The previous consideration of the irreversible magnetic self-field entry into a current-carrying type-II superconductor (SC) [Phys. Rev. B 49, 6950 (1994)] is extended to the case of an applied longitudinal magnetic field. The structure of the helical Abrikosov vortex is found exactly in the framework of the London approximation. The field-dependent critical current of a spontaneous entry of the right-handed flux helix against the surface Bean-Livingston barrier into the SC cylinder of arbitrary radius R is calculated, as well as the critical current of the flux-line instability with respect to the left-handed helical expansion. On the basis of these two mechanisms, a diagram of the resistive state in current-field coordinates is evaluated. The direction of the optimal helix for which the surface barrier is the least and which, hence, is the first to enter the sample turns out to coincide with that of the full magnetic field at the surface only in the case of a thick cylinder with R≫λ, where λ is the magnetic penetration depth. For the latter case, the generalized Silsbee’s rule of a breakdown of nondissipative state is formulated.

• Received 9 June 1994

DOI:https://doi.org/10.1103/PhysRevB.51.3686