Penetration of magnetic flux into hollow superconducting cylinders is investigated by magnetic moment measurements. The magnetization curves of a flat and a nanopatterned thin-walled superconducting Nb cylinders with a rectangular cross section are reported for the axial field geometry. In the nanopatterned sample, a row of micron-sized antidots (holes) was milled in the film along the cylinder axis. Magnetic moment jumps are observed for both samples at low temperatures for magnetic fields not only above Hc1, but also in fields lower than Hc1, i. e., in the vortex-free regime. The positions of the jumps are not reproducible and they change from one experiment to another, resembling vortex lattice instabilities usually observed for magnetic fields larger than Hc1. At temperatures above 0.66Tc and 0.78Tc the magnetization curves become smooth for the patterned and the as-prepared sample, respectively. The magnetization curve of a reference flat Nb film in the parallel field geometry does not exhibit jumps in the entire range of accessible temperatures.
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