Cylindrical Superconductor Research Articles

A numerical approach to levitated superconductors and its application to a superconducting cylinder in a quadrupole field

Abstract Magnetically levitated superconductors in the Meissner state can be utilized as micro-mechanical oscillators with large mass, high quality factors and long coherence times. In previous works analytical solutions for the magnetic field distribution around a superconducting sphere in a quadrupole field have been found and used to derive the trap parameters, while non-spherical geometries have only been investigated in a few idealized cases. However, superconductors of almost arbitrary shape can be used as levitators in a magnetic trap and, as the trap’s properties depend strongly on the superconductor’s shape, allow for a wider parameter regime to be accessed. Finite element models are suitable to obtain the field distribution around arbitrarily shaped superconductors in arbitrary fields, but have not yet been used widely in the context of levitated superconductors. Here we present a simple numerical model for this purpose and use it to calculate the field distribution around cylindrical superconductors in a quadrupole field and to evaluate the trap parameters. We find that the cylindrical shape, compared to spherical levitators, allows for substantially higher trap frequencies and coupling strengths. This in turn reduces the demands on vibration isolation and significantly eases the requirements for feedback cooling to the ground state. The numerical model is provided in a file repository and can easily be adapted to various geometries and trap fields.

The effect of the non-uniform critical current density on the magnetoelastic behavior of bulk superconductors: Case of a long cylindrical superconductor

In this paper, the effect of non-uniform critical current density on bulk superconductors is studied, the case of a long cylindrical superconductor with transport current is chose to discussed. The critical current density is distributed non-uniformly along the radius of the cylinder. Based on the Bean critical state model, the distributions of trapped magnetic flux and shielding current in the cylinder are investigated. Combined with the plane strain approach, the analytical expressions of magnetic flux pinning force and stress are obtained. The magnetostriction of the cylinder is also discussed. Results show that the non-uniform critical current density changes the distribution law of the shielding current and trapped magnetic flux in the cylinder. The increase of non-uniform parameters n leads to an obvious increase in the flux pinning force. Thus, a larger extreme value of the pinning stress is obtained, a bigger structure deformation is produced inside the superconducting cylinder. All those conclusions will provide a helpful guide for engineering application.

High performance one-step grown half-moon shaped YBCO bulk superconductors

High-temperature superconducting (HTS) undulator exploiting the high trapped field of HTS bulk superconductors enables the design of extremely short-period insertion devices for synchrotron light sources and free electron lasers. In such a promising application the trapped field performance and the uniformity of the HTS bulk superconductors are essential. In this study, the half-moon shaped YBa2Cu3O7−δ (YBCO) single-grain superconductors have been directly grown by the top-seeded melted-growth method. Half-moon shaped samples directly grown from preforms with four different type of seed crystal arrangements were compared with that cut from larger cylindrical bulk superconductors in regarding to the trapped magnetic fields and correspondingly the distribution. We found that the arrangement of seed crystals greatly affects the melt-growth process and hence the homogeneity of the samples. The one-step grown half-moon shaped samples show higher trapped field (B trap), 0.542 T for a 24 mm and 0.785 T for a 32 mm diameter sample, and better uniformity of trapped field distribution compared to that obtained from machining with B trap of 0.427 T and 0.528 T. It was found that the growth sectors would be restricted when the seed crystal was placed at the edge of a preform, and the angle of the seed crystal, parallel or 45° to the long edge would influence the melt growth as well.

Electromechanical behavior of a rectangular bulk superconductor with an inhomogeneous critical current density under pulsed-field magnetization

Bulk high-temperature superconductors are widely used in various superconducting devices for their high critical current density and the ability to trap large magnetic field. In some applications, bulk superconductors can be arranged in an array structure to increase the magnetic field strength. However, rectangular bulk superconductors can be arranged more compactly than commonly used cylindrical bulk superconductors. The unique shape of rectangular bulk superconductors results in different distributions of electromagnetic fields, temperature, and stress under a pulsed-field magnetization (PFM) than for cylindrical bulk superconductors. In bulk superconductors, growth sector boundaries and growth sector regions have different critical current density, resulting in an uneven critical current density. Therefore, in this study, the electromagnetic and mechanical behavior of non-uniform rectangular bulk superconductors during the PFM process is investigated. The corresponding distribution and variation in the magnetic field, current, temperature, and stress in the bulk are calculated and analyzed. The influence of rectangle aspect ratio on the electromagnetic and mechanical behavior is discussed. The calculation results show that the magnetic flux jumps occur accompanied by sudden changes in the temperature and pressure. The effect of the aspect ratio of rectangular bulk superconductors on their electromagnetic and mechanical properties is analyzed. The influence of preexisting cracks in a non-uniform rectangular bulk superconductor on the simulation results is discussed. The numerical results indicate that the presence of an edge crack exacerbates the magnetic flux jump as well as the jumps in the temperature and stress. However, a central crack has a relatively small effect on the stability of a bulk superconductor.

The possible effect of surface barriers on the magnetic levitation of cylindrical superconductors

Abstract Superconducting magnetic levitation force measurements on large field cooled cylindrical MgB2 bulks with different diameters and thicknesses are reported. For these experiments, a special set-up permitting one to measure forces up to 500 N was used. In contradiction to previous measurements, the obtained force hysteresis cycles could not be reproduced with the analytical mean field model proposed by Bernstein et al (2017 Supercond. Sci. Technol. 30 065007). The failure of the model has been attributed to surface barriers effects which were not taken into account in the model. This last one was accordingly modified in order that the measured force cycles could be reproduced. Contrary to most other models describing surface barriers effects, the modified model suggests that above a threshold field anti-vortices and not vortices enter the superconductor. This behaviour is related to the storage by the superconductor of the mechanical work done by the operator. In addition, it has turned out that the threshold field is a decreasing function of the critical surface current density of the samples. As a consequence, the surface barriers effects occur only if this quantity and the critical current density are large enough. Otherwise, the internal magnetic field of the superconductor could be computed and was seen to be a decreasing function of the thickness of the superconductors.

Analysis of mechanical behavior on anisotropic cylindrical superconducting materials with inclusions

Analysis of mechanical behavior on anisotropic cylindrical superconducting materials with inclusions

Metal composite T-junction terminals for MW-class aerospace electric power distribution

There is a recent surge in activity to develop high power electric (or hybrid electric) aircraft. Part of this development effort is the creation of lightweight and small volume high-performance motors and airborne power transmission cables. As part of the power transmission of a distributed propulsion aircraft will be T-terminals to extract power to individual motors from a “main” power cable. In this research, a standard pressed plate high purity Cu T-terminal, with cylindrical high-temperature superconducting cables (main cable current of 20 kA, branch cable current of 2.5 kA), were investigated using Multiphysics simulations. Then, a more geometrically optimized high purity Al-Cu composite T-terminal was simulated under similar conditions. Discussed are the influence of T-junction geometry, operating temperature (30 to 50 K), contact resistance, and magnetoresistance on joule losses of terminals with different masses. It is shown the Al-Cu terminal can greatly reduce joule losses/mass of the T-terminal while also having an intrinsic clamping force from thermal expansion of the Al shell of the composite structure.

Stress Analysis of Cylindrical Superconductors Based on Viscous Flux Flow and Flux Creep in the Demagnetization Process After ZFC

In this paper, the magnetoelastic problem of a long cylindrical superconductor placed in a time-dependent external magnetic field during the unloading phase after zero field cooling (ZFC) is investigated. The flux distribution equation considering the viscous flux flow effect and the flux creep effect is established, and the stress distribution equation of the long cylinder obtained by the strain method is modified on this basis. The results show that in the external magnetic field both viscous flux flow velocity and flux creep velocity will affect the stress distribution during low-frequency excitation, while the internal field flux distribution and stress distribution are mainly dominated by the viscous flux flow velocity during high-frequency excitation. In addition, the relationship between the viscous flux flow velocity and the external field excitation velocity and the relationship between the position r0 and the magnitude σr, max(r) of the local stress peak and the action parameter (v0, v1, dBa/dt, n) of the two effects are investigated.

Axion-radiation conversion by super and normal conductors

We have proposed a method for the detection of dark matter axion. It uses superconductor under strong magnetic field. As is well known, the dark matter axion induces oscillating electric field under magnetic field. The electric field is proportional to the magnetic field and makes charged particles oscillate in conductors. Then, radiations of electromagnetic fields are produced. Radiation flux depends on how large the electric field is induced and how large the number of charged particles is present in the conductors. We show that the electric field in superconductor is essentially identical to the one induced in vacuum. It is proportional to the magnetic field. It is only present in the surface because of Meissner effect. On the other hand, although the magnetic field can penetrate the normal conductor, the oscillating electric field is only present in the surface of the conductor because of the skin effect. The strength of the electric field induced in the surface is equal to the one in vacuum. We obtain the electric field in the superconductor by solving equations of electromagnetic fields coupled with axion and Cooper pair described by Ginzburg-Landau model. The electric field in the normal conductor is obtained by solving equations of electromagnetic fields in the conductor coupled with axion. We compare radiation flux from the cylindrical superconductor with that from the normal conductor with same size. We find that the radiation flux from the superconductor is a hundred times larger than the flux from the normal conductor. We also show that when we use superconducting resonant cavity, we obtain radiation energy generated in the cavity two times of the order of the magnitude larger than that in normal conducting resonant cavity.

Angle-Dependence of the Levitation Force From a Frustum-Shaped Magnet and Recessed Superconducting Bulk

The widespread application of superconducting magnetic levitation bearings is limited by their relatively low stiffness. Recently we investigated a novel thrust bearing geometry comprised of a conical frustum (or truncated cone) shaped permanent magnet levitating inside a matching tapered hole machined into a high-temperature superconductor bulk. This configuration was found to produce superior restoring forces and stiffness compared to the conventional cylindrical magnet and superconductor arrangement. Here, using H-formulation finite-element simulations, we evaluate the angle-dependence of the frustum on the levitation force. We find that the optimal angle is not universal, but depends on the mode of displacement as well as the frustum dimensions. Correlations with the incident magnetic flux are identified for estimating the angle best suited to the operating regime of the bearing.

Relativistic magnetic lensing of electron beams using superconducting spheres

In this paper, the theoretical design of magnetic electron lens made of macroscopic superconducting spheres in rotation is proposed. The relativistic quantum behavior of an electron in the magnetic field induced by rotating bulk superconductors is described based on the Dirac equation, and electron beam transport is manifested in specific cases. Based on this approach, the focal length of magnetic electron lens made of macroscopic superconductors is theoretically calculated. Subsequently, the characterization of relativistic electron beam manipulating capability of newly designed magnetic electron lens is carried out by variation of the system parameters. Owing to the ability to focus the relativistic electron beam in versatile and precise manner, this approach offers a new way to study a macroscopic system of superconductors based on special relativity, and it sets a milestone in the construction of a new generation of magnetic electron lenses with superconducting spheres. The model is inherited and developed based on previous calculations of the field induced by spherical and cylindrical superconductors (L.B. Holdeman, NASA TR R-443 (1975); R.G. Rystephanick, Can. J. Phys. 51 (1973) 789–794) and the quantum theory of electron propagation through an electron lens (R. Jagannathan, Phys. Rev. A 42 (1990) 6674).

A new method for detecting axion with cylindrical superconductor

We propose a method for searching dark matter axion in axion-photon conversion. We consider a superconductor of cylindrical shape under strong magnetic field. The dark matter axion generates oscillating electric field which induces oscillating superconducting current in the surface of the superconductor. The current gives rise to dipole radiation with the frequency ma/2π given by axion mass ma. We show that the radiation flux generated by the current is of the order of 10−18 W under magnetic field ∼3 T in the case of radius 1 cm and length 10 cm of the cylindrical superconductor. The large amount of the radiation flux arises because Cooper pairs with large number density (∼1022/cm3) is present in the superconductor. With the high detection sensitivity, we can simultaneously search wide bandwidth of the radio frequency with existing radio telescope.

Dependence of the Critical Temperature of Cylindrical Superconductors on the Boundary Conditions

The properties of long cylindrical superconductors with a diameter comparable with coherence length ξ have been investigated in the framework of the Ginzburg–Landau theory. The equations of the theory have been solved using the general boundary conditions for the order parameter. The use of such boundary conditions makes it possible to take into account the effect of the boundary of a cylinder on its superconducting properties. This is important for small-diameter cylinders, the properties of which significantly depend on the properties of their boundaries.

Chaotic Motions in Dynamic High-Tc Superconducting Levitation System with Thermal Effects

The chaotic motions were shown by the vibrations of a bulk permanent magnet (PM) supported by a cylindrical high-Tc superconductor (HTSC) under external disturbance in very early experiments. There are few theoretical studies on the nonlinear behaviors of the HTSC levitation system as the complex interaction between the HTSC and PM. In this paper, we developed a numerical program to analyze the nonlinear vibrations of the levitated PM coupled with the electromagnetic force, taking into account the heat diffusion on HTSC. When the levitation system displayed chaotic oscillations by vertical excitation, the electromagnetic and thermal characteristics of the HTSC will change. The dynamic responses are shown by comparing the calculation results in which the thermal effects are taken into account and not. The numerical results display the displacements of PM, magnetic levitation forces, the acceleration, and the maximum Lyapunov exponent. The results show that the thermal effect will influence the stability of the levitation system.

Determination of magnetic levitation force properties of bulk MgB2 for different permanent magnetic guideways in different cooling heights

Abstract In our study as different from the literature, the magnetic levitation force between a bulk MgB2 and two different permanent magnetic guideway (PMG) arrangements, which are Halbach and Conventional PMGs, were investigated in different cooling heights (CHs) and Field-Cooled (FC) condition at the temperatures of 37 K and 33 K. The cylindrical bulk MgB2 superconductor was fabricated by in-situ solid state reaction process with the diameter of 18 mm and the height of 5 mm. The XRD data indicates well developed MgB2 phase and the Jc value was obtained as 68 kA/cm2 at 30 K in the self-field. Experimental results show that MgB2 bulk above the Halbach PMG can exhibit better load capability at all the cooling heights between the bulk MgB2 and the PMG due to a more suitable magnetic field distribution. The maximum levitation force for Halbach PMG corresponds to 16.86 N whereas the conventional PMG shows 9.02 N at 37 K in cooling height of 77 mm. Additionally, the maximum levitation force increases while the CH increases because flux exclusion is more effective for larger CHs. It is considered that the experimental results obtained in study are very useful for future Maglev applications, because there are limited number of studies on magnetic levitation force of MgB2 bulk for different MgB2-PMG arrangements.

Mechanical response induced by flux jump in a cylindrical superconductor

The flux jump in bulk superconductors is accompanied by a rapid change in temperature and magnetic field, which can induce change in electromagnetic bodyforce and thermal stress. It is well known that bulk superconductors are brittle and have low mechanical strength, and thus, large electromagnetic bodyforce and thermal stress can cause damage of the bulk superconductor. In this paper, an electromagnetic-thermal-mechanical multi-physics model is adopted to compute the mechanical response of a bulk superconductor during flux jump in an external magnetic field. The results indicate that the flux jump in the bulk superconductors can also lead to the jump of the average electromagnetic force, temperature, stress, and strain. Meanwhile, it can be found that the flux jump can occur more easily with a faster change in the magnetic field, a lower ambient temperature, and a large-size superconductor. The results also show that the peak value of thermal strain is much larger than the strain generated by electromagnetic bodyforce during the flux jump. In addition, the change in strain has the same trend as that of the temperature. Thus, the strain may also be used to monitor the flux jump.

Flux jumps in ring-shaped and assembled bulk superconductors during pulsed field magnetization

Bulk (RE)BCO, where RE is a rare-earth element or yttrium, superconductors fabricated in the form of rings are potentially useful for a variety of solenoidal-type applications, such as small, high field nuclear magnetic resonance and electromagnetic undulators. It is anticipated that the practical exploitation of these technologically important materials will involve pulse field magnetization (PFM) and, consequently, it is important to understand the behavior of ring-shaped samples subjected to the PFM process. Macroscopic flux jumps were observed in PFM experiments on ring-shaped bulk samples when the peak applied field reaches a threshold magnitude, similar to behavior reported previously in cylindrical samples. Magnetic flux jumps inward when the thermal instability is triggered, however it subsequently flows outwards from the sample, resulting in a relatively low trapped field. This behavior is attributed to a variety of effects, including the inhomogeneity of the material, which may lead to the formation of localized hot spots during the PFM process. In order to further elucidate this phenomena, the properties of a structure consisting of a bulk superconducting ring with a cylindrical superconductor core were studied. We observe that, although a flux jump occurs consistently in the ring, a critical state is established at the boundary of the ring-shaped sample and the core. We provide a detailed account of these experimental observations and provide an explanation in terms of the current understanding of the PFM process.

Зависимость критической температуры цилиндрических сверхпроводников от граничных условий

The paper presents the results of a study of the properties of long cylindrical superconductors with a diameter of the order of coherence length ξ, performed in the framework of the Ginzburg-Landau theory (GL). Boundary conditions of general form are used for solution of the GL equa-tion for superconducting order parameter. Using such boundary conditions allows us to take into account the influence of the cylinder boundary on its superconducting properties. This ap-proach is important for small-diameter cylinders, whose properties significantly depend on the properties of their boundaries.

Efficient Numerical Modeling of the Magnetization Loss on a Helically Wound Superconducting Tape in a Ramped Magnetic Field

We investigate theoretically the dependence of magnetization loss of a helically wound superconducting tape on the round core radius $R$ and the helical conductor pitch in a ramped magnetic field. Using the thin-sheet approximation, we identify the two-dimensional equation that describes Faraday's law of induction on a helical tape surface in the steady state. Based on the obtained basic equation, we simulate numerically the current streamlines and the power loss $P$ per unit tape length on a helical tape. For $R \gtrsim w_0$ (where $w_0$ is the tape width), the simulated value of $P$ saturates close to the loss power $\sim(2/\pi)P_{\rm flat}$ (where $P_{\rm flat}$ is the loss power of a flat tape) for a loosely twisted tape. This is verified quantitatively by evaluating power loss analytically in the thin-filament limit of $w_0/R\rightarrow 0$. For $R \lesssim w_0$, upon thinning the round core, the helically wound tape behaves more like a cylindrical superconductor as verified by the formula in the cylinder limit of $w_0/R\rightarrow 2\pi$, and $P$ decreases further from the value for a loosely twisted tape, reaching $\sim (2/\pi)^2 P_{\rm flat}$.

Modeling of Current Density in Cylindrical Superconductors by Separation of Variables

The distribution of current density in bulk cylindrical superconductors is calculated by the method of separation of variables. The method is applied to conductors with and without the transport current in the transverse, longitudinal, or arbitrary directed magnetic fields. A significant reduction of the matrix equation is achieved due to the decomposition of the solution using the Fourier series over the polar angle. The method is validated on a range of test models comparing the results with the solutions found by the state-of-the-art finite-element analysis (FEA).