AC losses in macroscopic thin-walled superconducting cylinders
Measurements of the ac response represent a valuable method for probing the properties of superconductors. In the surface superconducting state (SSS), a current exceeding the surface critical current $I_\mathrm{c}$ leads to breakdown of SSS and penetration of external magnetic field into the sample bulk. An interesting free-of-bulk system in SSS is offered by thin-walled cylinders. According to the full penetration of magnetic flux (FPMF) model, each time the instant value of an ac field is equal to a certain critical value, the ac susceptibility $\chi$ will exhibit \emph{jumps} as a function of the ac field amplitude $H_\mathrm{ac}$ because of the periodic destruction and restoration of SSS in the cylinder wall. Here we study the low-frequency (128-8192\,Hz) ac response of thin-walled niobium cylinders under superimposed dc and ac magnetic fields applied parallel to the cylinder axis. In contrast to the FPMF model predictions, experiments reveal a \emph{smooth} $\chi(H_\mathrm{ac})$ dependence. To explain the experimental observations, we propose a phenomenological \emph{partial} penetration magnetic flux (PPMF) model, which assumes that after restoration of the superconducting state, the magnetic fields inside and outside the cylinder are unequal and the magnitude of the penetrating flux is random for every penetration. This model fits very well the experimental data on the temperature dependence of the first harmonic $\chi_1$ for any dc field and ac amplitude.