Levitation Force Between a Point Magnetic Dipole and Superconducting Sphere

The magnetic interaction between a point dipole and a superconducting sphere in the Meissner state is investigated in detail. It is demonstrated that the special case of perfect flux exclusion can be solved by the method of images when the dipole is vertically magnetized. The incorporation of a nonzero penetration depth is then made by developing the solution within London theory. The analytic solution, given in terms of an infinite series representation, is refined by exactly summing the perfectly diamagnetic response. Throughout, special cases of physical interest are discussed and applications to magnetic force microscopy and levitation are described.     

Calculation of Levitation Force between Small Superconducting Cylinder and Magnetic Ring in the Critical State

Levitation force between a small superconducting cylinder in the mixed state and a magnetic ring was calculated using the critical state model. The dependence of the levitation force on the size of the superconductor as well as the magnet was investigated. The finite size effect of the superconductor is included by demagnetizing factor approximation. The stiffness for the levitating system was calculated. The position of the maximum levitation force depends on the size of the superconductor and the magnet. Trend of the calculated force is in agreement with the experimental results.      

Levitation Force between a Horizontally Oriented Point Magnetic Dipole and a Superconducting Sphere

The magnetic interaction between a point dipole of horizontally oriented moment and a superconducting sphere in the complete Meissner state is investigated in detail. It is demonstrated that the levitation force for this configuration is precisely one half the value of the configuration with vertically oriented point dipole. An extension to other applied fields, still assuming the perfect flux exclusion state, is presented. The results have application to models for magnetic levitation and magnetic force microscopy.     

Magnetic Interaction Force and a Couple on a Superconducting Sphere in an Arbitrary Dipole Field

The calculation of the magnetostatic potential and levitation force due to a point magnetic dipole placed in front of a superconducting sphere in the Meissner state is readdressed. Closed-form analytical expression for the scalar potential function that yields the image system for an arbitrarily oriented magnetic dipole located in the vicinity of a superconducting sphere is given. Analytic expression for the lifting or levitation force acting on the sphere is extracted from the solution for a general dipole. A special case of our expression where the initial magnetic dipole makes an angle with the z-axis is derived. Our expression for the force in this particular case shows that a recently obtained result (J. Supercond. Nov. Magn. 21:93–96, 2008) for an arbitrary dipole is incorrect. A brief discussion of another erroneous result (J. Supercond. Nov. Magn. 15:257–262, 2002) for a transverse/tangential dipole–sphere configuration, corrected elsewhere recently, is reproduced. Correct expressions for the interaction energy with some limiting cases are also provided. The result derived here demonstrates that the value of the levitation force for a dipole that makes an angle with z-axis lies between the values for a radial dipole–sphere and transverse dipole–sphere configurations providing upper and lower bounds. It is found that for a magnetic dipole making an angle with z-axis, there exits a second force component along the negative y-direction, which influences a couple acting on the superconducting sphere. It is also shown that the couple is proportional to the second force component and that both the couple and second force components vanish for a radial dipole–sphere and transverse dipole–sphere configurations, respectively. These results appear to be new and have not had received due attention in the context of superconductivity.     

Size Effects on Levitation Force Between a Magnet and a Superconducting Thin Film in the Meissner State

The levitation force between a permanent magnetic disk and a thin superconducting disk in the Meissner state is calculated using the dipole–dipole interactions model. The levitation force as a function of the magnet and superconductor radii, the levitation height, and the superconductor thickness is studied under the assumption that the radius of the magnet is much smaller than the radius of the superconductor. Results showed an increase in the levitation force as a function of the radius of the superconducting disk. However, the levitation force decreases as the radius of the permanent magnetic disk increases. Demagnetizing effects are taken into account by considering the appropriate demagnetizing factor for the suggested system.     

Levitation Force Relaxation of HTS YBCO Bulk under Load

The loading capacity of the high temperature superconducting (HTS) maglev vehicle is closely relative to the maglev characteristics of the HTS bulk under the load. The investigation of the characteristics is necessary for the application of the HTS maglev vehicle. In our previous work, it was found that the levitation force relaxation increased with the increase of the reloading. In this paper, in terms of a HTS maglev system composed of the permanent magnetic guideway (PMG) and a HTS YBCO bulk, the levitation force relaxation under different loads is investigated by the numerical calculation and the experiment. It is found that the normalized relaxation rate of the levitation force increased with the increase of the load. The influence of the load on the current density distribution is also discussed in this paper. This work might be helpful for the research of the loading capacity of the HTS maglev vehicle.      

声悬浮的研究应用进展

声悬浮是一种新型无容器处理技术，悬浮力及悬浮稳定性是声悬浮研究的两个重要方面。本文在查阅大量文献的基础上，阐述了声悬浮的机理，论述了声悬浮技术的研究应用进展，最后讨论了声悬浮技术尚需解决的问题。     

立式锌锅高频磁场悬浮力和封流特性研究

本文采用专门设计的悬浮力和电磁封流实验装置,在铜、铝、锌高频磁场电磁悬浮力研究的基础上,讨论了电磁封流影响因素,得出了铜、铝、锌三种金属在固态和液态的不同工艺参数的影响规律,讨论了立式锌锅高频磁场电磁封流的可行性。     

Correlations Between Magnetic Flux and Levitation Force of HTS Bulk Above a Permanent Magnet Guideway

In order to clarify the correlations between magnetic flux and levitation force of the high-temperature superconducting (HTS) bulk, we measured the magnetic flux density on bottom and top surfaces of a bulk superconductor while vertically moving above a permanent magnet guideway (PMG). The levitation force of the bulk superconductor was measured simultaneously. In this study, the HTS bulk was moved down and up for three times between field-cooling position and working position above the PMG, followed by a relaxation measurement of 300 s at the minimum height position. During the whole processes, the magnetic flux density and levitation force of the bulk superconductor were recorded and collected by a multipoint magnetic field measurement platform and a self-developed maglev measurement system, respectively. The magnetic flux density on the bottom surface reflected the induced field in the superconductor bulk, while on the top, it reveals the penetrated magnetic flux. The results show that the magnetic flux density and levitation force of the bulk superconductor are in direct correlation from the viewpoint of inner supercurrent. In general, this work is instructive for understanding the connection of the magnetic flux density, the inner current density and the levitation behavior of HTS bulk employed in a maglev system. Meanwhile, this magnetic flux density measurement method has enriched present experimental evaluation methods of maglev system.     

Superconducting Sphere and Finite-Size Permanent Magnet: Force, Torque, and Alignment Effect Calculation

Using a local first-order interaction model, previously described, the force and torque between a superconducting sphere in the Meissner state and a finite-size permanent magnet are calculated. These findings are compared to results obtained by other models for the force based on the images method for a point magnetic dipole. It is demonstrated that the first-order calculation is a good approximation. Moreover, the torque between a superconducting sphere and a magnet in different positions and angular orientations is calculated for the first time. We describe the alignment effect that tends to align a magnet tangentially to the superconducting sphere surface. In addition, it is shown that the finiteness of the magnet reduces the magnitude of the repulsive force.     

Force Analysis of a Permanent Magnet and a Superconducting Hollow Cylinder

The interaction between a cylindrical magnet and a superconducting hollow cylinder in the Meissner state was analyzed using a dipole?Cdipole model. Analytical expression of the levitation force was derived as a function of the magnetic moment, radius of the magnet, radius, and thickness of the superconductor sample. The effect of the magnet??s dimensions on the levitation force was studied. The obtained results show that there is strong dependence of the levitation force on the magnetic dipole orientation at a small magnet?Csuperconductor distance.     

Effects of Parameters of High-Temperature Superconductor Levitation System on the Vertical Force in Zero-Field Cooling when a Permanent Magnet Is Laterally Traversing

The vertical force on a rectangular permanent magnet above a cylindrical high-temperature superconductor during lateral traverses is simulated in zero-field cooling. The calculations agree well with the previous experimental data, on the basis of which, the effects of initial cooling conditions, physical parameters, levitating height during lateral traverses and geometrical parameters on the vertical force are presented.     

Relationship of the Levitation Force Between Single and Multiple YBCO Bulks Above a Permanent Magnet Guideway Operating Dive-Lift Movement with Different Angles

In practical applications, the acceleration and deceleration motions inevitably happen in the operation of high temperature superconducting (HTS) maglev trains. For further research of the maglev properties of YBaCuO bulk above a permanent magnet guideway (PMG), by moving a fixed vertical distance, this paper studies the relationship of the levitation force between single and multiple YBCO bulks above a PMG operating dive-lift movement with different angles. Experimental results show that the maximal levitation force increment of two bulks than one bulk is smaller than the maximal levitation force increment of three bulks than two bulks. With the degree decreasing, the maximal levitation force increment of three bulks is bigger than the maximal levitation force increment of two bulks and one bulk, and the hysteresis loop of the levitation force of the three-bulk arrangement is getting smaller.     

Interaction Force Between a Magnetic Tip and a High Temperature Superconducting Cylinder

Based on the dipole-dipole model and the critical state model, we derived analytical expressions for the levitation force between the magnetic tip and the finite superconducting cylinder in two states: the Meissner state and the critical state. The effect of the geometrical parameters of the levitating system on the force was investigated.     

Effects of the relative speed of a magnet moving to and from a single-domain YBCO bulks on their interaction force

Two single-domain YBCO bulks with different grain orientations were used to investigate the effect of relative moving speed between the magnet and YBCO bulk, on their interaction force at LN₂ temperature under zero field cooling (ZFC) state. It is found that the levitation force of the sample S1 with c-axis perpendicular to the top surface is higher than that of the sample S2 with c-axis parallel to the top surface; the maximum levitation force (F_ML) is increasing with the increase of relative moving speed (V_RMS) between the magnet and the samples at first and reaches a peak value for sample S1 and a peak zone values for sample S2, then the F_ML decreases with the increase of V_RMS; the stiffness between the samples and the magnet is decreasing with the increase of the V_RMS. This result is useful for the application of superconducting levitation.     

球内接三通接头的设计及其展开图的计算机绘制

根据“球面上圆构造椭圆锥面”的原理,设计了球内接三通接头。对这种接头的表面展开进行了解析分析。进而确定了展开方法,并提供了按这种方法用计算机绘制的展开图例。     

Study of Screening Dependence Superconducting State Parameters of Cu<Subscript><Emphasis Type="Italic">C</Emphasis></Subscript>Zr<Subscript>100−<Emphasis Type="Italic">C</Emphasis></Subscript> Binary Metallic Glasses by a Pseudopotential

The screening dependence theoretical investigations of the superconducting state parameters (SSP) viz. electron–phonon coupling strength λ, Coulomb pseudopotential μ ^*, transition temperature T _C , isotope effect exponent α and effective interaction strength N _O V of ten binary Cu _C Zr_100−C (C=25, 30, 33, 35, 40, 45, 50, 55, 57 and 60) metallic glasses have been reported using Ashcroft’s empty core (EMC) model potential. Five local field correction functions proposed by Hartree (H), Taylor (T), Ichimaru–Utsumi (IU), Farid et al. (F), and Sarkar et al. (S) are used in the present investigation to study the screening influence on the aforesaid properties. It is observed that the electron–phonon coupling strength λ and the transition temperature T _C are quite sensitive to the selection of the local field correction functions, whereas the Coulomb pseudopotential μ ^*, isotope effect exponent α and effective interaction strength N _O V show weak dependences on the local field correction functions. The values of T _C obtained from the H-local field correction function are in qualitative agreement with available theoretical or experimental data and show almost linear nature with the concentration C of Cu element. A linear T _C equation is proposed by fitting the present outcomes for the H-local field correction function, which is in conformity with other results for the experimental data. Also, the present results are in qualitative agreement with other such earlier reported data, which confirms the superconducting phase in the metallic glasses.     

An Inverse Problem for the ac Magnetic Force Microscopy of Superconductors

A basic inversion problem for the magnetic force microscopy (MFM) of a semiinfinite superconductor in the Meissner state is formulated, ac Detection is assumed, with the MFM tip oscillating at angular frequency Ω. The coupling of all electrodynamic fields is treated, including a normal-current density in the superconductor. Under certain assumptions on the tip and superconductor geometry, a unique penetration depth λ(z) can be recovered from onedimensional force gradient measurements. This development opens new possibilities for the nondestructive evaluation of superconducting crystals and films.