Analysis of the quench propagation along Nb3Sn Rutherford cables with the THELMA code. Part I: Geometric and thermal models

The paper describes the new lumped thermal model recently implemented in THELMA code for the coupled electromagnetic–thermal analysis of superconducting cables. A new geometrical model is also presented, which describes the Rutherford cables used for the accelerator magnets. A first validation of these models has been given by the analysis of the quench longitudinal propagation velocity in the Nb₃Sn prototype coil SMC3, built and tested in the frame of the EUCARD project for the development of high field magnets for LHC machine. This paper shows in detail the models, while their application to the quench propagation analysis is presented in a companion paper.     

CUDI: A model for calculation of electrodynamic and thermal behaviour of superconducting Rutherford cables

CUDI is the extended Fortran code to calculate the electrodynamic and thermal behaviour of any type of Rutherford cable subject to global and/or local variations in field, transport current, and external heat release. The internal parameters of the cable can be freely varied along the length and across the width, such as contact resistances, critical current, cooling rates etc. In this way, all the typical non-uniformities occurring in a cable, e.g. broken filaments, strand welds, cable joints, and edge degradation can be simulated. Also the characteristics of the strands in the cable can be varied from strand to strand. Heat flows through the matrix, through the interstrand contacts, and to the helium are incorporated, as well as the self-field and self- and mutual inductances between the strands. The main features and structure of the program will be discussed.     

覆冰斜拉索驰振稳定性的理论研究

覆冰斜拉索可能会发生驰振振动并影响到斜拉桥的安全。在进行风洞试验对6种覆冰拉索模型测力的基础上,推导了覆冰拉索1阶模态驰振的运动微分方程,并采用龙格-库塔法进行求解,得到了拉索的驰振响应规律。以海南洋浦大桥为工程背景,研究了中跨最长拉索M18的驰振临界风速,研究了覆冰长度、拉索阻尼比等对驰振临界风速的影响。结果表明,在新月形、扇形和D形覆冰条件下,中跨最长拉索M18的驰振临界风速在10-15m/s范围内,远小于基本风速,存在发生驰振可能性;随着阻尼比的增加、覆冰长度的变短以及拉索长度的变短,驰振临界风速增加。     

Analysis of the quench propagation along Nb3Sn Rutherford cables with the THELMA code. Part II: Model predictions and comparison with experimental results

To improve the technology of the new generation of accelerator magnets, prototypes are being manufactured and tested in several laboratories. In parallel, many numerical analyses are being carried out to predict the magnets behaviour and interpret the experimental results. This paper focuses on the quench propagation velocity, which is a crucial parameter as regards the energy dissipation along the magnet conductor. The THELMA code, originally developed for cable-in-conduit conductors for fusion magnets, has been used to study such quench propagation. To this purpose, new code modules have been added to describe the Rutherford cable geometry, the material non-linear thermal properties and to describe the thermal conduction problem in transient regime. THELMA can describe the Rutherford cable at the strand level, modelling both the electrical and thermal contact resistances between strands and enabling the analysis of the effects of local hot spots and quench heaters. This paper describes the model application to a sample of Short Model Coil tested at CERN: a comparison is made between the experimental results and the model prediction, showing a good agreement. A comparison is also made with the prediction of the most common analytical models, which give large inaccuracies when dealing with low n-index cables like Nb₃Sn cables.     

Simulation of the cabling process for Rutherford cables: An advanced finite element model

In all existing large particle accelerators (Tevatron, HERA, RHIC, LHC) the main superconducting magnets are based on Rutherford cables, which are characterized by having: strands fully transposed with respect to the magnetic field, a significant compaction that assures a large engineering critical current density and a geometry that allows efficient winding of the coils. The Nb₃Sn magnets developed in the framework of the HL-LHC project for improving the luminosity of the Large Hadron Collider (LHC) are also based on Rutherford cables. Due to the characteristics of Nb₃Sn wires, the cabling process has become a crucial step in the magnet manufacturing. During cabling the wires experience large plastic deformations that strongly modify the geometrical dimensions of the sub-elements constituting the superconducting strand. These deformations are particularly severe on the cable edges and can result in a significant reduction of the cable critical current as well as of the Residual Resistivity Ratio (RRR) of the stabilizing copper. In order to understand the main parameters that rule the cabling process and their impact on the cable performance, CERN has developed a 3D Finite Element (FE) model based on the LS-Dyna® software that simulates the whole cabling process. In the paper the model is presented together with a comparison between experimental and numerical results for a copper cable produced at CERN.     

Quench factor analysis of aluminium alloys

Abstract

A model was developed almost 20 years ago which described how precipitation during the quench affected the development of properties of aluminium alloys during subsequent aging treatment. This model was the basis for an analytical process, known as quench factor analysis, that was used to predict the effects of quench path on corrosion characteristics and strength. The purpose of this paper is to provide a theoretical basis for the model and to review how quench factor analysis has been used in solving industrial problems. Several investigators have confirmed that quench factor analysis is an effective predictive method for all quenching conditions save one. The exception is when material has been quenched below the knee of the C-curve and subsequently reheated above the knee before the quench is complete. Applications include the design of quench systems, the development of quench practices which optimize combinations of high strength and low residual stress and distortion, and predictions of the magnitude of loss in strength as a result of unsuitable quenching conditions. By combining quench factor analysis with homogeneous nucleation theory, interactions between quenching and aging conditions have been clarified, and aging treatments have been developed which minimize the low and variable strengths caused by less than ideal quenching conditions. Quench factor analysis also adequately describes the rate of loss in toughness of an AA 6000 series extrusion alloy for those cooling conditions which produced commercially significant loss in strength. The latest use of quench factor analysis is in a specification for quenchants for aluminium alloys.

MST/573     

Transient stability of superconducting cables against thermal disturbance

The stability of a superconducting cable is investigated by measuring the heat flux cooled by liquid helium. It was found that the heater power needed to make the cable go to the normal state can be given by P_H = P_S + E_O (Δ T_m/τ, where, P_S is the steady heater power needed to make the cable go normal, E_O(ΔT_m), certain energy determined by the temperature increase of the superconducting cable as well as cooling conditions, and τ, the heating period. Therefore the permisable thermal disturbance becomes very large as the duration becomes shorter. The reason seems to be that a lot of heater energy is removed by the latent heat of liquid helium which exists just around the strands. Estimating the amount of liquid helium evaporated by the heater energy, superconducting cables seem to be stable against such thermal disturbance if liquid helium exists in contact with the cables by the amount of about 10 ～ 30% of the cable volume.     

AC loss properties of some Bi:2212/Ag Rutherford cables and a comparison with those of cables wound with NbTi and Nb3Sn

Calorimetric measurements of AC loss have been performed on Rutherford cables wound with NbTi, Nb₃Sn, and Bi:2212/Ag strands, respectively. For the NbTi cables, various strand coatings had been applied, while for the Nb₃Sn and Bi:2212/Ag cables the strand surfaces were just bare Cu or Ag, respectively. Most of the cables contained resistive cores: ribbons of kapton or titanium (NbTi cables), stainless steel (NbTi and Nb₃Sn cables), and nichrome-80 (Bi:2212/Ag cables). In all cases the cores were found to lead to a strong suppression of the face-on (field normal to the broad cable face) coupling current loss; to such an extent that even the Bi:2212/Ag cables, which would otherwise be severely cross-sintered, evinced acceptable coupling loss. For most of the cables side-by-side interstrand contact resistances have been calculated. An `effective interstrand contact resistance', R<sub>⊥,eff</sub>, has been defined, and an expression devised to enable its value in different-size cables to be converted to that of a `standard reference cable', R_{⊥,eff.,ref.}, for the purpose of intercomparison.     

ITER Side Correction Coil Quench model and analysis

Previous thermohydraulic studies performed for the ITER TF, CS and PF magnet systems have brought some important information on the detection and consequences of a quench as a function of the initial conditions (deposited energy, heated length). Even if the temperature margin of the Correction Coils is high, their behavior during a quench should also be studied since a quench is likely to be triggered by potential anomalies in joints, ground fault on the instrumentation wires, etc. A model has been developed with the SuperMagnet Code (Bagnasco et al., 2010) for a Side Correction Coil (SCC2) with four pancakes cooled in parallel, each of them represented by a Thea module (with the proper Cable In Conduit Conductor characteristics). All the other coils of the PF cooling loop are hydraulically connected in parallel (top/bottom correction coils and six Poloidal Field Coils) are modeled by Flower modules with equivalent hydraulics properties. The model and the analysis results are presented for five quench initiation cases with/without fast discharge: two quenches initiated by a heat input to the innermost turn of one pancake (case 1 and case 2) and two other quenches initiated at the innermost turns of four pancakes (case 3 and case 4). In the 5th case, the quench is initiated at the middle turn of one pancake. The impact on the cooling circuit, e.g. the exceedance of the opening pressure of the quench relief valves, is detailed in case of an undetected quench (i.e. no discharge of the magnet). Particular attention is also paid to a possible secondary quench detection system based on measured thermohydraulic signals (pressure, temperature and/or helium mass flow rate). The maximum cable temperature achieved in case of a fast current discharge (primary detection by voltage) is compared to the design hot spot criterion of 150 K, which includes the contribution of helium and jacket.     

Microwave enhanced stability of resistive states in superconducting channels

The results on electromagnetic field effect upon the currents at which phase-slip centers appear in a superconducting channel are given. It is shown that in the presence of external microwave field, the resistive states of superconducting channels become more stable to direct current than in zero field and, consequently, stabilization of the resistive states of the channel due to the Josephson radiation from the phase-slip centers is possible.     

Stability analysis of the LHC cables

The commissioning and operation of the LHC accelerator calls for better understanding of the stability margin of its superconducting magnets with respect to the perturbation spectrum expected during operation, such as wire motion, AC loss during ramps and in particular beam induced heat depositions. In this paper, the stability analysis of the cables for the LHC dipole for transient heat deposition is reported. The sensitivity of the stability margin to the parameters of the model is investigated and discussed. In particular, the helium content in the cable is shown to have a large impact on stability. In fact, we find that the most important parameter is the heat transfer into helium II and helium I. Furthermore, we quantify the influence of the interstrand thermal and electrical coupling on the cable stability in the several examples reported.     

Chronopotentiometric analysis of highly resistive media

Reciprocal derivative chronopotentiometry is shown to be well suited for performing electrochemistry in highly resistive solutions in connection to conventional-sized electrodes. The fundamentally different operational principles of reciprocal derivative chronopotentiometry (compared to controlled-potential voltammetry) reduces its susceptibility to solution resistance effects. The influences of the electrolyte concentration and constant current upon the reciprocal derivative chronopotentiometric peak area and potential are examined in different solvents. Well-defined, analytically useful peaks are observed in highly resistive media (with low electrolyte/analyte ratios). Narrower peaks, shifted to higher potential values, are observed upon increasing the solution resistance. Yet, the analytical signal (square root of the peak area) is nearly independent of the ohmic drop. The experimental results are compared with the theoretical predictions. Considerable ohmic drop distortions are observed in analogous voltammetric experiments. The defined chronopotentiometric peaks permit convenient quantitation of micromolar analyte concentrations in highly resistive media. Such observations open the door to new electrochemical applications of conventional electrodes that were previously restricted to ultramicroelectrodes.     

The propagation of the resistive region in high current density superconducting coils

A method is given describing the propagation phenomenon of the resistive region within the winding of superconducting coils wound from semi-stabilized filamentary conductors. The method permits the approximate calculation of the velocities of propagation of the normal conducting front in superconducting coils of high current density. The calculation is carried out assuming that the parameters of the conductor materials, the short sample data, and the heat transfer coefficient from the conductor into the ambient medium are given. The propagation velocities of the normal front have been measured in insulated wires freely immersed in liquid helium, in test samples using conventional interleaving material, and in a compact multilayer coil wound from the same wire. The calculated results are compared with experimental data.     

Quantitative analysis of endohedral metallofullerenes by Rutherford backscattering of protons

Samples containing endohedral metallofullerenes of gadolinium (Gd@C₈₂) and dysprosium (Dy@C₈₂) are investigated by the Rutherford backscattering of protons. It is shown that the concentration of endohedral metallofullerenes can be determined to within a few percent. The measured concentration of endohedral metallofullerenes Gd@C₈₂ and Dy@C₈₂ in samples prepared by selective multistep extraction is ∼60%. Pis’ma Zh. Tekh. Fiz. 25, 24–30 (May 26, 1999)     

Cr-Si-Ni电阻薄膜在模拟环境中的电学稳定性及腐蚀行为

研究了磁控溅射法制备的Cr-Si-Ni电阻薄膜在不同模拟环境介质溶液中的电学稳定性及腐蚀行为.结果表明,500℃热处理后纳米晶结构的Cr-Si-Ni电阻薄膜在25℃的模拟海洋、工业、酸性及碱性环境介质溶液中浸泡240h后,薄膜试样的相对电阻变化值(ΔR/R)分别为0.27%、0.08%、0.96%、3.31%.说明薄膜在上述4种环境中电学稳定性和耐腐蚀性能从高到低依次为:工业环境、海洋环境、酸性环境、碱性环境.薄膜在4种溶液中都能发生自钝化现象而在膜层表面形成SiO2保护层,形成的钝化膜在模拟的工业环境中最稳定.     

Fatigue crack propagation characteristics of high‐tensile steel wires for bridge cables

The viability of single edge cracked sheet test method for rapidly determining the crack propagation characteristics of steel wires was investigated. First, fatigue tests under 3 different stress ratios were conducted on the sheet specimens which were manufactured from a kind of widely used cable wires. The test data were analysed, and the crack growth rates of sheet specimens were constructed by Walker model. Then, a series of fatigue tests were performed on notched round‐bar specimens to verify the predictability of Walker model parameters. Moreover, the experimental results obtained in different studies on crack propagation characteristics of steel wires were discussed. The results show that the crack propagation characteristics of sheet specimens behave a certain dependence on depth. The sheet crack growth laws can be well used to predict the fatigue life of notched bar specimens when the mechanical heterogeneity is considered. For bridge cable steels, the rational values for the exponent parameter of Paris law, m, should be close to 3.     

Quantitative Rutherford backscattering spectrometry in-depth composition analysis of sputtered TaSi2 layers

Rutherford backscattering spectrometry was used to investigate sputtered films of tantalum silicide deposited with different ratios of tantalum and silicon. Conventional furnace annealing and halogen lamp annealing were applied. The indepth composition of the films depends on whether they are prepared on silicon or on silicon oxide.     

Improving core bond strength and dimensional stability of particleboard using polymer powder in core layer

Low density polyethylene powder (LDPE) was used as polymer binder in the core layer of three layer particleboard. In the first phase, six levels of the LDPE powder (5–30 wt.%) based on the composition by weight, were mixed with the core particles with 8 wt.% urea–formaldehyde (UF) resin. In the second phase, the LDPE powder content was kept constant at 10 wt.% in all treatments and the UF resin content applied to the core layer was decreased gradually from 8 to 4 wt.%. Thickness swelling and water absorption of the particleboards significantly decreased with increasing the LDPE content in the core layer. Similarly, incorporation of the LDPE powder into the core layer of the particleboard greatly improved internal bond strength. The flexural properties of the particleboards, the modulus of rupture (MOR) and modulus of elasticity (MOE), were positively affected by increasing LDPE content up to 10 wt.% but the further increment of the LDPE decreased the MOR and MOE. The UF resin content can be reduced in the core layer of the particleboard as a function of increasing the LDPE powder.     

超大跨径碳纤维主缆悬索桥施工阶段颤振稳定性研究

为明确超大跨径碳纤维主缆悬索桥施工过程中的颤振稳定性,采用状态空间法,对主跨3500m碳纤维主缆悬索桥10个施工阶段的颤振稳定性进行了分析,分别讨论了加劲梁刚度折减、阻尼比等参数对施工阶段颤振稳定性的影响,并研究了交叉索对改善悬索桥施工阶段颤振稳定性的作用,研究表明,同时布置竖向交叉索和水平交叉索可大幅提高超大跨径悬索桥施工阶段的颤振稳定性。