Critical current density and current distribution in field cooled superconducting disks

Abstract

Applications of bulk superconductors concern superconducting motors and generators, the levitation of vehicles, the generation of high magnetic fields with small size cryo-magnets, the shielding of magnetic fields and other applications. For all of them, it is essential to determine the critical current density, and to understand the effect of the shape and size of the bulks on the properties of interest. In this contribution, we show how the combination of levitation force and trapped field measurements allow one to determine the characteristics and the potential performances of superconducting disks using analytical modeling. As examples of applications we detail the effects of the magnetizing field and of the bulk sheet critical current density on the levitation force. An important result of the reported measurements is that in field-cooled samples, the shielding currents possibly do not flow along the whole thickness of the disks.

Calculation of the Forces Applied to a Superconductor in Levitation in an Inhomogeneous Magnetic Field

“…This hypothesis is inconsistent with the suggestion that as the temperature decreases, the behavior of the superconductor tends toward the Meissner limit, a situation in which the current flows on the superconductor surface facing the permanent magnet only [34]. In contrast, calculations performed using the mean-field model result in decreasing values of t as the temperature decreases [25,33], i.e., coming nearer to the Meissner limit. Otherwise, applying the mean-field model requires only measuring or calculating the vertical component of the magnetic field along the magnet axis for determining the levitation forces and along the magnet radius at different Z for calculating the lateral ones (see Appendix I).…”

“…for this part of the cycle. Otherwise, the measurements and calculations reported in [25,33] result in 𝑡 ≤ ℎ 2 for all the investigated samples and we have no insights on the current distribution for 𝑡 > ℎ 2…”

“…During the transition to the superconducting state at T c , the magnetic flux is channeled along the vortex lines, and the field vanishes elsewhere in the superconductor. As detailed in [25], below T c , for a constant applied field, the situation is frozen and no shielding current flows in the superconductor, the magnetic moment of which is equal to zero. Since the levitation force is due to the interaction of the shielding currents with the applied field, there is no levitation force at the cooling point (see Eq.…”

Superconducting magnetic levitation: principle, materials, physics and models

“…The mean field model. The mean field model [109,136] is an analytical model based on the CSM developed for systems with the cylindrical symmetry of figure 8 and d pm d s . It is based on the following aspects of the physics of FC type II superconductors mentioned in section 2.3: (i) no shielding current but pinned vortices are induced during field cooling and (ii) the generation of shielding current aims at restoring the field that existed during field cooling.…”

Angular dependence of vertical force and torque when magnetic dipole moves vertically above flat high-temperature superconductor*

“…In the studies of modelling superconducting magnetic levitation, many different numerical and analytical approaches, such as the models of solving differential Maxwell equations combining different relations between the electric field and the current density in superconductor, [19][20][21][22][23][24][25] the method based on the minimization of the magnetic energy [26,27] and the models based on the calculation of magnetic moments, [28][29][30][31][32][33][34][35][36][37] have been proposed. A very complete and comprehensive compilation for modelling magnetic levitation can be found in a recent review paper.…”