Superconducting Cylinder Research Articles

Crack problem in a functionally graded superconductor cylinder under pulsed field magnetization

In the paper, the fracture of functionally graded superconductor under pulsed magnetic field is numerically analyzed, and the effect of electromagnetic stress and thermal stress on crack problem under pulsed magnetic field is studied. A FEM model based on H formula and heat transfer equation is proposed for the electromagnetic thermal behavior of inhomogeneous superconductors with central cracks. The influence of the gradient parameter η of critical current density on the stress intensity factor was investigated. The numerical results show that the gradient parameter η has a great influence on the change of stress intensity factor caused by electromagnetic force and thermal strain with time, which makes the crack easy to expand. In addition, the results show that the electromagnetic stress decreases gradually with the increase of crack length, and the thermal stress has a significant effect on the stress intensity factor.

Screening properties of multiply connected ferromagnet–superconductor hybrid structures

Superconducting phase transition temperature T c of a ferromagnet/superconductor (SF) hybrid structure consisting of a hollow superconducting (S) cylinder (shell) with the central part (core) filled with a ferromagnetic (F) metal has been analyzed on the basis of linearized Usadel equations. It has been shown that the proximity effect between the S and F metals, as well as the exchange interaction, may induce an inhomogeneous superconducting state with Δ ~ exp(iLθ + ipz), which is characterized by nonzero circulation of phase L and wavenumber p describing the Larkin–Ovchinnikov–Fulde–Ferrell (LOFF) instability along the cylinder axis. The transitions between the states with different values of L and p, which are accompanied by a nonmonotonic dependence of superconducting transition temperature T c and effective magnetic field penetration depth Λ into the SF structure on the characteristic size of the ferromagnetic region, have been investigated.

An innovative experiment on superconductivity, based on video analysis and non-expensive data acquisition

In this paper we present a new experiment on superconductivity, designed for university undergraduate students, based on the high-speed video analysis of a magnet falling through a ceramic superconducting cylinder (Tc = 110 K). The use of an Atwood’s machine allows us to vary the magnet’s speed and acceleration during its interaction with the superconductor. In this way, we highlight the existence of two interaction regimes: for low crossing energy, the magnet is levitated by the superconductor after a transient oscillatory damping; for higher crossing energy, the magnet passes through the superconducting cylinder. The use of a commercial-grade high speed imaging system, together with video analysis performed using the Tracker software, allows us to attain a good precision in space and time measurements. Four sensing coils, mounted inside and outside the superconducting cylinder, allow us to study the magnetic flux variations in connection with the magnet’s passage through the superconductor, permitting us to shed light on a didactically relevant topic as the behaviour of magnetic field lines in the presence of a superconductor. The critical discussion of experimental data allows undergraduate university students to grasp useful insights on the basic phenomenology of superconductivity as well as on relevant conceptual topics such as the difference between the Meissner effect and the Faraday-like ‘perfect’ induction.

Semiconductor nanotube plasma

The theory of dispersion of surface plasma waves in semiconductor nanotubes is presented. The effect of screening the Coulomb field of a static point charge by a magnetized electron gas of a nanotube is investigated. The main properties of the semiconductor nanotube plasma, 3D plasma, and planar 2D plasma are compared. The dependences of the critical temperature and thermodynamic properties of a superconducting quantum cylinder on the characteristics of the system are studied.

Thermodynamic properties of a superconducting quantum cylinder and their fluctuations

A numerical and analytical investigation of thermodynamic properties of a magnetized superconducting quantum cylinder has been carried out. The dependence of the difference in the magnetizations of the superconducting and normal phases on the parameters of the nanotube, temperature, and magnetic field has been analyzed. The jump in the heat capacity of the superconducting and normal states at the critical temperature has been calculated. The fluctuation contribution to the thermodynamic properties of the nanotube at a temperature above the transition point has been studied.

Thermodynamic Properties of Superconducting Magnetized Nanotubes

A numerical study of the thermodynamic properties of a superconducting quantum cylinder in a longitudinal magnetic field is carried out. Closed-form expressions for the critical temperature, the free energy, the heat capacity jump, and the magnetization difference between the superconducting and normal phases as functions of the nanotube parameters are obtained in limit cases.

Stress and magnetostriction in an infinite hollow superconducting cylinder with a filling in its central hole

In this paper, the stress and magnetostriction induced by flux pinning in an infinite hollow cylinder of type-II superconductor with a non-superconductive filling in its central hole are analytically investigated. Based on the exponent model of critical state of superconductor, the magnetic and current distributions in the hollow cylinder superconductor are obtained firstly. The stress and magnetostriction of the composite superconductive cylinder are then formulated and the magnetoelastic behaviors are characterized analytically. The results show that the hoop stress concentration near the central hole is dominant due to the tension Lorentz force and it is certainly suppressed by filling a non-superconductive material in the hole. Without change of the magnetization characteristic of the superconductor, the filling material provides effective way to remedy the stress state at the verge of the hollow in the superconductive cylinder by adjusting its Young modulus. The magnetostriction of the composite cylinder under the cycled magnetic field is further presented. Effect of the applied maximum field, complete penetration field parameter and filling material parameter on the profile of the cycled magnetostriction for the composite superconducting cylinder is discussed in detail.

Magnetic field, temperature and mechanical crack performance of a GdBCO magnetic lens

Magnetic field concentration by using the diamagnetism of a superconductor is a novel technique that has been experimentally demonstrated in magnetic lenses. A magnetic lens consists of a hollow superconductor cylinder with a tapered inner diameter within which the magnetic flux is concentrated by diamagnetism. Magnetic lenses are very promising for use in compact high magnetic field systems. However, magnetic lenses with large inner diameters are required to facilitate sample access during use. In this study, an optimized GdBaCuO magnetic lens with large inner and outer diameters was designed and its performance was investigated in liquid nitrogen, liquid helium, and a cryocooler-cooled cryostat. A lens with an inner diameter of 12 mm was constructed by stacking three specially machined GdBaCuO bulk pieces. This magnetic lens cracked due to the large flux jump that occurred when the concentrated field of the magnetic lens exceeded 10 T at 4.2 K. The cracked lens was subsequently impregnated with epoxy resin. A concentrated field of 12.42 T was realized when the background field was 8 T at 20 K and no flux jumps occurred. This result demonstrates that this GdBCO magnetic lens is promising for use in compact superconducting magnet systems.

Superconductivity of a quantum cylinder

The thermodynamic potential of a superconducting quantum cylinder is calculated. The dependence of the critical temperature and heat capacity of the superconducting system on the surface electron density and nanotube radius is studied. It is shown that the critical temperature oscillates with variations in a parameter equal to the ratio of the Fermi energy to the dimensional confinement energy.

Alignment effect between a magnet over a superconductor cylinder in the Meissner state

Although forces between magnets and superconductors have been profusely studied in many previous papers, little attention has been paid to calculations or measurements of the torque exerted. In this paper, we focus on the equilibrium orientation of a magnet when it is levitating over a superconductor and present measurements for different positions and configurations. We compare these measurements with values predicted by our proposed local model. Agreement between predicted values and experimental values demonstrates that the model is useful for calculating torques in addition to forces. The angle of equilibrium varies along the path over the superconducting cylinder. Therefore, shape and size determine the angle of equilibrium of the magnet.

Three-Dimensional Pareto-Optimal Design of Inductive Superconducting Fault Current Limiters

The inductive-type superconducting fault current limiters (LSFCLs) mainly consist of a primary copper coil, a secondary complete or partial superconductor cylinder, and a closed or open magnetic iron core. Satisfactory performance of such device significantly depends on optimal selection of its employed materials and construction dimensions, as well as its electrical, thermal, and magnetic parameters. Therefore, it is very important to identify a comprehensive model describing the LSFCL behavior in a power system prior to its fabrication. When a fault occurs, the dynamic model should essentially characterize the overall phenomena to compare the simulation results by varying LSFCL parameters to maximize the merits of a fault current limiter while minimizing its drawbacks during the normal state. The principle object of this paper is to achieve a feasible and full penetrative approach in 3-D alignments, i.e., a Pareto-optimal design of LSFCLs by means of multicriteria decision-making techniques after defining the LSFCL model in a power system CAD/electromagnetic transients including dc environment.

Thermodynamical properties of a superconducting quantum cylinder

The thermodynamical potential of a superconducting quantum cylinder is calculated. The dependence of the critical temperature and the heat capacity of a superconducting system of the surface concentration of electrons and on the radius of the nanotube is studied.

Monochromatic infrared wave propagation in 2D superconductor-dielectric photonic crystal

Anomalous infrared monochromatic transmission through superconducting cylinders embedded in a dielectric and dielectric cylinders embedded in a superconductor is found. The transmitted frequency corresponds to the localized photonic mode in the forbidden photonic band. This localized mode appears when the symmetry of the photonic crystal is broken by a defect. This defect can be formed when supercon-ducting cylinder is removed from the node of the ideal two-dimensional lattice of superconducting cylinders in dielectric medium or one dielectric cylinder placed out of the node of the lattice of the dielectric cylinders in superconducting medium. The corresponding frequency was calculated for the YBa2Cu3O7 − δ supercon-ducting cylinders in vacuum.

Enhanced vortex heat conductance in mesoscopic superconductors

Electronic heat transport along the flux lines in a long ballistic mesoscopic superconductor cylinder with a radius of the order of several coherence lengths is investigated theoretically using both semiclassical approach and the full quantum-mechanical analysis of the Bogoliubov--de Gennes equations. The semiclassical approach is constructed analogously to the Landauer transport theory in mesoscopic conductors employing the idea that heat is carried by the quasiparticle modes propagating along the vortex core. We show that the vortex heat conductance in a mesoscopic sample is strongly enhanced as compared to its value for a bulk superconductor; it grows as the cylinder radius decreases. This unusual behavior results from a strongly increased number of single-particle transport modes due to giant mesoscopic oscillations of energy levels, which originate from the interplay between the Andreev reflection at the vortex core boundary and the normal reflection at the sample edge. We derive the exact quantum-mechanical expression for the heat conductance and solve the Bogoliubov--de Gennes equations numerically. The results of numerical computations confirm the qualitative Landauer-type picture and allow us to take into account the partial reflections of excitations. We analyze the effect of surface imperfections on the spectrum of core excitations. We show that the giant oscillations of core levels and thus the essential features of the heat transport characteristic to ideal mesoscopic samples hold for a broad class of surface imperfections as well.

From Flux Quantization to Superconducting Quantum Bits

One of the important predictions of the early phenomenological theories of superconductivity such as the London and Ginzburg–Landau (GL) theory is the quantization of magnetic flux in multiply connected superconductors, which is one of the first demonstrations of a quantum effect on a macroscopic scale. In this paper, which is devoted to Vitalij Lazarevich Ginzburg on the occasion of his 90th birthday, we analyze a superconducting cylinder acting as a flux box as well as a superconducting disk acting as a Cooper pair box in the framework of GL theory. We extend this analysis to leaky flux and Cooper pair boxes which are obtained by introducing weak links allowing for the entry and exit of flux quanta and Cooper pairs from the respective boxes at finite rates. Flux and Cooper pair slippage processes by coherent quantum tunneling result in effective two-level quantum systems forming the basis for flux and charge quantum bits presently considered for the solid-state implementation of quantum information processing. We show that the corresponding Hamiltonians describing the leaky flux and Cooper pair box can be transformed into each other by a canonical transformation.

Analysis of the magnetic distribution within a high-temperature superconductor magnetic shielding cylinder by use of the finite element method

Abstract It is important to know the distribution of the magnetic field within a magnetic shielding vessel for use in the design of an effective magnetic shielding vessel. From experiments and theoretical analysis, the distribution of the magnetic fields, the magnetic flux densities Bz and Br along the respective axial and radial directions z and r, within a high-temperature superconductor cylinder were found. Theoretical values for Bz and Br were determined by the use of the finite element method. The experimental values were found to agree well with the theoretical values. These results were found to be important criteria in the design of an effective magnetic shielding vessel.

Feasibility of Electric Power Transmission by DC Superconducting Cables

The electrical characteristics of dc superconducting cables of two power ratings were studied: 3 GW and 500 MW. Two designs were considered for each of the two power ratings. In the first design, the SUPPLY stream of the cryogen is surrounded by the high-voltage high-temperature superconductor cylinder. The RETURN stream of the cryogen is on the grounded side of the system. In the second design, both the SUPPLY and the RETURN streams of the cryogen are on the grounded side of the cable. Two electrical characteristics of these cables were studied: 1) fault currents and 2) current harmonics. It was concluded that neither the fault currents nor the current harmonics pose any problems in the operation of the dc superconducting cables.

Superconducting states of the cylinder with a single vortex in magnetic field according to the Ginzburg-Landau theory

Abstract Self-consistent solutions of the nonlinear Ginzburg-Landau (GL) equations are investigated numerically for a superconducting (SC) cylinder, placed in an axial magnetic field, with a single vortex on the axis (m=1). Two modes, which show the original state of the cylinder, SC or normal (s 0 andn 0), are studied. The field increase (FI) and the field decrease (FD) regimes are studied. The critical fields destroying the SC state withm=1 are found in both regimes. It is shown that in a cylinder of radiusR and GL-parameter ϰ, there exist a number of solutions depending only on the radial co-ordinater corresponding to different states such as M,e, d, p,i, n, $$\bar n$$ ,n *, and the state diagram on the plane of the variables (ϰ,R) is described. The critical fields corresponding to intrastate transitions and the onset of hysteresis are obtained. The critical fieldH 0(R) dividing the paramagnetic and diamagnetic states of the cylinder withm=1 is determined. The limiting fields of supercooling or superheating of the normal state at which the restoration of the SC state occurs are established. It is shown, that (in both casesm=1,0) there exist two critical parameters, $$\kappa _0 = {1 \mathord{\left/ {\vphantom {1 {\sqrt 2 = 0.707}}} \right. \kern-\nulldelimiterspace} {\sqrt 2 = 0.707}}$$ and $$\kappa _0 = 0.93$$ , which divide bulk SC into three groups (with $$\kappa< \kappa _0 ,\kappa _0 \leqslant \kappa \leqslant \kappa _c $$ and $$\kappa > \kappa _c $$ ), in accordance with the behavior in a magnetic field. The parameters $$\kappa _0 $$ and $$\kappa _c $$ mark the boundary for the existence of a supercooled normal $$\bar n$$ -state in FD-regime and a superheated SC M-state in FI-regime respectively. It is shown, that the value $$\kappa _* = 0.417$$ , which was claimed in a number of papers as related to type-I superconductors, is illusory.

Non-linear oscillations of the vortices in a hollow superconducting YBaCuO cylinder

A response of a hollow YBa 2Cu 3O 7− δ ceramic superconducting cylinder (at a mixed state) to the 100 kHz frequency alternating field was investigated. It was found that the response is non-linear and contains the odd harmonics of the excitation frequency. The amplitudes of the first, third and fifth harmonics are measured depending on an alternating field value h⩽1 Oe, applied to the cylinder external surface, and on a stationary magnetic field H⩽500 Oe driving the sample to the mixed state. For the results analysis a theoretical model of the vortices non-linear oscillations is proposed based on a non-linear vortex–vortex and vortex–surface interaction.

磁気遮へい型限流器用超電導円筒体における局部欠陥による熱暴走現象と欠陥進展メカニズム

Superconducting fault current limiters have been researched to protect electric power systems. We have developed a superconducting fault current limiter. As the active element, we choose Bi-2212 thick film for the superconductor cylinder. In order to attain practical use of the superconducting fault current limiter, larger scale superconducting cylinders must be developed. Processing energy increases as the size of the limiter is increased. If there are local defects in the superconducting cylinder and the processing energy is concentrated on them, there is a possibility that the cylinder will be damaged. We therefore investigated the thermal runaway propagation of the Bi-2212 thick film from a local heat point and how local defects affect the current-carrying capacity. The result is that the velocity of the thermal runaway propagation in the thick film from the local heat point is very slow. Thermal runaway doesn't propagate within a few milliseconds. If there are local defects such as cracks in the superconducting cylinder, the current will concentrate at the tip of the defect and the Joule temperature rises. The cracks then grow as the result of thermal stress. When a crack runs from end to end on the cylinder, superconductor on the cylinder melts due to arc discharge.