Magnetic levitation of superconductors in the critical state

Abstract

The vertical levitation force in a cylindrically symmetric system composed of a permanent magnet and a type-II superconductor is studied assuming the latter to be in a critical state. In a first step, a constant-fieldgradient approximation along the length of the superconductor is used to see the effects of the dependence of the critical current density on the internal magnetic field. In a second step, the theory is generalized in order to study the case when the field gradient is not constant, as is usually found in levitation experiments with bulk superconducting samples. The model results are discussed in relation to recent experimental data on magnetic levitation of high-T c superconductors, explaining the observed behavior and making some predictions for future experiments. ͓S0163-1829͑98͒00426-3͔

Stiffness and energy losses in cylindrically symmetric superconductor levitating systems

“…Several models have been presented. In [12] and [13] we proposed approximate analytical expressions for stiffness and losses, assuming both a small superconductor and approximate demagnetizing factors. In Ref.…”

Calculation of the hysteretic force between a superconductor and a magnet

“…17 Another explanation comes from Sanchez and Navau, 33 who claimed that this maximum is a result of the minimum in the derivative of the field produced by the PM, based on a constant-field-gradient model. 31 They concluded that the maximum depends crucially on the side ratio b/a, the larger the side ratio b/a, the closer the maximum shifts to zero PM-HTS separation. When b/a is sufficiently large, the maximum may not exist.…”

“…At the same time, the demagnetization effects caused by the finite size of the superconductor were disregarded. Navau and Sanchez 31 have accounted for the demagnetization by introducing a demagnetization factor. However, it should be pointed out that the use of demagnetization factors for superconductors in the mixed state in which current is distributed inside the bulk sample, is qualitatively invalid.…”

“…The extension of the image model to include another ''frozen'' image of the PM has been introduced to explain the dynamic stiffness of the system. 30 In a recent article Navau and Sanchez 31 reviewed the models based on the critical state. Early models considered only the extreme limits of complete flux exclusion or complete flux penetration; they thus described the behavior of type-I superconductors or type-II superconductors with very high critical current.…”

Measurement of Levitation Forces in High Temperature Superconductors

“…Moon et al measured the vertical forces on a levitating superconductor showing some of the main properties (Moon, 1988). This measurement has been extended by several groups in order to study the influence of orientation, material, or shape of superconducting samples, comparing, sometimes, thin films with bulk samples (Navau & Sanchez, 1998 (Schonhuber & Moon, 1994;Chan, et al, 1994;Torng & Chen, 1992).…”