Kim model for stress distribution in a hollow cylindrical superconductor

In the present work, the distributions of the stress induced by flux pinning in a cylindrical superconductor with a concentric elliptic hole are studied. The Kim model is considered for the critical state, and the analytical expression of the stress in the cylinder is derived when the concentric hole is circular. Based on the finite element method, at first, the validity of the calculation process and the accuracy of the numerical results are proved by comparing with the analytical results. Subsequently, the distributions of the stress are obtained for different ratio of the major axis and the minor axis of the elliptic hole. It is found that due to the effect of stress concentration, as the value of ratio the major axis and the minor axis becomes large, the radial and hoop stress in superconductor just increase significantly in the vicinity of the hole, and the variation of the hoop stress is more sensitive. These results have significant effects on the safety in applications of superconductor.     

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.      

Dynamics of shock waves caused by pulsed high-current electric discharges in gas. I. Toroidal (ring-shaped) shock wave

Dynamics of convergence and reflection of the toroidal (ring-shaped) shock wave (SW) in the torus plane and in the plane passing through its symmetry axis is experimentally studied. It is shown that such an SW is significantly amplified near the torus symmetry axis. The maximum amplification of the toroidal SW near its symmetry axis is estimated.     

Ion current distribution within a toroidal duct of a filteredvacuum arc deposition system

Vacuum arcs were established on a 90-mm-diameter Ti cathode in a deposition apparatus consisting of a spacer, 122 mm-diameter annular anode, quarter-torus magnetic macroparticle filter, and a deposition chamber. A toroidal magnetic field generally parallel to the torus walls of up to 20 mT was applied. The ion current in various cross-sections of the toroidal duct was measured using: 1) a disc probe of 130-mm diameter, oriented normal to the torus axis used to measure the transmitted ion current, and 2) a hollow cylindrical probe of 135-mm diameter and 25-mm height, whose axis coincided with the torus axis, used to measure ion current losses to the duct wall. The distribution of ion current loss was studied using an 8-segment hollow cylindrical multiprobe, where the individual probes were equally distributed on the circumference of a 130-mm-diameter circle. It was shown that: 1) the ratio of ion currents collected on the cylindrical and disc probes at first decreases with increasing the toroidal field, and then becomes approximately constant; 2) the presence of the large-diameter disc probe does not influence the value of the ion current on the cylindrical probe; and 3) the maximum ion current density near the torus walls is located in the +g direction and displaces in the -(B×g) direction with increasing the toroidal field, where g and B are the vectors of the centrifugal acceleration and the magnetic field, respectively     

A novel approach to calculate inductance and analyze magnetic flux density of helical toroidal coil applicable to Superconducting Magnetic Energy Storage systems (SMES)

In this paper, formulas are proposed for the self and mutual inductance calculations of the helical toroidal coil (HTC) by the direct and indirect methods at superconductivity conditions. The direct method is based on the Neumann’s equation and the indirect approach is based on the toroidal and the poloidal components of the magnetic flux density. Numerical calculations show that the direct method is more accurate than the indirect approach at the expense of its longer computational time. Implementation of some engineering assumptions in the indirect method is shown to reduce the computational time without loss of accuracy. Comparison between the experimental measurements and simulated results for inductance, using the direct and the indirect methods indicates that the proposed formulas have high reliability. It is also shown that the self inductance and the mutual inductance could be calculated in the same way, provided that the radius of curvature is >0.4 of the minor radius, and that the definition of the geometric mean radius in the superconductivity conditions is used. Plotting contours for the magnetic flux density and the inductance show that the inductance formulas of helical toroidal coil could be used as the basis for coil optimal design. Optimization target functions such as maximization of the ratio of stored magnetic energy with respect to the volume of the toroid or the conductor’s mass, the elimination or the balance of stress in some coordinate directions, and the attenuation of leakage flux could be considered. The finite element (FE) approach is employed to present an algorithm to study the three-dimensional leakage flux distribution pattern of the coil and to draw the magnetic flux density lines of the HTC. The presented algorithm, due to its simplicity in analysis and ease of implementation of the non-symmetrical and three-dimensional objects, is advantageous to the commercial software such as ANSYS, MAXWELL, and FLUX. Finally, using the presented algorithm, magnetic flux density lines in several examples are drawn.     

Magnetic field in a finite toroidal domain

The magnetic field structure in a domain surrounded by a closed toroidal magnetic surface is analyzed. It is shown that ergodization of magnetic field lines is possible even in a regular field configuration (with nonvanishing toroidal component). A unified approach is used to describe magnetic fields with nested toroidal (possibly asymmetric) flux surfaces, magnetic islands, and ergodic field lines.     

Flux conversion and evidence of relaxation in a high-beta plasma formed by high-speed injection into a mirror confinement structure

High-beta plasmoids can survive the violent dynamics of supersonic reflection off mirror structures, producing a stable high-beta field-reversed configuration (FRC). This shows both the robustness of FRCs and their tendency to assume a preferred plasma state, possibly conforming to a relaxation principle. The key observations are (1) approximate preservation of the magnetic helicity, (2) substantial conversion from toroidal to poloidal magnetic flux, (3) substantial toroidal flow, and (4) a high-beta quiescent final state. These results are from the Translation, Confinement, and Sustainment experiment where a disorganized plasmoid is injected at super-Alfvenic speed into a confinement chamber. After successive reflections from end mirrors, the plasmoid settled into a near-FRC state with high beta and low toroidal magnetic field. The flux conversion and helicity preservation are inferred by an interpretive model.     

Analyses of edge plasma characteristics in HL-2A

The edge plasma characteristics are studied by both a movable array of Mach/Reynolds stress/Langmuir 10-probes in the boundary region and the fixed flush probe arrays on the 4 divertor neutralization plates at the same toroidal cross-section in the HL-2A tokamak. The dependence of the Reynolds stress on poloidal flow in the edge plasma is analysed. The result indicates that the sheared poloidal flow in tokamak plasma can be induced by the radial gradient of Reynolds stress. In the divertor experiments of HL-2A, the profiles of the electron temperature, density and floating potential on divertor plates are measured by the flush probe arrays. The edge electron temperature in divertor configuration is higher than that in limiter configuration. The temperature asymmetry between outer and inner target plates is observed. The result of magnetic surface reconstructed from 18 Mirnov coils signals is presented. Both the particle recycling and the impurity flux in the bulk plasma during divertor discharges are discussed. Neutral gas pressure in divertor chamber, measured by fast ionization gauge during divertor discharge, is given.     

基于环磁美特材料的无线传能系统

传统的四线圈磁共振耦合无线传能系统已在移动电子设备、电动汽车无线充电中得以应用,然而,其传能效率仍然因其磁场空间分布的发散性而难以提高.为了克服上述缺点,我们提出了一种基于环磁美特材料、磁场更为局域的高效无线传能系统.该系统将四线圈系统中的一对磁谐振耦合线圈替换为具有环磁谐振特性的四个非对称开口谐振环.该环磁模式具有高Q值、低金属损耗以及辐射抑制的特性.实验结果表明,相对于四线圈系统,该系统的磁场更为集中,能量传输效率更高.     

Self-reversal phenomena of toroidal current by reversing the external toroidal field in helicity-driven toroidal plasmas

In order to understand self-organization in helicity-driven systems, we have investigated the dynamics of low-aspect-ratio toroidal plasmas by decreasing the external toroidal field and reversing its sign in time. Consequently, we have discovered that the helicity-driven toroidal plasma relaxes towards the flipped state. Surprisingly, it has been observed that not only toroidal flux but also poloidal flux reverses sign spontaneously during the relaxation process. The self-reversal of the magnetic fields is attributed to the nonlinear growth of the n=1 kink instability of the central open flux.     

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.     

Experimental identification of the kink instability as a poloidal flux amplification mechanism for coaxial gun spheromak formation

The magnetohydrodynamic kink instability is observed and identified experimentally as a poloidal flux amplification mechanism for coaxial gun spheromak formation. Plasmas in this experiment fall into three distinct regimes which depend on the peak gun current to magnetic flux ratio, with (I) low values resulting in a straight plasma column with helical magnetic field, (II) intermediate values leading to kinking of the column axis, and (III) high values leading immediately to a detached plasma. Onset of column kinking agrees quantitatively with the Kruskal-Shafranov limit, and the kink acts as a dynamo which converts toroidal to poloidal flux. Regime II clearly leads to both poloidal flux amplification and the development of a spheromak configuration.     

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介绍了HL-2M环向场线圈的基本结构设计及其承受的电磁载荷,分析了水平预加载、中心柱预应力筒以及环向抗扭支撑对线圈匝间剪切应力的影响.结果表明,水平预加载及预应力筒在中心柱内产生的压应力有利于提高中心柱的抗扭刚度;环向支撑刚度增加可减小线圈的面内剪切应力.在正常运行工况下,环向场线圈的最大匝间剪切应力小于8MPa,其结构设计满足线圈强度要求.对于大破裂瞬态事件,匝间最大剪切应力约12MPa,接近绝缘材料的剪切疲劳极限,建议采取破裂抑制措施避免该情况发生.     

Formation mechanism of a circumferential roller in a drying biofluid drop

Using the methods of theoretical thermohydromechanics, a model of protein roller formation at the periphery of a drying biofluid drop is constructed. As basic mechanisms of mass transfer-, temperature-, concentration-, and gravity-induced convections are considered, which produce a global toroidal flow with an ascending fluid filament at the center, dipping fluid along the free surface, and compensatory centripetal flow at the bottom. The shape of the protein roller is analyzed under the assumptions that the material deposition rate is proportional to the (i) material concentration and (ii) material flux.     

Energy Characteristics of Wave Fields Radiated from Elementary Oscillators in a Nondispersive Medium Moving with Subluminal Velocity

We study the energy characteristics of fields radiated from electric, magnetic, and toroidal dipoles in a nondispersive medium moving with velocity lower than the speed of light in this medium. The angular dependences of Abraham's energy-flux density of electromagnetic field are analyzed. In particular, it is shown that if the medium velocity is high enough, then the radial component of the vector of energy-flux density is negative in a certain angular range. Expressions for the electromagnetic energy flux through a sphere of large radius are obtained. It is shown that if the velocity of a moving medium is high enough, then the energy flux is negative and its absolute value can exceed the energy losses of sources.     

聚变堆环向场D形线圈应力计算

本文用有限元素法求解了托卡马克型聚变堆环向场D形线圈的应力分布。计算结果表明,拉应力结果与JET环向场D形线圈的结果一致,沿导体的剪应力很小,近似为纯张力线圈。     

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为环向场线圈防倾覆结构及其它支撑部件的设计提供依据,采用有限元实体模型分析方法,通过电磁-结构耦合计算对HL-2M装置的环向场线圈进行电磁力分析。计算结果表明,在目前的防倾覆结构和一般的运行情况下,环向场线圈所受最大剪切应力约为7.2MPa,在材料许用应力范围之内。     

Momentum-transfer scattering cross section and the Aharonov-Bohm effect on a toroidal solenoid

The quantum-mechanical Aharonov-Bohm effect in the diffraction of charged particles by a toroidal solenoid containing a magnetic field is investigated. The total and differential elastic scattering cross sections depend on the magnetic flux inside the solenoid, even in the presence of a “black” ring-shaped screen which prevents charged particles from entering the region where the magnetic field is localized. Relations describing the momentum-transfer cross section for the elastic scattering of charged particles by a toroidal solenoid are obtained in the eikonal approximation and in a unitary model of scattering with a sharp jump in the partial amplitudes. The momentum-transfer scattering cross section is proportional to the average transfer of the longitudinal momentum of the scattered particle and can be expressed in terms of a force operator. It is shown that in the absence of a screen the momentum-transfer scattering cross section of toroidal solenoid is indeed determined only by the part of the incident beam that intersects the inner region of the toroidal solenoid, where the magnetic field intensity and, therefore, the Lorentz force are nonzero. At the same time, the momentum-transfer cross section for the scattering of charged particles by a toroidal solenoid covered by a “black” ring-shaped screen does not depend on the magnetic flux inside the solenoid and is identical to the momentum-transfer cross section for diffraction by the same screen. The contribution from scattering by an opening in the screen, which depends on the magnetic flux, is completely compensated by the contribution of the interference of the scattering amplitudes of the opening and the “black” screen.     

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.     

Nondiffusive transport in tokamaks: three-dimensional structure of bursts and the role of zonal flows

Large scale transport events are studied in simulations of resistive ballooning turbulence in a tokamak plasma. The spatial structure of the turbulent flux is analyzed, indicating radially elongated structures (streamers) at the low field side which are distorted by magnetic shear at different toroidal positions. The interplay between self-generated zonal flows and transport events is investigated, resulting in significant modifications of the frequency and the amplitude of bursts. The propagation of bursts is studied in the presence of a transport barrier generated by a strong shear flow.