Effect of axial conduction and metal-helium heat transfer on the local stability of superconducting composite media

The growth or collapse of a local normal zone in a superconducting winding structure saturated with single phase liquid helium (composite superconductor) is studied analytically. The history of a given temperature disturbance is derived from the solution to the transient heat conduction equation in a one-dimensional infinite solid with temperature dependent rate of internal heat generation, communicating laterally with a channel filled with stagnant helium. The combined diffusion by axial heat conduction and lateral heat transfer to the helium channel and its effect on the collapse or growth behaviour of a local disturbance is presented analytically. The paper develops a theoretical criterion for local stability (recovery) expressed in terms of dimensionless groups accounting for heat generation in the normal zone, metal axial conduction cooling, lateral cooling provided by the helium channel and, most importantly, the amount and spatial extent of the sudden release of energy responsible for the local disturbance.     

Transient heat transfer model for normal zone propagation. Part 1 — theory of a bare helium-cooled superconductor

The paper presents a physical model, involving no adjustable parameters of transient heat transfer for normal zone propagation in a composite helium-cooled superconductor. Evaluations are given showing that the main contribution to transient heat flux is made by transverse heat conduction in the coolant. When the zone front passes through a fixed point, the temperature at that point increases drastically, a great temperature gradient appears in coolant which results in transient cooling of the superconductor. The zone propagation equation becomes an integro-differential with a convolution integral. The transient heat transfer intensity is characterized by the introduced dimensionless parameter ?.The problem has been solved analytically for the model with constant coefficients and jump-wise heat release. Formulae have been obtained for the propagation and recovery velocities describing the effect of transient heat transfer (via parameter ?).     

Normal phase propagation along a current carrying superconducting wire and its heat transfer to a cooling He II bath

A theoretical and experimental study of the longitudinal propagation velocity of a normal phase along a superconducting cylindrical wire suspended in a superfluid helium bath is presented. The theoretical model supposes a moving nonplanar separating boundary between the normal and superconducting phases and takes into account the latent heat absorbed during the destruction of the superconducting state. The comparison of the measured and calculated normal zone propagating velocities versus the circulating electrical currents shows an excellent agreement for all the bath temperatures considered. A boundary thermal conductance across the wire wall and superfluid helium bath interface is inferred by adjusting the calculated velocities with the experimental data. The deduced boundary thermal conductance is similar to the Kapitza conductance in the sense that both are proportional to the superfluid helium bath temperature raised to a constant power. Furthermore the deduced boundary conductance seems unaffected by the dynamical aspect of the longitudinal destruction process of the superconducting state and by the heat flux range across the solid and He II separating boundary covered by the normal zone propagation velocity versus the circulating electrical current plots. To the authors knowledge this is the first study of heat transfer using the data obtained from longitudinal normal zone propagation experiments.     

Stability of composite superconductors with high resistive barriers

Current distribution in a composite superconductor (CS) with high resistive barriers between the superconducting filaments and a stabilizing matrix in the presence of a normal zone is calculated. Normal zone propagation current is studied analytically, it appears to be strongly dependent on the normal zone length. It is concluded that normal zones exist which are stable with respect to current variations. A classification of CS evolution based on transport current and normal zone length is presented.     

Normal zone initiation in composite superconductors

The initiation of superconducting state instability in composite superconductors due to heat disturbances is investigated. The instability development results as a rule in the transition of the superconductor into the resistive state and normal zone propagation along the conductor. It is shown that in the case of high current density, thick conductors and poor cooling the heat power necessary to initiate the instability may be small compared to the heat power necessary to warm the superconductor to the temperature of the resistive transition.     

Propagation of normal zone in superconducting tapes due to heating in near-electrode area

Local disturbances of thermal stability in the superconducting materials may initiate the formation of the normal zones. One of the reasons for these disturbances is thermal processes in metal leads connected to the superconductor. Here, superconducting tapes with metal leads are analyzed thermally and from the point of view of current distribution. The results show that the Joule's heat, generated in the vicinity of the metal-superconductor junction may initiate propagation of a normal zone in the superconductor and may cause its thermal runaway.     

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.     

Normal zone propagation along superconducting films deposited on wide substrates

The propagation of a normal zone in a long superconducting film on a dielectric or conducting substrate is studied analytically. The obtained expressions for the normal zone propagation velocity allow to analyze the effect of the thermal resistance between the film and substrate and the width of the substrate. The results are expanded into the cases of the normal zone propagation in a meander and in parallel films.     

Heat conduction and thermal stabilization in YBCO tape

Yttrium barium copper oxide (YBCO) coated conductors are widely used in the conduction-cooled superconducting magnets with rapid development in refrigeration technologies at present. ‘Quench’ is a state that refers to the irreversible and uncontrolled superconductor to resistive transitions in the superconductor. The propagation of ‘quench’ or ‘normal zone’ has different characteristics in these high temperature superconductors (HTS) compared to low temperature superconductors. The superconductor to normal index, known as ‘n’ is much flatter in HTS. The hot spot emerging in local region due to quench and non-uniform critical current may cause permanent damage to whole HTS tape and hence the magnet winding pack. Thus it is necessary to determine the temperature profile along the length of HTS tape under a given energy (joule heating) such that propagation of the hot spot developed locally can be prevented early. In this study, a one dimensional, time dependent heat diffusion equation with appropriate boundary conditions are used to describe the consequences of the normal zone propagation resulting in the temperature diffusion in a HTS tape. The results demonstrate the necessity of adequate cooling of the edges of the flat HTS tapes to prevent irreversible normal zone transitions.     

The rate of transverse propagation of normal zone in aluminum-stabilized superconducting windings

Transverse propagation of the normal zone in superconducting windings of a conductor with a copper-aluminum stabilizing matrix was measured in compounded and uncompounded model coils. The special coil design enables one to simulate the one-dimensional propagation of normal zone in the winding in the radial direction.     

Propagation velocity for a force cooled superconductor

We studied numerically the propagation velocity in a force cooled superconducting cable. The numerical model comprised a one dimensional model for the copper/superconducting matrix and a one dimensional model for the helium flow. The propagation velocity appears to keep rising with time rather than becoming constant as assumed in many theories. This is mainly caused by the induced pressure waves that cause a temperature rise of the coolant away from the normal conducting zone. Mass flow rate, initial disturbance and conductor length are less important parameters. Operation pressure and wetted perimeter have an important influence on propagation velocity.     

40-T混合磁体外超导线圈迫流氦流动摩擦系数分析

40-T混合磁体外超导磁体使用4.5 K超临界氦进行迫流冷却。迫流氦在管内电缆导体(CICC)内的流动过程受到摩擦阻力的影响会造成一定的压降和热量产生,同时由外界带来的热量也会由迫流氦带走来让磁体保持在超导温区。使用了超导磁体实际运行过程中的实验数据计算不同导体结构下雷诺数与摩擦系数的变化关系,利用Katheder经验公式对实验的摩擦系数进行了重新拟合,给出了适用于该导体摩擦系数的经验公式。     

Normal zone propagation velocity in a superconducting wire with a copper-aluminum stabilizing matrix

Results of measurements of the normal zone propagation velocity in superconducting wires with a copper-aluminum stabilizing matrix are presented. The measurements were made using test coils which reproduce the structure of real, compound and noncompound, magnets. Onedimensional propagation of the normal zone in the winding was simulated by means of a special coil design. Pis’ma Zh. Tekh. Fiz. 23, 52–57 (July 12, 1997)     

导热相复合陶瓷微波烧结传热模式数值分析

根据微波加热的特点,采用二维稳态导热数值分析法,建立了导热相复合陶瓷微波烧结的传热模式. 研究了导热相的浓度、导热相弥散分布状况、基质类型以及保温方式对复合陶瓷内部二维稳态温度场分布的影响,并设计了导热相SiC晶须复合TZP陶瓷的微波烧结致密化实验,对建立的复合陶瓷的微波烧结传热模式进行了验证. 结果表明：导热相复合陶瓷设计时宜选取具有高导热系数的基体,保持导热相有较高的浓度,使导热相均匀分布于基体中,且微波烧结传热宜采用合适的保温设施.     

Theory of normal-zone propagation along a superconducting wire with allowance for thermal-relaxation processes

For high velocity of a longitudinal propagation of a normal zone along a superconducting wire, one should take into account heat-flux relaxation processes. In such cases these waves are described by a hyperbolic heat-transfer equation, which involves not only the heat-source function but also its derivative. The relaxation effects lead to a limitation of possible values of the normal-zone velocities and to the nonuniqueness of wave solutions. Moreover, the relationships that determine the temperature field in a wire and the propagation speed of the normal zone are obtained. The transient boundary condition between the wire and substrate (e.g., helium bath) is deduced from a heat-flux relaxation theory.     

Basic models for thermal stability and zone propagation calculations for a.c. superconductors

A.c. superconductor stability within the framework of four basic models is analysed, with each model illustrating specific features in a.c. superconductor behaviour. Expressions are obtained for the minimum zone existence current, minimum propagation current, the limiting current at high frequencies (large Ω parameter), and also the parameter α corresponding to a fully stabilized a.c. superconductor. A.c. superconductors are shown to have a larger stability factor than d.c. ones. The propagation of normal and resistive zones in a.c. superconductors is studied numerically within a wide frequency range. The current dependences of the zone propagation velocity for each model are obtained. It is shown that taking into account a variable magnetic field gives rise to a system in which the conductor within the cycle becomes fully superconducting.     

Thermal Behavior of Perfect and Imperfect Contact Composite Slabs Under the Effect of the Hyperbolic Heat Conduction Model

This work studies the heat transfer mechanisms during rapid heating of two-layer composite thin slabs from a macroscopic point of view using the hyperbolic heat conduction model. The composite slabs consist of two thin metal layers which may be in perfect or imperfect thermal contact. The effects of parameters such as the two films' thickness ratio, thermal conductivity ratio, heat capacity ratio, thermal relaxation time, and interfacial heat transfer coefficient on the thermal behavior of the composite slabs are investigated.     

Electron scattering and the lattice thermal conductivity of superconducting transition metal alloys

The mechanism of heat energy transport by phonon carriers which are primarily scattered by conduction electrons is re-examined for concentrated alloys in the normal and superconducting phases. The large increase in the normal state lattice thermal conductivity observed experimentally for concentrated niobium alloys, compared with the pure metal, is explained qualitatively as due to the diminished importance of scattering by d-electrons, compared with s-electrons, when the mean free path for the former becomes less than the typical phonon wavelength. Evidence is presented for the existence of a gap-less type of superconductivity in the concentrated alloys for both s and d-electrons.     

The quenching of large superconducting coils

The growth of a normally conducting region in a superconducting coil is related to the propagation of such a region along a superconducting wire. The theory is compared with observations on two large coils which incorporated close coupled secondary windings, so that the voltage across the normal region could be observed directly. Reasonable agreement is found.