We review the modeling progress of the magnetic response of hard type-II superconductors (SCs) using the critical-state model (CSM). We focus on magnetization loops when a uniform field is applied to the SC and on the levitation forces that appear when the applied field is nonuniform. Different analytical and numerical solutions of the CSM are discussed, and the main characteristics and parameters of the magnetization loops and levitation forces are reviewed. Although this paper does not pretend to be an exhaustive review of the modeling of type-II SCs or of the superconducting levitation studies, a general overview of some important theoretical models used to understand the hard type-II SC macroscopic behavior is presented.

Comments and Corrections Corrections to "Macroscopic Modeling of Magnetization and Levitation of Hard Type-II Superconductors: The Critical-State Model"

Contrary to the interaction between two magnets with opposite magnetizations directions, the interaction between a permanent magnet and a superconductor can be stable and result in magnetic levitation. This property can be exploited for the development of high velocity rotating bearings with no mechanical contacts and for the development of levitated trains. In this review, we focus on this last application. After a brief description of the other techniques developed for levitating trains and the resulting achievements, we describe the magnet-superconductor interaction and remind of the realizations achieved in this field. Then, we give insights on the properties of the employed magnets and arrangement of magnets and we detail the characteristics and the fabrication processes of the most frequently used superconductors. Focusing on physics, we detail the procedures generally used for measuring the vertical (levitation) and the lateral (guidance) forces in magnetic levitation and the results obtained from experiments. We detail and give a critical review of the various models proposed for reproducing the force measurements. In the conclusion we give insights on the possible future developments of the technology.

Superconducting magnetic levitation: principle, materials, physics and models

After the first man-loading high temperature superconducting (HTS) Maglev demonstration had been tested successfully years ago, its future application attracts more and more researchers and engineers. This paper reviews the recent development of HTS Maglev system in China. In the past seven years, quasi-static forces, dynamic characteristics and running performances have been studied by three self-developed HTS maglev measurement systems and 11-ch vibration measurement apparatus. Some practical problems are considered in details for further engineering application of HTS Maglev train, such as running along the forward direction with inhomogeneous magnetic field, construction cost estimation, propulsion optimization, and so on. On the other hand, a systematic method is introduced to analyze or optimize the force interaction between bulk high temperature superconductor and permanent magnetic guideway. Primary running parameters and data are obtained for the safety design of future HTS Maglev system. Furthermore, a low-mid speed HTS Maglev test line is blueprinted with a maximum speed of 100 km/h, which will be the first step of practical HTS Maglev engineering application.

Recent Development of High Temperature Superconducting Maglev System in China

Single domain YBCO bulk superconductors have been fabricated with different vertical temperature gradients (VTG) by a modified top-seeded infiltration and growth (TSIG) process with a new solid phase (Y2O3+BaCuO2) and a new liquid phase (Y2O3+6CuO+10BaCuO2). It is found that the angle α (between the upper surface and interface of a- and c-growth sectors) is very sensitive to the VTG, which means that the growth rate in c-axis direction (Rc) can be changed by the VTG, according to tan α = Rc/Ra; Ra is the growth rate in the a-axis direction. It is also found that the 4-fold growth sectors did not cover the whole surface of the sample grown with a positive VTG, and the volume fraction of the single c-axis growth sector (Vfc) is 37.5% of the sample grown with a zero VTG, but it is reduced to 25% by a positive VTG, and enlarged to 53.6% by a negative VTG. The results of levitation force and trapped field of the samples show that a negative (or positive) VTG can improve (or reduce) levitation force and trapped...

Effects of Vertical Temperature Gradient on the Growth Morphology and Properties of Single Domain YBCO Bulks Fabricated by a New Modified TSIG Technique

Single domain YBCO superconductors with different additions of Bi2O3 have been fabricated by top seeded infiltration and growth process (TSIG). The effect of Bi2O3 additions on the growth morphology, microstructure and levitation force of the YBCO bulk superconductor has been investigated. The results indicate that single domain YBCO superconductors can be fabricated with the additions of Bi2O3 less than 2 wt%; Bi2O3 can be reacted with Y2BaCuO5 and liquid phase and finally form Y2Ba4CuBiOx(YBi2411) nanoscale particles; the size of the YBi2411 particles is about 100 nm, which can act as effective flux pinning centers. It is also found that the levitation force of single domain YBCO bulks is increasing from 13 N to 34 N and decreasing to 11 N with the increasing of Bi2O3 addition from 0.1 wt% to 0.7 wt% and 2 wt%. This result is helpful for us to improve the physical properties of REBCO bulk superconductors.

New method for introducing nanometer flux pinning centers into single domain YBCO bulk superconductors

The levitation forces between a single-domain YBCO bulk and several magnets of different sizes have been measured at 77 K to investigate the effect of the magnet size on the levitation force. It is found that the levitation force reaches a largest (peak) value when the size of the magnet approaches that of the superconductor when the other conditions are fixed. The absolute maximum attractive force (in the field-cooled state) increases with the increasing of the magnet size, and is saturated when the magnet size approaches that of the superconductor. The maximum attractive force in the field-cooled (FC) state is much higher than that of the maximum attractive force in the zero field-cooled (ZFC) state. The results indicate that the effects of magnetic field distribution on the levitation force have to be considered during the designing and manufacturing of superconducting devices.

https://iopscience.iop.org/article/10.1088/0953-2048/16/7/308/pdf

The effect of magnet size on the levitation force and attractive force of single-domain YBCO bulk superconductors

A levitation force and magnetic field distribution measurement system in three dimension has been designed and constructed, which can be used for the levitation force measurement between a superconductor and a magnet, or magnet to magnet in three dimensions; and for the measurement of magnetic field distribution in three dimensions according to your need in space. It can also give out the dynamical changing result of magnetic field density with time during levitation force measurement. If we change the sensor of the detector of the measurement system, it also can be used for other kinds of measurement of physical properties. It is a good device for the measurement of magnetic properties of materials. In addition the device can also be used to work at carving in three dimensions.

A levitation force and magnetic field distribution measurement system in three dimensions

Models of two small Maglev cars have been made. The track was paved with NdFeB magnets. The arrangement of the magnets made it easy to get a uniform magnetic field distribution along the length of the track and a magnetic field gradient in the lateral direction. When the car with YBCO bulk superconductors was field cooled to LN2 temperature at a certain distance above the track, the car could be automatically levitated over the track and moved along the track without any obvious friction. The model can be used to demonstrate the Meissner effect and a fast transportation system to students and adults.

/pdf/a-small-maglev-car-model-using-ybco-bulk-superconductors-332irgioaz.pdf

A small Maglev car model using YBCO bulk superconductors

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The effect of magnet size on the levitation force and attractive force of single-domain YBCO bulk superconductors

A levitation force and magnetic field distribution measurement system in three dimensions

A small Maglev car model using YBCO bulk superconductors