hich at high fields is larger for sample $B$ [@MIT]. An expanded view of the magnetization curves at low fields is shown in the lower panel of Fig. \[f5\]. The fields of the first jumps, $H^*$, are around 20 Oe and 10 Oe, while the number of jumps in magnetic fields up to 100 Oe are 5 and 7 for samples $A$ and $B$, respectively. Jumps of the magnetic moment were observed in a wide range of magnetic fields, including fields below $H_{c1}$ for both samples. This behavior is reminiscent of magnetic flux jumps in Nb thin films for $H_0$ perpendicular to the film surface [@NOWAK; @STAM]. The jumps observed in these papers were interpreted as a thermomagnetic instability of the Abrikosov vortex lattice [@NOWAK; @STAM]. However, existence of jumps in fields below than $H_{c1}$ and parallel to the surface have been reported in our recent work only [@Katz1]. $H_{c1}$ is $\approx 350$ Oe at 4.5 K in our samples. Direct determination of $H_{c1}$ for thin-walled cylindrical samples is impossible due to magnetic moment jumps at low fields. However, the estimation of $H_{c1}$ can be done using magnetization curves of the planar film as it shown in inset to Fig.\[f13\].

ac response
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The effective ac magnetic susceptibility of the sample in the external field $H(t)=H_0(t)+h_{ac}\sin (\omega t)$ is given by $$\label{Eq2}
M(t)=Vh_{ac}\sum_n\{\chi_n^{'} \sin (n\omega t)-\chi_n^{''}\cos (n\omega t)\},$$ and it exhibits the appearance of the ac field penetration into the sample, i.e. $\chi_1^{'}\neq -1/4\pi$, ac losses $\chi_1^{''}>0$ and harmonics of the fundamental frequency, $\chi_n$. Here, $M(t)$ is the magnetic moment of the sample and $V$ is its volume. In what follows we consider the results of the ac measurements in both PBP and SF modes.

![(Color online). Field dependences of $\chi_1(H_0)$ of samples $A$ and $B$ in the PBP mode at 1465 and 293 Hz, upper and lower panels, respectively. Measurements were done at 4.5 K. Arrows on the lower panel show $H_{c3}$ for both samples.[]{data-label="f5aa"}](Fig5a.eps "