained their solutions in terms of hypergeometric functions whose static limit is the toroidal harmonics. The cylindrical solutions in terms of Bessel functions can also be recovered by taking the appropriate large aspect ratio limit. The eigenmodes, with arbitrary toroidal and poloidal mode numbers, have been obtained by applying the boundary conditions on the metallic walls of infinite conductivity, and they cannot be distinguished as TE or TM modes. Eigenfrequencies for various toroidal and poloidal mode numbers are plotted against the inverse aspect ratio. First-order approximations to the fields in the toroidal cavity have also been derived     

Radial magnetosonic eigenmodes in a toroidal plasma with an ion-ion hybrid layer

The conditions for excitation of a standing magnetosonic wave structure in the region between the ion-ion hybrid cut-off layer and an antenna situated near the wall on the outside of a toroidal plasma have been derived. It is shown that low-order radial eigenmodes may be excited under usual conditions, but the order of the mode increases as the plasma density and its size increase. Such radial eigenmodes are shown to be more easily tracked than the usual magnetosonic toroidal eigenmodes.     

An analytic solution of the stationary MHD equations for a rotating toroidal plasma

An analytic MHD equilibrium for an axisymmetric torodial plasma with toroidal and toroidal flow is obtained in the limit of small ratio of poloidal to toroidal magnetic field and small beta. For a critical value of the poloidal velocity a limitation of the domain of validity of the solution appears.     

Sustained stabilization of the resistive-wall mode by plasma rotation in the DIII-D tokamak

Values of the normalized plasma pressure up to twice the free-boundary stability limit predicted by ideal magnetohydrodynamic (MHD) theory have been sustained in the DIII-D tokamak. Long-wavelength modes are stabilized by the resistive wall and rapid plasma toroidal rotation. High rotation speed is maintained by minimization of nonaxisymmetric magnetic fields, overcoming a long-standing impediment [E. J. Strait, Phys. Rev. Lett. 74, 2483 (1995)]]. The ideal-MHD pressure limit calculated with an ideal wall is observed as the operational limit to the normalized plasma pressure.