The magnetic levitation forces exerted on a high-temperature superconducting ͑HTS͒ disk by a cylindrical permanent magnet ͑PM͒ are calculated from first principles for superconductors with finite thickness. The current j( ,z) and field B( ,z) profiles in the HTS in the nonuniform magnetic field generated by the PM are derived. The levitation force depends nonlinearly on the critical current density j c and on the thickness of the HTS. The flux creep is described by a current-voltage law E( j)ϭE c ( j/ j c ) n , from which we show that the levitation force depends on the speed at which the PM approaches or recedes from the HTS, which accounts for the experimentally observed force creep phenomenon. The stiffness of the system is derived by calculating minor force loops. The numerical results reproduce many of the features observed in experiments.

The growth mechanism of the Bi-2223 phase was studied using multifilamentary Ag/Bi-2223 tapes manufactured by the powder-in-tube method. X-ray powder diffraction was performed to analyze the developments of Bi-2201, Bi-2212, and Bi-2223 phases during sintering periods at high temperatures. Transmission electron microscopy (TEM) was used to investigate the growth mechanism of the 2223 phase. TEM images indicated that 2201 and Ca2CuO3 crystals come together to form platelets of 2223. The structural phase transformation established a structural frame of the 2223 crystal. There were some vacant defects retaining in the established 2223 crystal cells at copper and oxygen sites after the phase transformation, and the Cu/O compound at high temperatures would diffuse into 2223 cells and occupy the corresponding vacancies to complete the 2223 crystal structure. The present work provides an evidence for growing the 2223 phase from the 2201 phase and Ca2CuO3 in the samples studied.

Index Terms-AC susceptibility, high temperature superconductor, perpendicular and parallel field, pinning potential.