Stiffness and energy losses in cylindrically symmetric superconductor levitating systems

Abstract

Stiffness and hysteretic energy losses are calculated for a magnetically levitating system composed of a type-II superconductor and a permanent magnet when a small vibration is produced in the system. We consider a cylindrically symmetric configuration with only vertical movements and calculate the current profiles under the assumption of the critical state model. The calculations, based on magnetic energy minimization, take into account the demagnetization fields inside the superconductor and the actual shape of the applied field. The dependence of stiffness and hysteretic energy losses upon the different important parameters of the system such as the superconductor aspect ratio, the relative size of the superconductor-permanent magnet, and the critical current of the superconductor are all systematically studied. Finally, in view of the results, we provide some trends on how a system such as the one studied here could be designed in order to optimize both the stiffness and the hysteretic losses.

Trade-off modeling of superconducting levitation machines: theory and experiment

“…In our case, the value of J c enters the theory, but as shown in Fig.2 it is high enough (recall the small hysteresis). Also, we note that the maximum value of K zz at b/a ≈ 1 is a feature already reported by other authors that apply similar numerical techniques within the critical state formalism [19].…”

“…(16) with i/N just replaced by ceil(i/N) 2 Apply Eqs. (17,18,19) to generate the matrix m. Next, one introduces the physical process (relative displacements) and iteratively solves the problem, i.e. : gets the supercurrent g−vector |J n ≡ { i (t n )} This is done by:…”

Enhanced stability by field cooling in superconducting levitation with translational symmetry

“…11,17,18,20 From our calculations, we find that vertical stiffness zz is always positive, i.e., stable equilibrium, for all configurations, as in the ZFC case, 18 independent of the cooling point. We define the vertical ͑horizontal͒ magnetic stiffness zz ͑ yy ͒ per unit length as the change in the vertical ͑horizontal͒ force due to a change in the vertical ͑horizontal͒ position of the SC, zz / L ‫ץ͑−=‬ / ‫ץ‬z͒F z / L ͑ yy / L ‫ץ͑−=‬ / ‫ץ‬y͒F y / L͒.…”

Critical state in finite type-II superconducting rings

“…22,23 This model has also been developed for the case of J c depending on the internal field 10 and has been applied to the study the critical state penetration in other geometries such as multifilamentary tapes. 9 In general, the procedure allows us to calculate current profiles as long as the direction of the induced currents is known.…”