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We suggest an explanation of the observations of the glowing filaments in a superconducting cavity. We show that the motion of a charged particle in a multicell rf cavity and of a dust particle in a single-cell rf cavity can be stable. The analysis of stability is illustrated by numerical calculations. This effect may also explain the possible failure of high gradient tests of superconducting cavities, which are planned to be used in the linear accelerators for XFEL.