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Low loss YBCO based flexible conductors for AC operation must have a filamentary structure with filament width below 0.1 mm. MO images of structured YBCO films showed that the flux penetration is less homogeneous in YBCO filaments on Ni substrates than that in filaments on LaAlO, which indicates that the patterning may affect the critical current density in narrow filaments. To see the effect of patterning on the filament critical current we studied I-V curves and critical currents of YBCO rings with various widths ranging from 0.3 mm down to 0.02 mm. The rings were prepared by a standard lithographic process. To avoid problems with current contacts, the current in the rings was induced by external magnetic field and electric field-current characteristics were determined by a Hall probe method.