[en] For the purpose of ensuring azimuthal coherent stability of electron rings in collective ion accelerators, a model problem has been solved which makes possible to trace the peculiarities of the ring impedance depending on the geometrical parameters of the structure. The coupling impedance of the cylindrical layer (E-layer) of relativistic electrons in an open periodic structure of the ''squirrel cage'' type is calculated. An approximate expression for the impedance of the first harmonics is obtained. The dependence of the coupling impedance on geometrical parameters of the structure has been investigated