High-order resonances of electron-ion oscillation (one-dimensional model)

Density oscillations of uniformly charged electron-ion layers with coincident boundaries are studied in the framework of the linear perturbation theory. The consideration is based on the strict solution of the problem of electrostatic oscillations in the layer of charged particles with uniform density, discovered by F. J. Sacherer. It is found that electron-ion layers are subjected to resonance instability which leads to forming clusters in the phase space. The resonance widths and the instability growth rates are calculated