Maximum allowable currents in YBa$_2$Cu$_3$О$_7$ superconducting tapes as a function of the coating thickness, external magnetic field induction, and cooling conditions

Maximum allowable (ultimate) currents stably passing through an YBa$_2$Cu$_3$О$_7$ superconducting current-carrying element are determined as a function of a silver (or copper) coating thickness, external magnetic field induction, and cooling conditions. It is found that if a magnetic system based on yttrium ceramics is cooled by a cryogenic coolant, currents causing instabilities (instability onset currents) are almost independent of the coating thickness. If, however, liquid helium is used as a cooling agent, the ultimate current monotonically grows with the thickness of the stabilizing copper coating. It is shown that depending on cooling conditions, the stable values of the current and electric field strength preceding the occurrence of instability may be both higher and lower than the a priori chosen critical parameters of the superconductor. These features should be taken into account in selecting the stable value of the operating current of YBa$_2$Cu$_3$О$_7$ superconducting windings.