 of Fig.\[f11a\]. This jump takes place in magnetic fields near $H_{c2}$ of sample $B$. Decreasing of ac losses and harmonics jump near $H_{c2}$ in a swept field was observed in single crystal Nb [@GENKIN22; @MT]. However, single crystal Nb has a well defined vortex structure and $H_{c2}$ but it is not the case with our sample.

conclusion
==========

We have studied the dc and ac magnetic properties of thin-walled cylinders of superconducting Nb with and without a row of antidots. Experiment showed that the critical current density is higher in the isthmus between antidots than in the film itself. The dc magnetization curves demonstrate an "avalanche”-like penetration of the magnetic flux into the cylinder for both samples. The effect was observed at a temperature of 4.5 K and completely disappeared at 7 and 5.5 K for samples $A$ and $B$, respectively. Such a behavior resembles a thermomagnetic instability of vortices but it was observed in fields below $H_{c1}$ of the films, i.e. in a vortex-free state. The effect of end faces, consisting in that the magnetic force lines is bending near the sample ends, could be another reason for flux jumps. The influence of the sample end faces on the flux jumps in such samples has to be studied using a local probe technique.

The ac response of thin-walled cylinders with and without antidots is strongly nonlinear and perturbation theory cannot explain the experimental data. The ac response of $A$ and $B$ samples is similar in the point-by-point mode. However, in the swept field mode there is a qualitative difference between losses for samples $A$ and $B$. Thus, at low magnetic fields, losses in sample $B$ are lower than in sample $A$. There are jumps in $\chi_1$, $\chi_2$ and $\chi_3$ in high magnetic fields for sample $B$, but these quantities are smooth functions of the magnetic field in sample $A$.

We demonstrate that field dependences of $\chi_1^{''}$ and $\chi_3$ have the same shapes in the point-by-point mode with high accuracy. In the swept field mode the shapes of