The dynamics of magnetic field penetration into thin-walled superconducting niobium cylinders is experimentally investigated. It is shown that magnetic field penetrates through the wall of a cylinder in a series of giant jumps with amplitude 10 - 20 Oe and duration of a few $mu$s. The jumps take place when the total current in the wall, not the current density, exceeds some critical value. In addition there are small jumps and/or smooth penetration, and their contribution can reach 20% of the total penetrating flux. It is demonstrated that the magnetic field inside the cylinder exhibits several oscillations. The number of giant jumps reduces with temperature.
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