Superconducting trapped-field magnets: Temperature and field   distributions during pulsed field activation
  We calculate the temperature and magnetic field distributions in a bulk superconductor during the process of pulsed-field magnetic activation. The calculations are based on the heat diffusion equation with account of the heat produced by flux motion, and the critical state model with temperature dependent critical current density. For a given activation time the total amount of trapped flux is maximum for an optimal value B_opt of the maximal applied field. We analyze how B_opt and the trapped flux depend on the material parameters and the field ramp rate. 
S. Braeck, D. V. Shantsev, T. H. Johansen, and Y. M. Galperin