Hard Superconductors Research Articles

Stability of magnets levitated above superconductors

The stability of a permanent magnet levitated above a slab of hard superconductor is considered. The force on a dipole magnet over a perfectly diamagnetic disk is calculated. It is found that the radial component of the force is directed outward and is 10%–20% of the image (vertical) force near the edge. Estimates of the magnetic friction force due to flux motion in a hard superconductor are made using Bean’s model. The magnitude of the magnetic friction is large enough to stabilize the magnet over most of the disk for typical values of the critical current in ceramic superconductors (∼103 A/cm2), but too small for the highest values reported (>106 A/cm2). It is conjectured that flux trapping due to inhomogeneities gives rise to transient restoring forces.

Bean model extended to magnetization jumps

I extend the phenomenological Bean model of magnetization in hard superconductors to include the trains of magnetization jumps seen at low temperature in moderate-to-high magnetic fields. As in the original Bean model, no particular mechanisms for flux pinning are invoked. The extended model correctly accounts for the general dependence of the size of the magnetization jumps on sample size and critical current density. The data together with the model show that the shielding fields are approximately equal after each jump.

Thermomagnetic shock waves in hard superconductors

The non-linear dynamics of the critical state in hard superconductors has been studied taking into account the effect of dispersion and dissipation. Stationary thermomagnetic shock waves have been found to exist in superconductors. Estimates have been obtained for the velocity and width of the shock-wave front. It has been shown that shock waves found are stable with respect to small disturbances of the wave profile. A possible version of thermomagnetic instability-i.e. magnetic flux jump-evolution is suggested.

Hysteresis loss of a round superconductor carrying a d.c. transport current in an alternating transverse field

Abstract The hysteresis loss in a cylindrical hard superconductor is investigated theoretically adopting the critical state model for the case that an alternating field is applied transverse to the conductor carrying a d.c. transport current. The shape of the cross-section of the shielded region in the superconductor is approximated to an ellipse. To simulate the winding of superconducting magnets, the magnetic interaction between the superconductor components is taken into account. The total hysteresis loss is analysed as a sum of the magnetization loss and the loss due to the dynamic resistance. The calculated losses for a wide range of amplitude of the alternating field are given in graphs which clearly show how the transport current and the interaction between the superconductors affect the hysteresis.

Influence of magnetic history on flux jump fields

A formalism describing the fields at which flux jumps occur in hard superconductors has been confirmed by the description of an experimentally observed shift of flux jump fields in the second hysteresis loop of a Nb3Al superconducting sample. By fitting the theoretical model to experimental data, values of the proportionality parameter between the stability limit and the flux jump field, the first stability limit, and the first penetration field have been estimated.

On the theory of thermomagnetomechanical instability in hard superconductors

The thermomagnetomechanical instability of the critical state in hard superconductors has been investigated, taking into account the dependence of critical current density jc on magnetic field value H in a sample. The conditions for emergence of the thermomagnetomechanical instability have been found for an arbitrary critical state model. Samples with various geometries have been considered under different conditions of external cooling. The criteria obtained have been compared with the analogous ones found on the basis of Bean's critical state model (1914). It is shown that the dependence of jc on H can reduce noticeably the critical state stability threshold.

Flux jumps in hard superconductors in decreasing magnetic field

The results of calculations of higher flux jumps positions in hard superconductors in decreasing magnetic field have been presented. It has been shown that flux jumps and corresponding stability limits are dependent on maximal magnetic field value in the cycle, which influences mainly first stability limit in decreasing field. Positions of other flux jumps have been determined for two simple physical relations between stability limit and flux jumps field. Maximal number of flux jumps and full stability limit field have been in both cases also discussed Calcul des positions superieures des sauts de flux dans des supraconducteurs de type II, en champ magnetique decroissant. Variation des sauts de flux et des limites de stabilite correspondantes avec la valeur maximale du champ magnetique pendant le cycle, avec une forte influence sur la 1ere limite de stabilite en champ decroissant. Discussion du nombre maximal de sauts de flux et du champ a la limite de complete stabilite, dans deux cas

Sound reflection at normal zone boundary in hard and composite superconductors

The reflection of sound at the normal zone boundary in hard superconductors and in superconducting composites is investigated. The value of the reflection coefficient is found and it is shown that it reaches a maximum at low (less than 105-106 s-1) frequencies. The observation of the reflected acoustic signal allows one to find the position of the normal zone in the sample, the propagating velocity of the normal zone, and to evaluate the temperature in the normal phase.

Limited flux jumps in hard superconductors

Limited flux jumps in superconductors are investigated under the conditions when the heating of the sample is not too high. The surface temperature rise, electric field and magnetic flux change associated with the instability development are calculated. The theory is compared with experiments, and a satisfactory agreement is found.

Hard superconductor losses with local imperfections

On the basis of the electrodynamic equations for hard superconductors the hysteresis losses have been calculated in the presence of local imperfections within the conductors. Two-dimensional solutions for magnetic flux and current density have been obtained with a disturbance method. An analysis of the solution allows the possibility of macrovortices to be present in the superconductors with non-uniformity of thickness and critical current density. It follows from the formulae developed for the losses in the superconductors with imperfections, that the losses at a given point are essentially defined by the thickness and value of the critical current density. The losses are obtained as a function of the conductor curvature radius. The losses within a curved conductor are shown to be greater than that in the straight one.

Scaling law in voltage — current characteristics of hard superconductors

From scaling laws for pinning we have suggested scaling laws for voltage — current characteristics of type II superconductors. After linearization of J c dependence on magnetic field B, temperature T and stress ϵ, they lead to exponential dependence of the voltage E on these parameters. In order to obtain general scaling laws, then the temperature, field and stress dependence of the denominator J 0 in E = E 0 exp [(J−J c)/J 0] should also be determined. The generalization of the instability criterion leads to the conclusion that the prestrain of the superconducting material can enhance or deteriorate the stability of the winding.

A computer approach to the nonlinear hysteretic problem of electromagnetic field computation in hard superconductors for loss evaluation

The computation of the losses in superconducting wires requires the solution of electromagnetic problems with a complicated constitutive equation of the superconducting material, which is nonlinear with hysteresis, under time-varying conditions. Analytical and numerical procedures which can be found in the literature about this problem present a very limited application range and cannot be applied to cases of practical interest. In the paper a procedure is presented, by which most of the drawbacks are eliminated. The critical state model developed by Bean, Kim et al is used, in both the forms with constant critical current density and with critical current density function of the magnetic field. In this model the magnetic field penetrates the superconductor entering from the boundary by fronts. These fronts cannot reverse their velocity and represent interfaces with unknown geometric shapes. A package has been implemented to solve this problem, some example of field solution are given and the results are discussed.

Plastic strain and flux jumps in hard and composite superconductors

A study is made into the effect of the critical current density dependence upon the value of plastic strain on the critical state stability in hard and composite superconductors under conditions of plastic yield of the material. There have been found criteria of the critical stable stability relative to the jointly developing magnetic flux jumps and plastic strain jerks.

Critical state stability in type-II superconductors and superconducting-normal-metal composites

This review is devoted to the problem of critical state stability in hard superconductors and superconducting normal composites. An introduction is given to the properties of hard and composite superconductors, and to the qualitative nature of the physical processes that occur in these materials in the critical state. The dynamics of the development of instabilities of various kinds are treated in detail. Stability criteria are obtained and discussed, and theory is compared with experiment. The interaction between flux jumps and plastic strain jerks and the training phenomenon in superconductors are also covered.

Thermomagnetic effects, stability and oscillations in the critical state in hard superconductors

The influence of thermomagnetic (Ettingshausen and Nernst) effects on the stability and dynamics of the critical state in hard superconductors has been considered. Both the criteria for stability against flux jumps and the nature of a developing instability have been investigated in some simple cases. It is shown that thermomagnetic effects lead to essential changes in the dynamics of the critical state. The extent of the regime within which thermomagnetic effects lead to oscillations of the temperature and electric field during a flux jump has been investigated in terms of characteristic parameters that depend on material properties and temperature.

On the theory of the training phenomenon in superconductors

The critical state stability is investigated taking into account the plastic yield of hard and composite superconductors. The conditions have been found at which the magnetic flux jumps occur, co-developing with the plastic deformation jerks. It is shown that the interaction of mechanical and thermomagnetic instabilities can reduce appreciably the critical state stability threshold. The effect of the transport current on stability is investigated. The conditions of weak external cooling (in particular, the adiabatic case) are considered. A possible explanation of the training phenomenon is suggested.

Critical state stability and training phenomenon

The critical state stability in hard and composite superconductors has been studied under conditions of plastic yield of the material. There has been found the criterion of critical state stability with respect to the jointly developing magnetic flux jump and plastic strain jerk. Based on the obtained results, the authors have offered an interpretation of the training phenomenon in superconductors.

The critical state stability and oscillations in hard superconductors

The limited thermomagnetic instabilities in the critical state have been investigated in hard superconductors under an incomplete penetration of the magnetic flux into the sample and under different external cooling conditions. A flat plate is considered in an external magnetic field parallel to the plate surface. Conditions have been found under which it is possible to observe the electric field and temperature oscillations in a sample; their period and number have been evaluated. The theory is compared with the reported experimental data.

Application of flux trapping in hard superconductors to magnetic shielding and magnetic levitation

A thermally switched magnetic shield which can both shield against and trap magnetic fields is described. The shield, consisting of a NbTi sheet, can trap stably fields of up to 0.3T, and shield against fields of up to 0.35 ± 0.05 T, when the in superconducting state It provides large attenuation of alternating magnetic fields in the presence of a steady trapped field. It is shown to significantly reduce the eddy current damping of the mechanical vibration of a superconducting sample in a magnetic field, by shielding nearby normal metal surfaces. A specific application to magnetic levitation of gravitational radiation antennae is discussed.

Flux jumps under time-dependent external conditions

The authors investigate the influence of the time-dependent external conditions on the stability criterion of the critical state in a hard superconductor with respect to flux jumps. It has been shown that the existence of a non-linear region in the current-voltage characteristic can result in a significant delay of the onset of the instability. The methods developed by the authors make it possible to define the dependence of the stability criterion on the rate of change of the external parameters (magnetic field, temperature etc). The total theoretical results have been compared with the experimental data.