Heat Transfer between the Superconducting Cables of the LHC Accelerator Magnets and the Superfluid Helium Bath

In this thesis work we investigate the heat transfer through the electrical insulation of superconducting cables cooled by super fluid helium. The cable insulation constitutes the most severe barrier for heat extraction from the superconducting magnets of the CERN Large Hadron Collider (LHC). We performed an experimental analysis, a theoretical modeling and a fundamental research to characterize the present LHC insulation and to develop new ideas of thermally enhanced insulations. The outcome of these studies allowed to determine the thermal stability of the magnets for the LHC and its future upgrades. An innovative measurement technique was developed to experimentally analyze the heat transfer between the cables and the super fluid helium bath. It allowed to describe the LHC coil behavior using the real cable structure, an appropriate thermometry and controlling the applied pressure. We developed a new thermally enhanced insulation scheme based on an increased porosity to super uid helium. It aims at withstanding large heat loads, as needed for the High Luminosity LHC upgrade (HL-LHC). Experimental measurements of the new insulation showed a major improvement of heat extraction compared to the present state-of-the-art used in the LHC. We developed a theoretical heat transfer model quantitatively explaining the experimental results of the LHC and HL-LHC insulations. We identified the heat extraction mechanisms, mainly occurring through super fluid helium micro-channels. The average micro-channels dimensions were estimated to vary between few and dozens of µm, depending on the insulation scheme. In the model we considered the known laws describing the dynamic regimes of super fluid helium. However such laws were never demonstrated to be valid in the narrow channels typical of the cable insulation. We developed a new experimental device to investigate heat transport through microchannels. Micro-fabrication techniques were used to etch the channels down to a depth of 16 µm. We measured the classical laminar and turbulent regimes, thus demonstrating the validity of such heat transport laws independently from the channel geometrical shape and size down to these dimensions. To conclude, we used the obtained experimental and theoretical heat transfer results to determine the LHC and HL-LHC magnets stability. We estimated their quench margin and compared it to the beam induced heat deposit. The resulting difference allows a safe operation of the magnets

Slip-stick mechanism in training the superconducting magnets in the Large Hadron Collider

Superconducting magnets can exhibit training quenches during successive powering to reaching nominal performance. The slip-stick motion of the conductors is considered to be one of the mechanisms of training. In this paper we present a simple quantitative model where the training is described as a discrete dynamical system matching the equilibrium between the energy margin of the superconducting cable and the frictional energy released during the conductor motion. The model can be solved explicitly in the linearized case, showing that the short sample limit is reached via a power law. Training phenomena have a large random component. The large set of data of the LHC magnet tests is postprocessed according to previously defined methods to extract an average training curve for dipoles and quadrupoles. These curves show the asymptotic power law predicted by the model. The curves are then fit through the model, which has two free parameters. The model shows a good agreement over a large range, but fails to describe the very initial part of the training

Protection estimates for the 13 kA bus bars interconnections at 3.5 - 4.5 TeV

This memorandum provides alternate estimates of the critical additional resistance Radd of the 13 kA superconducting bus bars interconnections (IC), both for the LHC main bending (MB) dipole and main quadrupole (MQ) magnets. The calculations are performed using the 1-D thermo-electrical model described in [1], based on the definition of transverse local heat transfer coefficient towards the cooling helium bath established from the analysis of short sample tests performed in 2009 and 2010. Details on the model and its validation are not discussed here. The most pessimistic (adiabatic), most optimistic (full cooling) and most likely (partial cooling) critical additional resistances are provided, depending on the bus-bar and cable RRR, dump time constant, and space distribution of the defect, for beam energy between 3.5 and 4.5 TeV

A 120 mm Bore Quadrupole for the Phase I LHC Upgrade

The phase I LHC upgrade foresees the installation of a new final focusing for the high luminosity experiences in order to be able to focus the beams in the interaction points to ß* 0.25 cm. Key element of this upgrade is a large bore (120 mm) superconducting quadrupole. This article proposes a magnet design that will make use of the LHC main dipole superconducting cable. Due to the schedule constraints and to the budget restrictions, it is mandatory to integrate in the design the maximum number of features successfully used during the LHC construction. This paper presents this design option and the rationales behind the several technical choices

Stability analysis of the Interconnection of the LHC Main Superconducting Bus Bars

The operation of the Large Hadron Collider calls for a thorough analysis of the thermo-electric behavior of the 13 kA superconducting bus-bars connecting its dipole and quadrupole main magnets. This presentation reports a synthesis of the work performed jointly by researchers and students at CERN and at the University of Bologna as a contribution to the understanding of the LHC incident occurred on September 19th 2008. This work is complementary to the analyses carried out at CERN by the MPE group. The aim of the work is to analyze the stability of the interconnections as far as the quality of manufacturing, operating conditions and protection system parameters are concerned. A first part of the work is devoted to the development of a numerical model suitable for the analysis of the faulty interconnections. The main type of defect analyzed is the lack of solder among the superconducting cable and the copper stabilizer components at the interface between bus bar and splice. The evaluation of the critical defect length limiting the maximum safe current for powering the magnets without risk of thermal runaway is provided, as a function of the RRR of cable and stabilizer, decay time constant of the LHC circuit, spatial distribution of the defect and cooling conditions. A second part of the work is related to the modeling of the heat transfer mechanism between the main superconducting bus bar and the surrounding helium bath. This study is aimed to analyze a set of experimental measurements on the heat transfer coefficient of the main bending dipole bus bars performed at CERN. The final part of the work consists in a preliminary analysis of the heat transfer mechanisms involved in the stability experiments of defective interconnections performed in the FRESCA facility

Steady-State heat transfer through micro-channels in pressurized He II

The operation of the Large Hadron Collider superconducting magnets for current and high luminosity future applications relies on the cooling provided by helium-permeable cable insulations. These insulations take advantage of a He II micro-channels network constituting an extremely efficient path for heat extraction. In order to provide a fundamental understanding of the underlying thermal mechanisms, an experimental setup was built to investigate heat transport through single He II channels typical of the superconducting cable insulation network, where deviation from the macro-scale theory can appear. Micro-fabrication techniques were exploited to etch the channels down to a depth of ~ 16 μm. The heat transport properties were measured in static pressurized He II and analyzed in terms of the laminar and turbulent He II laws, as well as in terms of the critical heat flux between the two regions

Analysis of Defective Interconnections of the 13 kA LHC Superconducting Bus Bars

The interconnections between Large Hadron Collider (LHC) main dipole and quadrupole magnets are made of soldered joints of two superconducting cables stabilized by a copper bus bar. The 2008 incident revealed the possible presence of defects in the interconnections of the 13 kA circuits that could lead to unprotected resistive transitions. Since then thorough experimental and numerical investigations were undertaken to determine the safe operating conditions for the LHC. This paper reports the analysis of experimental tests reproducing defective interconnections between main quadrupole magnets. A thermo-electromagnetic model was developed taking into account the complicated sample geometry. Close attention was paid to the physical description of the heat transfer towards helium, one of the main unknown parameters. The simulation results are reported in comparison with the measurements in case of static He I cooling bath. The outcome of this study constitutes a useful input to improve the stability assessment of the 13 kA bus bars interconnections

Stability analysis of the LHC cables for transient heat depositions

The commissioning and the exploitation of the LHC require a good knowledge of the stability margins of the superconducting magnets with respect to beam induced heat depositions. Previous studies showed that simple numerical models are suitable to carry out stability calculations of multi-strands cables, and highlighted the relevance of the heat transfer model with the surrounding helium. In this paper we present a systematic scan of the stability margin of all types of LHC cables working at 1.9 K against transient heat depositions. We specifically discuss the dependence of the stability margin on the parameters of the model, which provide an estimate of the uncertainty of the values quoted. The stability margin calculations have been performed using a zero-dimensional (0-D) numerical model, and a cooling model taking into account the relevant helium phases which may appear during a stability experiment: it includes Kapitza thermal resistance in superfluid He, boundary layer formation and heat transfer in He I, and considers the transition from nucleating boiling to film boiling during He gas formation

Research and Application on Clustering Algorithms for Genetic Data

摘要 作为数据分析中的两个重要工具，聚类分析（Clustering）和形式概念分析（FCA）在数学、计算机科学和生物学等各个科学领域得到广泛的应用。在生物学研究领域，基因芯片因其研究对象的复杂，产生了大量的基因表达数据；人们希望能够了解这些数据里面包含的重要信息，因此如何高效地使用这两个数据分析工具，成了目前研究的热点。 目前虽然提出了一些经典的聚类分析和建立概念格的算法，包括层次聚类分析、K-means算法和SOMs等。但是这些算法或多或少存在着时间复杂度大、对初始聚类中心敏感和聚类结果不稳定等缺点，且层次聚类和K-means算法需要预输入合适的类数值，这对未知数据集结构的研究人员是难以...Abstract As two of the most important tools of the data analysis, Clustering and Formal Concept Analysis (FCA) have been widely used in the area of Mathematics, Computer Science, Biology and so on. For the biological research area, gene chips have produced a considerable amount of gene expression data. Additionally, these data carry much important information. Therefore, the problems of how to us...学位：理学硕士院系专业：信息科学与技术学院智能科学与技术系_人工智能基础学号：3152008115332