Modelling stability in superconducting cables

Stability is one of the key issues in the design of a superconductor, and indeed deserves much attention in the magnet design and analysis. Stability-oriented design procedures and calculations involve the detailed knowledge of the response of the cable to thermal, fluid dynamic and electric transient phenomena that are difficult to tackle analytically in cables. This has justified a significant numerical modelling effort in the field. This paper reviews basic stability models and presents selected advances in the methods developed and results obtained. A unified, semi-continuum model is proposed for stability analysis of cables. The time scales of relevance during stability transients are identified and analysed.     

Current distribution in multistrand superconducting cables — experimental methods and results

It is widely acknowledged that current non-uniformity is a major source of reduction of quench currents in superconducting multistrand cables at non-steady state conditions. Recently we performed several experimental studies on the current non-uniformity in CICC and AC cables. In this paper we present the summary of the experimental methods used. Indirect methods with use of local magnetic field sensors can provide general information about non-uniformity inside CICCs and other large size cables. Indirect methods may be used in real superconducting devices. Direct measurements of the current in each strand provide exact information about the current distribution, but they need special sample preparations. Because no method is perfect, the best idea is to use them as complementary to each other in the study of a certain type of a cable. The results obtained from the measurements of the current non-uniformity in CICC and AC cables by both methods are briefly discussed.     

The transport current redistribution between the core layers on the models of HTS cables

The multilayer conductors with insulated and non-insulated layers are analyzed. The space–time current redistributions between the layers of the conductor are investigated for the next parameters: values of electric resistance at the current leads, transverse contact electric resistance between the layers, the model length, time, the conductor dimension, the current—its peak value, the change law and the ramp of the total current input. Most of the published test results for short (from 1 to 10 m) conductor models do not reflect the true current distribution of the real long length cable conductors. The criterion of experimental model constructions and, in particular, the calculation of its minimum length are presented. The calculations demonstrate the electromagnetic processes in real cable conductors.     

超导电缆的性能检测方法研究

超导电缆与常规电缆在电磁特性上有很大差异。因此,有必要对其试验内容、性能检测方法和试验设备进行研究和规范。文中从超导电缆的电磁特性出发,探讨了超导电缆的试验内容及性能检测方法,并重点介绍了超导电缆交流损耗的测量方法。     

Transient stability of AC multi-strand superconducting cables

AC application, it is necessary to estimate the stability of multi-strand superconducting cable. Therefore, we have been studying the transient stability of non-insulated multi-strand cable when one strand in a cable turns into the normal state locally. In the quench process, local temperature rise produced by current redistribution among strands is not desirable for stability. In a previous work, we discussed the effect of Cu matrix allocated to each strand on the transient stability and showed that the Cu matrix allocation can improve the stability of non-insulated multi-strand cable through mainly numerical simulations. In this paper, we carried out experiments on three kinds of non-insulated three-strand cables; one consists of NbTi/CuNi strands and the others consist of NbTi/Cu/CuNi strands having different cross-sectional arrangement. These sample strands have almost the same diameter, the same matrix to superconductor ratio and the same B–J characteristics to evaluate the effect of Cu allocation quantitatively. We choose to define the transient stability in terms of the minimum quench energy (MQE) at each DC transport current. We also investigated the transient stability of sample cables when quench is initiated in two or three (all) strands simultaneously.     

Magnetic- and stress-fields of cylindrical non-uniform current density superconducting coils

Superconducting coils with an inhomogeneous current density distribution yield more field for less volume of superconductor. The advantages of these systems are lower costs and an improved cooling. The latter is important for high field magnets. Mechanical stresses induced by the electromagnetic forces are the limiting factor in designing such coils. The inhomogeneous current field is produced by a set of concentric subcoils. The radial and tensile stresses and the radial displacements in the subcoils are calculated. This calculation requires the field-shape in the coils. An exact calculation shows a linear decrease of the field with the radius in each subcoil. Thus the stress-calculations are very simple and one does not need a computer. As an example this method is applied to a 10 T-magnet with three subcoils. In this case the results of our exact calculation differ from the approximation of Kilbet al., Steklyet al. and from the magnetic pressure estimateB ²/2μ ₀ up to a factor of three.     

Influence of the multilayer HTS-cable conductor design on the current distribution

The work presents the basic principles of the multilayer cable conductor design to achieve the maximum current-carrying capacity and the minimum losses in a superconductor and constructive cable elements. The multilayer conductors of two to ten layers are analyzed. The results show that the traditional core design with alternative winding directions from layer to layer is useful only for two-layer conductor. The conductor with more layers must have either the layers wound in one direction but with different pitch lengths or two layer groups wound with different pitch lengths. Only for these cases, the balanced design can be realized and current distribution will be uniform. In such balanced design, the interlayer electrical voltage and as a result, the coupling losses, are absent and interlayer electrical insulation is not needed. The recommendations to achieve the maximum critical current as a function of conductor dimensions are derived.     

高温超导电缆导体层电流分布研究

通过建立高温超导电缆等效电路模型,并提出电流分布等效数学方程,求得高温超导电缆导体层电流分布。绕制一根0.2m长110kV/2kA高温超导电缆样缆,并进行载流能力实验,得到各层电流分布结果。分析发现,各层电流分布的实验结果与理论计算结果吻合,从而验证电流分布计算模型的正确性,以及调整绕制角度对均匀层间分流的有效性。研究结论对以后更长高温超导电缆的载流能力分析具有一定的指导意义。     

超导磁体电流引线氦气流阻研究

超导磁体电流引线中氦气流阻是设计电流引线时的一个很重要参数。计算电流引线片中氦气流阻比较好的方法是采用有限元软件F luent。由于氦气模型庞大的有限元单元数,因此该文中对模型进行了简化和分段,相邻模型段间采用流量边界条件和压力边界条件进行耦合。     

AC coupling losses in superconducting multistage cables with and without additional co-twisted copper strands

A simple technique is proposed to evaluate interstrand AC coupling losses deposed in superconducting multistage cables under low excitation of the transverse homogeneous time-varying magnetic field. The technique uses the superposition of the solutions for the induced coupling currents and interstrand or intersubcable AC losses in pairs of strands or subcables, constituting a multistage cable. The technique is valid under assumption of no resistance offered by strands and subcables for the longitudinal currents. The method allows one also to take into account the effect of additional co-twisted pure copper strands or subcables.     

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用有限元软件Fluent对EAST超导磁体电流引线中氦气流阻进行了计算。计算中对氦气模型进行了简化和分段,相邻两段模型间采用流量边界条件和压力边界条件进行耦合。计算结果表明:氦气的压力降主要集中在靠近室温端;气体模型厚度越薄,氦气压力降越大;通过电流引线的电流越大,氦气的压力降越大;在引线片凸纹的狭窄处氦气速度很大,在靠近室温端时最大可以达到21m.s-1左右。     

超导磁体气冷电流引线优化设计

提出了一种较为准确的计算超导磁体气冷电流引线最优长横比与电流引线末端流向低温容器热量的方法。根据电流引线的热平衡方程,利用程序设计,采用反复迭代、逐步逼近的方法,并以无氧铜材料为例,计算了10kA电流引线的长横比与流入低温容器的最小漏热。     

The similarities in loss creation in LTS and HTS cables

The coupling current losses represent an essential contribution to AC losses in most practical superconducting conductors. The origin of this loss type is well known, being caused by induced currents in different loops consisting of superconducting and non-superconducting parts. However, the ‘current pattern' in different conductor types (strands, flat or round cables, more complicated cable structures, CICC) varies appreciably. These differences are mainly due to geometrical effects (size and shape of filaments and/or strands, their spatial distribution, conductor aspect ratio, demagnetization effects). Although the general knowledge about AC losses in low temperature cable structures is by far not complete (mainly at higher frequencies, in inhomogeneous fields and for inhomogeneous cable structure), an attempt is made to summarize those results which can be adopted to high T_c conductors and some remarks are made about new features of AC losses in these conductor types.     

Review of conductor development for use in high-temperature superconducting cables

Summary This paper reviews and assesses the progress in conductor development across the world in advancing high-temperature superconducting science and technology towards the fabrication of superconducting transmission cables operating at 77 K. Materials, fabrication routes and the feasibility of high-temperature superconducting cables will be discussed. Paper presented at the ?VII Congresso SATT?, Torino, 4–7 October 1994.     

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阐述了FAIR收集环二极超导磁体电流引线的基本原理,给出了电流引线的主要参数及初步设计方案,提出了使用复合材料和通过结构优化以减小电流引线的漏热,并根据电流引线的传热特性进行了漏热的分析和计算,实验结果验证了概念设计的可行性。     

Incomplete-penetration hysteresis losses in transmission line cables

At 77 K, the resistivity of ceramic, high-temperature superconductors grows gradually rather than sharply with increasing current. The critical-state theory of hysteresis losses therefore needs to be modified. This has been done for slab conductors whose resistivity can be taken proportional to a power of the current density. Simple formulas have been derived in the limiting cases of incomplete penetration and full penetration when the losses are driven either by a sinusoidal transport current or a sinusoidal external magnetic field. These formulas can be applied to multilayer transmission line cables once the current distribution within and among the layers has been determined. This distribution has been calculated (in the incomplete penetration limit) by solving Maxwell's field equations. A formula is presented for the dependence of the hysteresis loss on winding angle. The formula is used to determine the optimum winding angle.     

FAIR收集环二极超导磁体电流引线的概念设计

阐述了FAIR收集环二极超导磁体电流引线的基本原理,给出了电流引线的主要参数及初步设计方案,提出了使用复合材料和通过结构优化以减小电流引线的漏热,并根据电流引线的传热特性进行了漏热的分析和计算,实验结果验证了概念设计的可行性。     

Study of superconducting state parameters of alkali–alkali binary alloys by a pseudopotential

A detailed study of the superconducting state parameters (SSP) viz. electron–phonon coupling strength λ, Coulomb pseudopotential μ^*, transition temperature T_C, isotope effect exponent and effective interaction strength N_OV of ten alkali–alkali binary alloys i.e. Li_1−xNa_x, Li_1−xK_x, Li_1−xRb_x, Li_1−xCs_x, Na_1−xK_x, Na_1−xRb_x, Na_1−xCs_x, K_1−xRb_x, K_1−xCs_x and Rb_1−xCs_x are made within the framework of the model potential formalism and employing the pseudo-alloy-atom (PAA) model for the first time. We use the Ashcroft’s empty core (EMC) model potential for evaluating the superconducting properties of alkali alloys. Five different forms of local field correction functions viz. Hartree (H), Taylor (T), Ichimaru–Utsumi (IU), Farid et al. (F) and Sarkar et al. (S) are used to incorporate the exchange and correlation effects. A considerable influence of various exchange and correlation functions on λ and μ^* is found from the present study. Reasonable agreement with the theoretical values of the SSP of pure components is found (corresponding to the concentration x = 0 or 1). It is also concluded that nature of the SSP strongly depends on the value of the atomic volume Ω₀ of alkali–alkali binary alloys.     

Numerical calculation of current density distributions in high temperature superconducting tapes with finite thickness in self field and external field

The current density distribution of high temperature superconducting (HTS) tapes is modeled for the combined case of an alternating self and applied magnetic field. This numerical analysis is based on the two-dimensional Poisson equation for the vector potential. A one-dimensional current (z-direction) and a one-dimensional applied field (y-direction) are assumed. The vector potential is rewritten into an equation of motion for the current density J(x,y,t). The model covers the finite thickness of the conductor and an n-power E–J relation. The magnetic field dependence of J_c is also included in this E–J relation. A time-dependent two-dimensional current distribution that is influenced by the aspect ratio of the conductor and the material properties in E=f(J,B) is calculated numerically. The numerical results are compared with the experimental results for the AC loss of a tape driven by a transport current. Finally, a total AC loss factor is given for two cases in magnetic field direction, perpendicular and parallel to the conductor broad side.