Cylindrical Superconductor Research Articles

Effect of induced shielding current transmission in longitudinal direction on levitation force of melt grown single-domain YBa2Cu3O7-x cylindrical superconductor

A novel layer deletion method is used to experimentally investigate the effect of induced shielding current transmission (ISCT) in the longitudinal direction on the levitation force of a single-domain YBa2Cu3O7−x (YBCO) cylindrical superconductor (ϕ30×7 mm). In the experiment the sample was gradually sliced into two equal sheets, at the middle height along a diameter with 5 mm every step. The experimental results show that the levitation force is closely related with the ISCT in the longitudinal direction. Any layer deletion, even a small piece of layer deletion can reduce the levitation force of the sample. After the whole layer was deleted the levitation force can diminish about 50%. It is also found that the levitation force is directly proportional to the effective factor of surface area, which is equal to the top surface area divided by the total surface area parallel to the top surface of the sample.

A Finite Element Approximation of a Variational Inequality Formulation of Bean's Model for Superconductivity

We introduce a finite element approximation of a variational formulation of Bean's model for the physical configuration of an infinitely long cylindrical superconductor subject to a transverse magnetic field. We prove an error between the exact solution and the approximate solution for the current density and the magnetic field in appropriate norms of order h1/2+\dt. Numerical simulations for a variety of applied magnetic fields are also presented.

Exact solution of the London equation for current carrying inhomogeneous cylindrical superconductors

We have solved exactly the London equation for the magnetic field and current density distribution inside an inhomogeneous cylindrical superconductor bearing an overall subcritical assigned current I. The inhomogeneity consists in a sudden jump in the London penetration depth. The presence of two such jumps (with obvious generalization to n jumps) serves as a model to a cylindrical superconductor in which different size regions, with different penetration depths follow one another. We illustrate how the flowing current is distorted by the presence of these interfaces.

Skin temperature changes induced by strong static magnetic field exposure.

High intensity static magnetic fields, when applied to the whole body of the anesthetized rat, have previously been reported to decrease skin temperature. The hypothesis of the present study was that in diamagnetic water, molecules in the air play significant roles in the mechanism of skin temperature decrease. We used a horizontal cylindrical superconducting magnet. The magnet produced 8 T at its center. A thermistor probe was inserted in a subcutaneous pocket of the anesthetized rats to measure skin temperature. Animals (n=10) were placed in an open plastic holder in which the ambient air was free to move in any direction (group I). Animals (n=10) were placed in a closed holder in which the air circulation toward the direction of weak magnetic field was restricted (group II). Each holder was connected to a hydrometer to measure humidity around the animal in the holder. The data acquisition phase consisted of a 5 min baseline interval, followed by inserting the animal together with the holder into the center of the magnet bore for a 5 min exposure and a 5 min postexposure period outside the bore. In group I, skin temperature and humidity around the animal significantly decreased during exposure, followed by recovery after exposure. In group II, skin temperature and humidity did not decrease during the measurement. The skin temperature decrease was closely related to the decrease in humidity around the body of the animal in the holder, and the changes were completely blocked by restricting the air circulation in the direction of the bore entrance. Possible mechanisms responsible for the decrease in skin temperature may be associated with magnetically induced movement of water vapor at the skin surface, leading to skin temperature decrease.

Destructive and non-destructive determination of the transport current density radial distribution: Application to Bi-2212 textured rods

Destructive and non-destructive methods to estimate the radial distribution of the transport critical current, J c( r), of long cylindrical superconductors are presented. The non-destructive method is based on the measurement of self-field AC losses as a function of the current amplitude, Q( I 0) and takes into account the E– J characteristics of the material. Both methods have been used to derive the J c( r) profiles of long and thin Bi-2212 rods textured by laser-induced zone melting techniques. The obtained results have been correlated with the microstructure of the samples and their critical temperature.

Upper critical field and location of surface nucleation of superconductivity

In this paper we improve the estimate obtained by Lu–Pan on the value of the upper critical field HC3(κ) for a cylindrical superconductor with cross section Ω being an arbitrary 2-dimensional smooth bounded domain. We also show that, when a homogeneous magnetic field is applied along the axis of the cylinder with magnitude of the field close to HC3, superconductivity nucleates first at the surface of the sample where the curvature of ∂Ω is maximal.

Analytical model for the levitation force between a small magnet and a superconducting cylinder in the critical state

In this work a simple analytical model is presented, which allows to obtain closed-form expressions for the maximum magnetic field trapped by a cylindrical superconductor as well as the levitation force between the sample and a small magnet. Previous models of this kind could not properly account for the behaviour of the repulsion force with the variation of the sample dimensions. In particular, the so-called J s+ J v model (J. Appl. Phys. 72 (1992) 1013) incorporates size effects by means of a surface current density ( J s) which tends to zero for disc-shaped samples. However, we show that the features encountered both in experimental works and numerical models reported in the literature can be reproduced by a suitable modification of the J s+ J v model. Analytical expressions of the levitation force are obtained as a function of length and radius of the sample and as well the superconductor–magnet distance.

Surface Superconductivity¶in Applied Magnetic Fields Above H C 2

In this paper we study the surface superconductivity phenomenon of type 2 superconductors under applied magnetic fields above the critical field . We show that, for a cylindrical superconductor of infinite height placed in a homogeneous applied magnetic field, H e 3, with H lying in between and keeping away from and , superconductivity persists uniformly at a thin sheath surrounding the entire lateral surface of the sample. As the applied field decreases gradually, superconductivity in the surface sheath becomes strong and develops into a surface superconducting state, while the interior of the sample remains close to the normal state.

Penetration of an external field change with arbitrary angle into a saturated superconducting filament

In many applications of superconductivity the magnetization of a saturated cylindrical superconducting filament is perturbed by an external field change. Especially in superconducting accelerator magnets local field changes have an impact on the magnetization in the coil. We analyze the behavior of the current distribution and magnetization of a single filament for field changes with different amplitudes and at arbitrary angles with respect to the original background field. Formulas are developed and the behavior of the magnetization is demonstrated.

Resistive disturbance location influence on superconducting winding quench performance

In this paper, computational model of the resistive zone propagation based on the heat transfer and the superconductor critical state model was adopted in order to compute some quench characteristics of the cylindrical superconducting (SC) winding: temperature, current density, resistive zone resistance, and voltage. The resistive disturbance location influence on the quench performance is investigated to find the winding areas that are vulnerable to quench behavior and may be decisive for stability protection.

Investigation of the cylindrical superconducting coil quench behavior

In the small cylindrical superconducting coil, quench and material properties are dependent on the highly nonuniform magnetic flux density distribution that is also changing during a quench process. This paper presents the numerical evaluation of the in-time transition temperature, operating temperature and heat power density distributions, and maximum operating temperature, superconductor current density, resistive zone resistance and voltage time changes, as well. The above characteristics are also used to work out their dependence on quench initiation position.

Levitation force between a superconductor and a permanent magnet with cylindrical symmetry

In order to understand the levitation phenomena of superconductors (SCs), experiments are often realized by studying the levitation force between a cylindrical SC and a coaxial permanent magnet. In this work, we study these experiments by theoretical models we have derived in two stages. In the first stage, we assume both that the SC has no demagnetizing effects and that the applied field is vertical in the SC volume. Within these approximations, we derive simple analytical models that can explain the main features of levitation. In a second step, we present a numerical model which simulates the general case, including the effect of demagnetizing fields in the SC and the application of an arbitrary external field that keeps the cylindrical symmetry. The conditions for using either the simplified analytical models or the complete numerical one are discussed.

Vortex state in mesoscopic cylinders. Variational approach

A simple variational model is proposed to analyze the superconducting state in long cylindrical type-II superconductor placed in the external magnetic field. In the framework of this model, it is possible to solve the Ginzburg–Landau (GL) equations for the states with axially symmetric distributions of the order parameter. Phase transitions between different superconducting states are studied in the presence of external magnetic field and an equilibrium phase diagram of thin cylinder is obtained. The lower critical field of the cylindrical type-II superconductor with arbitrary values of radius and GL parameter is found. The field dependence of the magnetization of thin cylinder, which can carry several magnetic flux quanta, is calculated.

Defining regions of normal and anomalous skin effect of sintered Bi-based superconductors by the SRPM method

An attempt to develop a method to simultaneously estimate both the resistivity /spl rho/ and the magnetic penetration depth /spl lambda/ by vectorially measuring the difference in the impedance between two circular solenoid coils, one with and the other without a cylindrical superconductor, has been made. It was ascertained that the regions of normal and anomalous skin effect can be defined from the frequency dependence of the difference in the impedance between the two coils. The mean free path of electrons l is evaluated by applying the frequency dependence of the difference in the impedance of the coils to the anomalous skin effect region. The values of /spl rho/, /spl lambda/ and l of Bi-based sintered bulks with different J/sub c/ were evaluated at liquid N/sub 2/ temperature.

AC and DC magnetization of finite cylindrical and orthorhombic superconductors

It is well known that demagnetizing effects arising in samples of finite length may drastically modify the magnetic response of superconductors. In this work we report the study of how demagnetizing effects influence the response of finite superconductors of cylindrical and orthorhombic shape in the Meissner state. We have measured both the ac susceptibility and dc magnetization of a set of niobium samples with different dimensions. We compare the experimental results with calculations from a model based on energy minimization in the superconductor. A good agreement is observed for a wide range of sample sizes.

Some Implications of Gravitational Superconductivity

We construct a gravitational superconducting model composed of gravitational London equations, gravitational Meissner and shielding effects, a gravitational fluxoid, and oscillation modes of a particle beam in a thin cylindrical gravitational superconductor. This model is applied to the study of neutron stars. An experiment to check the gravitational shielding in a terrestrial laboratory using the Supertrons of Matsuzawa is proposed as well.

Enhancement of tensile stress near a hole in superconducting trapped-field magnets

The mechanical stress caused by flux pinning in a cylindrical superconductor with a concentric hole is investigated theoretically. Exact expressions for the radial and hoop stress are derived using the critical-state model. Stress profiles during a magnetization process often used to activate high-Tc superconductors as strong trapped-field magnets are presented and analyzed in detail. It is shown that due to the hole the tensile hoop stress is enhanced by a factor of 2 or more, depending on the hole diameter. The dramatic increase in cracking probability is emphasized.

The force-free case in three-dimensional superconductors: a computational study

Abstract We investigate the formation and motion of vortices in a three-dimensional cylindrical superconductor using a computer simulation which solves the relevant Ginzburg-Landau equations. We look particularly at the case of a cylindrical superconductor with an external current density and magnetic field applied in the direction of the cylinder axis. The magnetic field lines which result from the applied current density are circular and perpendicular to the applied field lines. Two types of competing vortex form which tend to become twisted, causing the vortices to be pinned by each other up to a critical current density. We show snapshot pictures illustrating the vortex behaviour in this case just above and below Jc and also comment on the formation of vortices at very high current densities.

AC loss measurements of a high critical temperature superconductor transporting sinusoidal or non-sinusoidal current

In electrical engineering, static converters generate harmonics; consequently the losses in the conductors increase. To use High-Tc superconductors for current transportation, it is important to evaluate and to measure their losses. Under the assumption that the superconductor is only exposed to its self-field, Bean's model is used to compute these losses. This work deals with the losses in a cylindrical High-Tc superconductor current-lead. It is made of compacted composite of Bi-Pb-Sr-Ca-Cu-O-2223, the value of its critical current is about 100 A (measured with I /spl mu/V/cm criteria). Two types of measuring methods are used. The first of them uses a differential amplifier associated with a computer, which calculate the instantaneous power by numerical integration. The second series of experiments, valid only with sinusoidal current, are made using a lock-in amplifier measuring the R.M.S. voltage. The value of transport current is high enough to be compatible with applications. Both methods give nearly the same results for sinusoidal signal. Measurements are made with non-sinusoidal current, to do that the superconductor sample is fed by a dimmer switch. The experiments show that the losses are essentially a function of the maximum value of the current, not of the firing angle. We conclude that the shape of the current is not important compared to its peak value.

Convergence of Meissner Minimizers of the Ginzburg--Landau Energy of Superconductivity as $\kappa\to +\infty$

The Meissner solution of a smooth cylindrical superconducting domain subject to a uniform applied axial magnetic field is examined. Under an additional convexity condition the uniqueness of the Meissner solution is proved. It is then shown that it is a local minimizer of the Ginzburg--Landau energy ${\cal E}_\kappa$. For applied fields less than a critical value, the existence of the Meissner solution is proved for large enough Ginzburg--Landau parameter $\kappa$. Moreover it is proved that the Meissner solution converges to a local minimizer of a certain energy ${\cal E}_\infty$ in the limit as $\kappa \rightarrow \infty$. Finally, it is proved that for $\kappa$ large enough the Meissner solution is not a global minimizer of ${\cal E}_\kappa$.