Several physical effects allow free floatation of solid and even liquid matter. Materials may be levitated by a jet of gas, by intense sound waves, or by beams of laser light. In addition, conductors levitate in strong radio-frequency fields, charged particles in alternating electric fields, and magnets above superconductors or vice versa. Although levitation by means of ferromagnets is unstable, supper-conductors may be suspended both above and below a magnet as a result of flux pinning. Levitation is used for containerless processing and investigation of materials, for frictionless bearings and high-speed ground transportation, for spectroscopy of single atoms and microparticles, and for demonstrating superconductivity in the new oxide superconductors.

https://science.sciencemag.org/content/sci/243/4889/349.full.pdf

Levitation in Physics

The Flux-Line Lattice in Type-II Superconductors†

Recently it was found that the transverse flux bundle size estimated from the observed irreversibility field in terms of the flux creep theory takes much smaller values than the prediction from the elastic correlation length of the fluxoid lattice. This is more remarkable for the case of larger correlation length, i.e., for superconductors with a weaker flux pinning strength. It is assumed that the flux bundle size is determined so that the critical current density under the flux creep is maximized. This assumption is analogous to the irreversible thermodynamic principle for the linear dissipation systems that the energy dissipation is minimized. The obtained flux bundle size is proportional to the one-third power of the value derived from the elastic correlation length. Qualitative and quantitative agreements are obtained between the prediction and the experiments. The theoretical result also explains the observed finite relaxation rates at ultra-low temperatures which have been believed to be explained only by the quantum tunneling mechanism.

On the flux bundle size in weakly pinned superconductors

We report on the effects of neutron irradiation in superconducting ${\mathrm{MgB}}_{2}$ single crystals. Transmission electron microscopy investigations reveal large radiation-induced defects with dimensions comparable to the superconducting coherence length. Accordingly, measurements of the magnetic moment show pronounced modifications of the reversible and irreversible properties after irradiation. In particular, we concentrate on the emergence of a second peak (fishtail), situated near ${H}_{c2}$ at low neutron fluences, but extending over a large part of the superconducting phase diagram at high doses. The history dependence of the critical current density on the low-field side of the fishtail region is studied by measuring minor hysteresis loops and interpreted in terms of an order-disorder transition of the vortex lattice.

Fishtail effect in neutron-irradiated superconducting MgB 2 single crystals

A theoretical treatment is given of a superconducting reed clamped at one end and performing flexural vibrations in a homogeneous longitudinal magnetic fieldB
a. When the flux lines are rigidly pinned the reed behaves like an ideal diamagnet whose bending distorts the external field. This generates a magnetic restoring force (line tension) ∝B

 2
 which is independent of the reed thicknessd, whereas the mechanical restoring force (stiffness) is ∝d
3. Therefore, the resonance frequency ω/2π of a thin superconducting reed increases drastically when a fieldB
a is applied, or for a givenB
a, when the reed is cooled below its critical temperatureT
c. With decreasing pinning strength (characterized by Labusch's parameter α) the resonance frequency decreases, ω2→ω2–ω
 pin
 2
 where ω
 pin
 2
 ∝α−1, and an attenuation Γ
 v
 ∝α−2 occurs due to the viscous motion of flux lines. For larger vibration amplitudes an additional, amplitude-dependent damping Γ
 h
 ∝α−3 occurs due to the hysteretic losses caused by elastic instabilities during flux motion.

A Superconducting Vibrating Reed Applied to Flux-Line Pinning. I. Theory

Homogenized ${\mathrm{V}}_{3}$Si crystals were irradiated with fast neutrons at conditions which result in a proportionality between the induced defect density and the neutron fluence. The critical current density is corrected for differences in the fluence dependence of the upper critical field and of the Ginzburg-Landau parameter. The resulting rise of the volume pinning force is investigated as a function of the density of the weak interacting defects. A second power law which points to a collective interaction is observed at low defect densities and at low fields. With increasing defect density and increasing field, this quadratic dependence vanishes abruptly and an almost linear relation dominates. The exponent of this first power law decreases continuously with further increase of field or defect density. These observations are compared with the collective pinning theory.

Experimental study on the collective theory of flux pinning in a high-field superconductor

Measurements of the critical current density, the reversible displacement of flux lines and the reversible penetration depth of a small acfield were made on V 3 Si samples with various defect structures. The dependences of these quantities on the superconducting properties and on the kind and concentration of the crystal defects are different from each other. It is shown that a correlation of these three parameters proposed first by Campbell is consistent with the measured values.

A comparison of pinning parameters in V3Si

Investigating the correlation between the critical current density and the defect structure of A15 superconductors V3Si crystals were irradiated with fast neutrons in order to produce voids. Due to a high irradiation temperature the decrease of the critical temperature is completely prevented by self-annealing. Pinning by the void structure does not obey a temperature scaling relation.

R. Meier-Hirmer

Papers

Experimental study on the collective theory of flux pinning in a high-field superconductor

A comparison of pinning parameters in V3Si

Critical temperature and critical current of V3Si with voids induced by fast neutron fluence of 1021 cm-2

Radiation induced changes in critical superconducting properties of V3Si