A theoretical study of ion plasma oscillations

A theoretical study is made of oscillations in an ion plasma, which is in an electron beam. The effect of ion motion on the electrons is neglected, and the ions and the electrons are assumed to have constant and equal density in the equilibrium position. Symmetric and transverse oscillations are studied, both in planar and cylindrical geometry. For planar geometry, the frequency of oscillations for both symmetric and transverse modes is independent of amplitude, while the frequency increases with amplitude for cylindrical symmetric oscillations. For both cylindrical and planar geometry, the presence of the anode boundaries reduces the frequency for transverse ion oscillations, but does not affect the frequency for symmetric-type oscillations.