Ac power loss for superconducting strips of arbitrary thickness in the critical state carrying a transport current

The magnetic field and current distributions are computed numerically for a superconducting strip in the critical state with infinite length, but finite thickness and width. The width-to-thickness ratio is varied from 1 to 100, covering the range from square bars to thick films. For some intermediate aspect ratios the sheet (integrated over thickness) current shows a solution close to the 2D one determined by Norris. However, for large aspect ratios (> 10) the current and field distributions differ significantly from the 2D solution, because the Norris solution does not take into account land thus does not shield) the transverse field parallel to the strip. Power loss exponents are calculated and found to vary from roughly 3 in a square bar to 4 in a high aspect ratio thin strip. In particular in the thin strip case the power loss exponents are current dependent owing to the contribution of the loss caused by the transverse magnetic field. The maximum magnetic fields occurring are calculated.