Effect of transport currents on the critical state of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ thin films

After preparation of the remanent critical state, the normal component of the local time-dependent magnet field ${\mathit{B}}_{\mathit{z}}$ near the surface of a ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ thin film was measured before, during, and after the application of a transport current. The results are shown to be consistent with new calculations of ${\mathit{B}}_{\mathit{z}}$ for the thin film geometry. The calculated behavior in a thin film is shown to be substantially different from that of the Bean critical state in a long slab in a parallel field. In slab geometry, starting from the remanent critical state, ‖J(x)‖ is always equal to ${\mathit{J}}_{\mathit{c}}$, whereas in thin films a continuous distribution of current densities J(x) is found. This feature results in a unique distribution of the magnetic field ${\mathit{B}}_{\mathit{z}}$ and unusual magnetic relaxation behavior in the presence of a transport current.