Numerical simulations of the mutual effect among the superconducting   constituents in a levitation system with translational symmetry
  By the introduction of a generalized magnetic vector potential, which contains the contributions of both the magnetic and electric parts, and the use of the Ampere's law within the quasistatic approximation as the state equation, the partial differential equations for governing the electromagnetic properties of superconductors as well as the surrounding coolant were established and numerically discretized by resorting to the finite-element technique and finite-difference scheme, respectively, in the spatial and temporal domain. In conjunction with an analytic method to calculate the magnetic field generated by permanent magnet, we compiled a numerical tool for performing an intricate study of the mutual effect among the superconducting constituents in a superconducting levitation system with translational symmetry. Taking a superconducting unit with three constituents inside as a practice, we simulated the electromagnetic responses of this unit while moving in the nonuniform magnetic field generated by permanent magnet guideway and, identified the influences of the mutual effect on the levitation force as well as on the distributions of the magnetic flux density, the supercurrent density, and the levitation force density by comparing to an envisaged reference, one constituent was simulated with all the rest absent to remove the mutual effect. The insights attained by the present study, mostly being inaccessible from the experiments, are aimed to provide useful implications for the design of a superconducting levitation system for the transit and analogous purposes, which usually employ multiple superconductors to achieve the desired capability. 
Guang-Tong Ma, Huan Liu, Xing-Tian Li, Han Zhang, and Yuan-Yuan Xu
cond-mat.supr-con