Simulation of Dynamic Levitation Force Taking Flux Creep Into Account

This work compares dynamic levitation force measurements, at different approaching speeds, with levitation force simulations that take flux creep into account. This was done using a power-law electric field current-voltage relationship that can be derived from the Anderson-Kim model. The algorithm for the simulation starts from the analytical expressions of the classical electromagnetic theory to write the integral equation of the time derivative of the current density inside the superconductor, depending on the geometry of the system and the configurations of the applied field. Then, using the Method of Moments, the analytical integral equation was written in its matrix formulation. The current density in each time step is obtained by a simple integral rule (method of Euler). From the current density profile in the superconductor, the levitation force between a permanent magnet and a superconductor, with finite cylindrical geometry, is calculated. The current density profile depends on the approaching speed. The results of the simulations were compared favorably with the experimental measurements.