A model for calculating magnetic forces between monolithic YBa2Cu3O7-δ superconductors

One of the fundamental barriers to the use of electromagnetic launchers is the high power required to reach launch speed in a reasonable distance. It has been proposed that large external power supplies can be avoided by using superconducting persistent currents in the barrel of the launcher to store energy. With this application in mind, the use of melt-textured YBCO for these persistent current magnets was studied. Presented in this paper is the development of a model for calculating the current distribution and magnetic force for two YBCO rings, each with a trapped field such that an attractive force is developed between them. Two different methods were used to calculate current as a function of time. The first is a differential equation for the time dependence of the current distribution, which is solved using the four-step vector Runge-Kutta method. The second method limits the local current density to its critical value. The integral equation for force at each time step is solved using the finite sum method. Results from the model were compared to quasistatic experiments and found to agree to within 10%. The model was then used to predict behavior of a melt-textured YBCO launcher at speeds up to 10 000 m/s. The results show that energy transfer is almost independent of speed for a properly designed launcher, and heating due to flux flow is minimal.