Experimental Studies on the Sustainment of Splieromak Plasmas by an Inductive Drive of the Toroidal Current

Sustainment of spheromak plasmas produced in an external equilibrium field has been demonstrated with a center current transformer (ohmic heating (OH) coil) which is used to inductively drive the toroidal current of the plasma. The OH coil is covered by a cylindrical metal liner. It provides the stability against the tilt and shift motions of spheromaks at the expense of the simple connection of its geometry. Since the spheromak is characterized by the elimination of external toroidal fields in association with nonconservation of a toroidal flux during magnetic relaxation, the metal liner was made electrically disconnected from the main vacuum vessel (spheromak mode). In the experiments, existense of the dynamo effect, meaning automatic generation of toroidal flux similar to that of a reversed field pinch (RFP), is observed. Measured MHD activity consists of multihelicity helical modes with toroidal mode numbers N = 1-3. In order to investigate the difference between spheromaks and RFP's in the MHD activity during sustainment, experiments have also been made with the metal liner of the OH coil connected with the vessel (RFP mode). The dynamics of the MHD activities observed are compared with those obtained from the three-dimensional MHD simulations by Katayama and Katsurai [18], and their implication in the dynamo effect is discussed.     

基于垂直引线和调制电流的三线环形磁导引

提出了一种在单层原子芯片上实现闭合且导引中心无磁场零点的环形磁导引的新方案. 芯片表面刻蚀的导线结构由同心等距三环线构成, 三环线的电流引线垂直于芯片表面. 加载直流电流后, 这种构型即可在芯片表面附近产生闭合的环形磁导引. 交流调制三环线电流后, 环形磁导引的势能极小值附近不再存在磁场零点且其磁场起伏小. 这种方案可用于基于物质波干涉的原子芯片陀螺仪研究.     

Tokamak equilibria with reversed current density

Observations of nearly zero toroidal current in the central region of tokamaks (the "current hole") raises the question of the existence of toroidal equilibria with very low or reversed current in the core. The solutions of the Grad-Shafranov equilibrium equation with hollow toroidal current density profile including negative current density in the plasma center are investigated. Solutions of the corresponding eigenvalue problem provide simple examples of such equilibrium configurations. More realistic equilibria with toroidal current density reversal are computed using a new equilibrium problem formulation and computational algorithm which do not assume nested magnetic surfaces.     

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.     

Generation of stable mixed-compact-toroid rings by inducing plasmacurrents in strong E rings

In the RECE-Christa device, hybrid-type compact toroid rings are generated by inducing large toroidal plasma currents I_p in strong electron rings using a thin induction coil positioned along the ring axis. Starting from field-reversal values δ_p =50-120% of the original pure fast-electron ring, the induced plasma current I_p raises δ to a maximum value of up to 240% with I_p contributing more than 50% of the total ring current. The generated hybrid compact toroid configurations appear gross-stable during the full I_p pulse length (half-amplitude width about 100 μs)     

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     

Effects of three-dimensional electromagnetic structures on resistive-wall-mode stability of reversed field pinches

In this Letter, the linear stability of the resistive wall modes (RWMs) in toroidal geometry for a reversed field pinch (RFP) plasma is studied. Three computational models are used: the cylindrical code ETAW, the toroidal MHD code MARS-F, and the CarMa code, able to take fully into account the effects of a three-dimensional conducting structure which mimics the real shell geometry of a reversed field pinch experimental device. The computed mode growth rates generally agree with experimental data. The toroidal effects and the three-dimensional features of the shell, like gaps, allow a novel interpretation of the RWM spectrum in RFP's and remove its degeneracy. This shows the importance of making accurate modeling of conductors for the RWM predictions also in future devices such as ITER.     

Toroidal current generation by lower hybrid waves in a WT-1 device

A toroidal current driven by a lower hybrid wave (LHW) is obtained by applying RF power to a toroidal plasma produced by electron cyclotron resonance. The direction as well as the magnitude of the current depend on the supplementary vertical and horizontal magnetic fields, which is explained by confinement of current-carrying electrons in a toroidal device.     

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。     

识别TdeV托卡马克等离子体的边界和中心位置

用虚壳原理可以得到TdeV托卡马克等离子体边界、电流中心和X点,用最小二乘法可以确定Glad-Shafranov方程解中的待定参数。用探针测量极向磁场,初始时等离子体电流被看作是线电流,然后被虚壳电流代替。这个虚壳电流在等离子体内部产生负的约束磁场,在等离子体外部产生的磁场与等离子体电流产生的磁场一致,所用的叠代法充分快,可以在两次放电间给出等离子体图象,重建的位形与TV成像非常一致。     

Spontaneous formation of closed-field torus equilibrium via current jump observed in an electron-cyclotron-heated plasma

Spontaneous current jump resulting in the formation of closed field equilibrium has been observed in electron-cyclotron-heated toroidal plasmas under steady external fields composed of a toroidal field and a relatively weak vertical field in the low aspect ratio torus experiment device. This bridges the gap between the open field equilibrium maintained by a pressure-driven current in the external field and the closed field equilibrium at a larger current. Experimental results and theoretical analyses suggest a current jump model that is based on the asymmetric electron confinement along the field line appearing upon simultaneous transitions of field topology and equilibrium.     

Minimum dissipative relaxed states in toroidal plasmas

Relaxation of toroidal discharges is described by the principle of minimum energy dissipation together with the constraint of conserved global helicity. The resulting Euler-Lagrange equation is solved in toroidal coordinates for an axisymmetric torus by expressing the solutions in terms of Chandrasekhar-Kendall (C-K) eigenfunctions analytically continued in the complex domain. The C-K eigenfunctions are obtained as hypergeometric functions that are solutions of scalar Helmholtz equation in toroidal coordinates in the large aspect-ratio approximation. Equilibria are constructed by assuming the current to vanish at the edge of plasma. For the m=0, n=0 (m and n are the poloidal and toroidal mode numbers respectively) relaxed states, the magnetic field, current, q (safety factor) and pressure profiles are calculated for a given value of aspect-ratio of the torus and for different values of the eigenvalue λ _{r 0}. The new feature of the present model is that solutions allow for both tokamak as well as RFP-like behaviour with increase in the values of λ _{r 0}, which is related directly to volt-sec in the experiment.     

Thermoelectric transport effect in superconducting indium

A magnetic flux has been generated within a hollow toroidal cavity whose walls consisted of superconducting indium and lead. The origin of the flux is attributed to a thermoelectric transport effect induced by a temperature gradient in the toroid. The flux was found to diverge rapidly near the transition temperature of indium and to be several orders of magnitude larger than predicted by existing theory.     

东方超环上低杂波驱动等离子体环向旋转实验研究

旋转和旋转剪切能抑制磁流体不稳定性和增强等离子体约束.低杂波电流驱动作为未来聚变堆上可能的旋转驱动手段,探索低杂波在现有托卡马克装置上驱动等离子体旋转的驱动机制,可以为未来的聚变堆上旋转预测提供重要参考.在东方超环托卡马克装置上,早期发现了2.45 GHz的低杂波能有效驱动等离子体旋转的现象,认为是边界旋转的改变导致芯部旋转的同电流方向的增加造成的.更高频率下4.6 GHz低杂波电流驱动可以更有效地驱动同电流方向的等离子体旋转.本论文分析在欧姆背景等离子体下,不同功率的低杂波对等离子体环向旋转的影响,研究安全因子剖面变化对环向旋转的关系,利用功率调制获得了低杂波驱动旋转实验中的环向动量输运系数变化情况,发现环向动量扩散系数(χφ)、环向动量箍缩系数(Vpinch)的数值大小趋势是从芯部向靠外的区域逐渐变大.这与低杂波驱动环向旋转时,环向旋转速度由靠外的区域向芯部传递的特性吻合.     

Theoretical Optimization of Stellarators

Net current free toroidal ("stellarator") confinement is studied with a combination of several methods: a complete set of analytical vacuum fields for finding favorable vacuum field configurations; three-dimensional MHD codes for finite-?, equilibrium computations; the expansion of a general toroidal equilibrium around its magnetic axis as guideline for the computational search in configurational space and for finite-?, MHD stability; Monte Carlo simulations for particle containment; continuous modular coil systems generating the configurations considered. Results are: vacuum field configurations with sizeable Q = 0, 1, 2, 3 helical fields, substantial twist number (? 1/2), significant reduction of the parallel current density, and vacuum magnetic well exist for a toroidal aspect ratio of 15-20 and can be generated by modular coils whose excursions from meridional planes are small compared to the toroidal period length. In these configurations, the finite-? toroidal shift is strongly reduced, so that a larger ? value (factor 2-4) than in the equivalent Q = 2 stellarator can be achieved. Stability calculations do not exclude the possibility of stable equilibria of this kind with (?) ? 0.05-0.1; transport calculations without electrical field show improvement-as compared to the Q = 2 stellarator-in the collisional and plateau regimes.     

Replica-symmetric solutions of a dilute Ising ferromagnet in a random field

We use the replica method in order to obtain an expression for the variational free energy of an Ising ferromagnet on a Viana-Bray lattice in the presence of random external fields. Introducing a global order parameter, in the replica-symmetric context, the problem is reduced to the analysis of the solutions of a nonlinear integral equation. At zero temperature, and under some restrictions on the form of the random fields, we are able to perform a detailed analysis of stability of the replica-symmetric solutions. In contrast to the behaviour of the Sherrington-Kirkpatrick model for a spin glass in a uniform field, the paramagnetic solution is fully stable in a sufficiently large random field.     

Scattering by a slender void in a homogeneous conducting wire rope

A thin prolate spheroidal void in an infinite conducting circular cylinder is used to model a broken strand in a wire rope. The rope is excited by an azimuthal magnetic line current which is a model for a thin toroidal coil. The anomalous external fields are computed from the induced electric and magnetic dipole moments of the void. The results have applications to nondestructive testing of wire ropes.     

周期场聚焦电子束

引言 自从发现“强聚焦效应”可以应用在粒子加速器内以后,人们知道利用周期磁场能把离子束控制得更细,于是可以减少磁铁的需要量。因此近年来为了改建或新设计各种类型粒子加速器,对周期场聚焦离子束或电子束方面曾进行了很多研究工作。另一方面人们也开始研究用周期电场和磁场聚焦各种电子管内的电子束,例如行波管内电子束的聚焦等。聚焦电子束的主要特点在於必要考虑空间电荷。     

Elimination of Compressive Stress in Helical-Toroidal-Coil Advanced Structure for Reactor Plasmas

Calculations of inductance for helical toroidal coils are of great interest to researchers since they are the basis of optimal design with target functions such as the maximization of the ratio of the stored magnetic energy with respect to the volume of the toroid or the used conductor, the elimination or the balance of stress in certain coordinate directions, and the attenuation of leakage flux. In this paper, using Neumann's equation, formulas are presented to calculate the self-inductance and mutual inductance of the helical toroidal coil in superconductivity conditions. It is shown that calculation of self-inductance is similar to that of mutual inductance if the diameter of the conductor's cross section is smaller than 0.4 of the minor radius. Comparison between experimental and empirical results with numerical results indicates that the presented formulas are highly reliable. Plotting contours for the magnetic flux density shows that a special design approach must be taken so that the coil eliminates the leakage flux. It is also shown that the optimal design of the coil to eliminate or balance the stress in certain coordinate directions requires selection of geometrical parameters from accurate inductance equations, and therefore, the use of approximate equations for this purpose is not recommended.      

Theoretical investigation of the possibility of isotope separation during motion of charged particles in the electromagnetic field of a cylindrical capacitor and a linear current flowing along its axis

A characteristic feature of the trajectories of charges moving in constant axisymmetric radial electric and azimuthal magnetic fields, whose strengths are inversely proportional to the center from the symmetry axis is the exponential dependence of the turning points on the parameters of motion. This leads to a noticeable difference in the trajectories for isotope ions, which makes it possible to obtain a new method for their electromagnetic separation. The trajectories of isotopes being separated are studied theoretically. The conditions under which the trajectories are closed and form toroidal surfaces (storage vortex rings) have been determined earlier. These results are given for convenience in analyzing another problem, associated with the formation of such ionic toroidal vortex surfaces (stable in Wood’s sense) during a streak lightning discharge in the atmosphere (ball lightning model).