Theory for lateral stability and magnetic stiffness in a high-T c superconductor-magnet levitation system

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Abstract
A quantitative first‐order theory for the lateral force between a permanent magnet and a type‐II superconductor is presented. The levitation configuration discussed is that of a long rectangular bar magnet placed above a finite‐sized rectangular superconductor. The central issues of stability and stiffness (elastic spring constant) associated with lateral vibrations are discussed. Closed‐form expressions for both the force and stiffness are derived, thus bringing out clearly the significance of both geometrical dimensions and the magnetic response of the superconductor. It is assumed that the superconductor is either a sintered granular or consists of grains embedded in a nonactive matrix (composite) so that only intragranular shielding currents are important. The predicted behavior as a function of levitation height agrees very well with existing experimental results.