An analysis of the electrostatic plasma instabilities excited by the application of a strong, uniform, alternatingudelectric field is made on the basis of the Vlasov equation.udA very general dispersion relation is obtained and discussed. Under the assumption W 2 O » C 2 pi. (where wO is the applied frequency and wpi the ion plasma frequency) a detailed analysis is given for wavelengths of the order of or large compared with the Debye length. It is found that there are two types of instabilities: resonant (or parametric) and nonresonant.udThe second is caused by the relative streaming of ions and electrons, generated by the field; it seems to exist only if wO is less than the electron plasma frequency wpe. The instability only appears if the field exceeds a certain threshold, which is found.
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